All papers (22263 results)

Last updated:  2024-06-19
Limits on the Power of Prime-Order Groups: Separating Q-Type from Static Assumptions
George Lu and Mark Zhandry
Subgroup decision techniques on cryptographic groups and pairings have been critical for numerous applications. Originally conceived in the composite-order setting, there is a large body of work showing how to instantiate subgroup decision techniques in the prime-order setting as well. In this work, we demonstrate the first barrier to this research program, by demonstrating an important setting where composite-order techniques cannot be replicated in the prime-order setting. In particular, we focus on the case of $q$-type assumptions, which are ubiquitous in group- and pairing-based cryptography, but unfortunately are less desirable than the more well-understood static assumptions. Subgroup decision techniques have had great success in removing $q$-type assumptions, even allowing $q$-type assumptions to be generically based on static assumptions on composite-order groups. Our main result shows that the same likely does not hold in the prime order setting. Namely, we show that a large class of $q$-type assumptions, including the security definition of a number of cryptosystems, cannot be proven secure in a black box way from any static assumption.
Last updated:  2024-06-19
The Complexity of the Crossbred Algorithm
Damien VIDAL, Sorina IONICA, and Claire Delaplace
The Crossbred algorithm is currently the state-of-the-art method for solving overdetermined multivariate polynomial systems over $\mathbb{F}_2$. Since its publication in 2015, several record breaking implementations have been proposed and demonstrate the power of this hybrid approach. Despite these practical results, the complexity of this algorithm and the choice of optimal parameters for it are difficult open questions. In this paper, we prove a bivariate generating series for potentially admissible parameters of the Crossbred algorithm.
Last updated:  2024-06-19
Leveled Homomorphic Encryption Schemes for Homomorphic Encryption Standard
Shuhong Gao and Kyle Yates
Homomorphic encryption allows for computations on encrypted data without exposing the underlying plaintext, enabling secure and private data processing in various applications such as cloud computing and machine learning. This paper presents a comprehensive mathematical foundation for three prominent homomorphic encryption schemes: Brakerski-Gentry-Vaikuntanathan (BGV), Brakerski-Fan-Vercauteren (BFV), and Cheon-Kim-Kim-Song (CKKS), all based on the Ring Learning with Errors (RLWE) problem. We align our discussion with the functionalities proposed in the recent homomorphic encryption standard, providing detailed algorithms and correctness proofs for each scheme. Additionally, we propose improvements to the current schemes focusing on noise management and optimization of public key encryption and leveled homomorphic computation. Our modifications ensure that the noise bound remains within a fixed function for all levels of computation, guaranteeing correct decryption and maintaining efficiency comparable to existing methods. The proposed enhancements reduce ciphertext expansion and storage requirements, making these schemes more practical for real-world applications.
Last updated:  2024-06-19
Perfectly-secure Network-agnostic MPC with Optimal Resiliency
Shravani Patil and Arpita Patra
We study network-agnostic secure multiparty computation with perfect security. Traditionally MPC is studied assuming the underlying network is either synchronous or asynchronous. In a network-agnostic setting, the parties are unaware of whether the underlying network is synchronous or asynchronous. The feasibility of perfectly-secure MPC in synchronous and asynchronous networks has been settled a long ago. The landmark work of [Ben-Or, Goldwasser, and Wigderson, STOC'88] shows that $n > 3t_s$ is necessary and sufficient for any MPC protocol with $n$-parties over synchronous network tolerating $t_s$ active corruptions. In yet another foundational work, [Ben-Or, Canetti, and Goldreich, STOC'93] show that the bound for asynchronous network is $n > 4t_a$, where $t_a$ denotes the number of active corruptions. However, the same question remains unresolved for network-agnostic setting till date. In this work, we resolve this long-standing question. We show that perfectly-secure network-agnostic $n$-party MPC tolerating $t_s$ active corruptions when the network is synchronous and $t_a$ active corruptions when the network is asynchronous is possible if and only if $n > 2 \max(t_s,t_a) + \max(2t_a,t_s)$. When $t_a \geq t_s$, our bound reduces to $n > 4t_a$, whose tightness follows from the known feasibility results for asynchronous MPC. When $t_s > t_a$, our result gives rise to a new bound of $n > 2t_s + \max(2t_a,t_s)$. Notably, the previous network-agnostic MPC in this setting [Appan, Chandramouli, and Choudhury, PODC'22] only shows sufficiency for a loose bound of $n > 3t_s + t_a$. When $t_s > 2t_a$, our result shows tightness of $ n > 3t_s$, whereas the existing work shows sufficiency for $n > 3t_s+t_a$.
Last updated:  2024-06-19
A Formal Treatment of End-to-End Encrypted Cloud Storage
Matilda Backendal, Hannah Davis, Felix Günther, Miro Haller, and Kenneth G. Paterson
Users increasingly store their data in the cloud, thereby benefiting from easy access, sharing, and redundancy. To additionally guarantee security of the outsourced data even against a server compromise, some service providers have started to offer end-to-end encrypted (E2EE) cloud storage. With this cryptographic protection, only legitimate owners can read or modify the data. However, recent attacks on the largest E2EE providers have highlighted the lack of solid foundations for this emerging type of service. In this paper, we address this shortcoming by initiating the formal study of E2EE cloud storage. We give a formal syntax to capture the core functionality of a cloud storage system, capturing the real-world complexity of such a system's constituent interactive protocols. We then define game-based security notions for confidentiality and integrity of a cloud storage system against a fully malicious server. We treat both selective and fully adaptive client compromises. Our notions are informed by recent attacks on E2EE cloud storage providers. In particular we show that our syntax is rich enough to capture the core functionality of MEGA and that recent attacks on it arise as violations of our security notions. Finally, we present an E2EE cloud storage system that provides all core functionalities and that is both efficient and provably secure with respect to our selective security notions. Along the way, we discuss challenges on the path towards bringing the security of cloud storage up to par with other end-to-end primitives, such as secure messaging and TLS.
Last updated:  2024-06-19
Privacy-Preserving Dijkstra
Benjamin Ostrovsky
Given a graph $G(V,E)$, represented as a secret-sharing of an adjacency list, we show how to obliviously convert it into an alternative, MPC-friendly secret-shared representation, so-called $d$-normalized replicated adjacency list (which we abbreviate to $d$-normalized), where the size of our new data-structure is only 4x larger -- compared to the original (secret-shared adjacency list) representation of $G$. Yet, this new data structure enables us to execute oblivious graph algorithms that simultaneously improve underlying graph algorithms' round, computation, and communication complexity. Our $d$-normalization proceeds in two steps: First, we show how for any graph $G$, given a secret-shared adjacency list, where vertices are arbitrary alphanumeric strings that fit into a single RAM memory word, we can efficiently and securely rename vertices to integers from $1$ to $V$ that will appear in increasing order in the resulting secret-shared adjacency list. The secure renaming takes $O(\log V)$ rounds and $O((V+E)\log V)$ secure operations. Our algorithm also outputs in a secret-shared form two arrays: a mapping from integers to alphanumeric names and its sorted inverse. Of course, if the adjacency list is already in such an integer format, this step could be skipped. Second, given a secret-shared adjacency list for any graph $G$, where vertices are integers from $1$ to $V$ and are sorted, there exists a $d$-normalization algorithm that takes $O(1)$ rounds and $O((V+E))$ secure operations. We believe that both conversions are of independent interest. We demonstrate the power of our data structures by designing a privacy-preserving Dijkstra's single-source shortest-path algorithm that simultaneously achieves $O\left((V +E) \cdot \log V \right)$ secure operations and $O(V \cdot \log V \cdot \log \log\log V)$ rounds. Our secure Dijkstra algorithm works for any adjacency list representation as long as all vertex labels and weights can individually fit into RAM memory word. Our algorithms work for two or a constant number of servers in the honest but curious setting. The limitation of our result (to only a constant number of servers) is due to our reliance on linear work and constant-round secure shuffle.
Last updated:  2024-06-20
CoGNN: Towards Secure and Efficient Collaborative Graph Learning
Zhenhua Zou, Zhuotao Liu, Jinyong Shan, Qi Li, Ke Xu, and Mingwei Xu
Collaborative graph learning represents a learning paradigm where multiple parties jointly train a graph neural network (GNN) using their own proprietary graph data. To honor the data privacy of all parties, existing solutions for collaborative graph learning are either based on federated learning (FL) or secure machine learning (SML). Although promising in terms of efficiency and scalability due to their distributed training scheme, FL-based approaches fall short in providing provable security guarantees and achieving good model performance. Conversely, SML-based solutions, while offering provable privacy guarantees, are hindered by their high computational and communication overhead, as well as poor scalability as more parties participate. To address the above problem, we propose CoGNN, a novel framework that simultaneously reaps the benefits of both FL-based and SML-based approaches. At a high level, CoGNN is enabled by (i) a novel message passing mechanism that can obliviously and efficiently express the vertex data propagation/aggregation required in GNN training and inference and (ii) a two-stage Dispatch-Collect execution scheme to securely decompose and distribute the GNN computation workload for concurrent and scalable executions. We further instantiate the CoGNN framework, together with customized optimizations, to train Graph Convolutional Network (GCN) models. Extensive evaluations on three graph datasets demonstrate that compared with the state-of-the-art (SOTA) SML-based approach, CoGNN reduces up to $123$x running time and up to $522$x communication cost per party. Meanwhile, the GCN models trained using CoGNN have nearly identical accuracies as the plaintext global-graph training, yielding up to $11.06\%$ accuracy improvement over the GCN models trained via federated learning.
Last updated:  2024-06-18
FABESA: Fast (and Anonymous) Attribute-Based Encryption under Standard Assumption
Long Meng, Liqun Chen, Yangguang Tian, and Mark Manulis
Attribute-Based Encryption (ABE) provides fine-grained access control to encrypted data and finds applications in various domains. The practicality of ABE schemes hinges on the balance between security and efficiency. The state-of-the-art adaptive secure ABE scheme, proven to be adaptively secure under standard assumptions (FAME, CCS'17), is less efficient compared to the fastest one (FABEO, CCS'22) which is only proven secure under the Generic Group Model (GGM). These traditional ABE schemes focus solely on message privacy. To address scenarios where attribute value information is also sensitive, Anonymous ABE (${\rm A}^{\rm 2}$BE) ensures the privacy of both the message and attributes. However, most ${\rm A}^{\rm 2}$BE schemes suffer from intricate designs with low efficiency, and the security of the fastest key-policy ${\rm A}^{\rm 2}$BE (proposed in FEASE, USENIX'24) relies on the GGM. In this paper, we propose novel fast key-policy and ciphertext-policy ABE schemes that (1) support both AND and OR gates for access policies, (2) have no restriction on the size and type of policies or attributes, (3) achieve adaptive security under the standard DLIN assumption, and (4) only need 4 pairings for decryption. As our ABE constructions automatically provide ciphertext anonymity, we easily transform our ABE schemes to ${\rm A}^{\rm 2}$BE schemes while maintaining the same features and high-level efficiency. The implementation results show that all our schemes achieve the best efficiency comparing to other schemes with adaptive security proven under standard assumptions. Specifically, our ABE schemes perform better than FAME and are close to FABEO. Our key-policy ${\rm A}^{\rm 2}$BE scheme performs close to the one in FEASE and our ciphertext-policy ${\rm A}^{\rm 2}$BE outperforms the state-of-the-art (Cui et al., ProvSec'16).
Last updated:  2024-06-18
DualRing-PRF: Post-Quantum (Linkable) Ring Signatures from Legendre and Power Residue PRFs
Xinyu Zhang, Ron Steinfeld, Joseph K. Liu, Muhammed F. Esgin, Dongxi Liu, and Sushmita Ruj
Ring signatures are one of the crucial cryptographic primitives used in the design of privacy-preserving systems. Such a signature scheme allows a signer to anonymously sign a message on behalf of a spontaneously formed group. It not only ensures the authenticity of the message but also conceals the true signer within the group. An important extension of ring signatures is linkable ring signatures, which prevent a signer from signing twice without being detected (under some constraints). Linkable ring signatures offer advantages in applications where full anonymity might jeopardise the intended purpose, such as privacy-oriented cryptocurrencies like Monero. In this work, we introduce post-quantum ring signature (DualRing-PRF) and linkable ring signature (DualRingL-PRF) schemes whose security solely rely on symmetric-key primitives (namely, Legendre PRF and power residue PRF). Our construction of the ring signature departs from previous approaches with similar security assumptions, offering the most competitive signature sizes for small and medium-sized rings. In particular, for a ring size of 16, DualRing-PRF has a communication overhead 1.4 times smaller than the state-of-the-art scheme proposed by Goel et al. (PETS’21). Furthermore, we demonstrate the extension of DualRing-PRF to incorporate linkability and non-slanderability. Compared to the existing one-time traceable ring signature (a variant of linkable ring signature) by Scafuro and Zhang (ESORICS’21), our construction supports many-time signing and achieves significantly smaller signature sizes when ring size exceeds 16. This advantage becomes more pronounced as the ring size increases.
Last updated:  2024-06-20
Side-Channel and Fault Resistant ASCON Implementation: A Detailed Hardware Evaluation (Extended Version)
Aneesh Kandi, Anubhab Baksi, Peizhou Gan, Sylvain Guilley, Tomáš Gerlich, Jakub Breier, Anupam Chattopadhyay, Ritu Ranjan Shrivastwa, Zdeněk Martinásek, and Shivam Bhasin
In this work, we present various hardware implementations for the lightweight cipher ASCON, which was recently selected as the winner of the NIST organized Lightweight Cryptography (LWC) competition. We cover encryption + tag generation and decryption + tag verification for the ASCON hash function and ASCON AEAD. On top of the usual (unprotected) implementation, we present side-channel protection (threshold countermeasure) and triplication/majority-based fault protection. To the best of our knowledge, this is the first protected hardware implementation of ASCON with respect to side-channel and fault inject protection. The side-channel and fault protections work orthogonal to each other (i.e., either one can be turned on/off without affecting the other). We present ASIC and FPGA benchmarks for all our implementations (hash and AEAD) with/without countermeasures for varying input sizes.
Last updated:  2024-06-18
SoCureLLM: An LLM-driven Approach for Large-Scale System-on-Chip Security Verification and Policy Generation
Shams Tarek, Dipayan Saha, Sujan Kumar Saha, Mark Tehranipoor, and Farimah Farahmandi
Contemporary methods for hardware security verification struggle with adaptability, scalability, and availability due to the increasing complexity of the modern system-on-chips (SoCs). Large language models (LLMs) have emerged as a viable approach to address these shortcomings in security verification because of their natural language understanding, advanced reasoning, and knowledge transfer capabilities. However, their application to large designs is limited by inherent token limitation and memorization constraints. In this paper, we introduce SoCureLLM, an LLM-based framework that excels in identifying security vulnerabilities within SoC designs and creating a comprehensive security policy database. Our framework is adaptable and adept at processing varied, large-scale designs, overcoming the abovementioned issues of LLM. In evaluations, SoCureLLM detected 76.47% of security bugs across three vulnerable RISC-V SoCs, outperforming the state-of-the-art security verification methods. Furthermore, assessing three additional large-scale RISC-V SoC designs against various threat models led to the formulation of 84 novel security policies, enriching the security policy database. Previously requiring extensive manual effort to craft, these newly generated security policies can be used as guidelines for developing secured SoC designs.
Last updated:  2024-06-18
SoK: Programmable Privacy in Distributed Systems
Daniel Benarroch, Bryan Gillespie, Ying Tong Lai, and Andrew Miller
This Systematization of Knowledge conducts a survey of contemporary distributed blockchain protocols, with the aim of identifying cryptographic and design techniques which practically enable both expressive programmability and user data confidentiality. To facilitate a framing which supports the comparison of concretely very different protocols, we define an epoch-based computational model in the form of a flexible UC-style ideal functionality which divides the operation of privacy-preserving networks into three phases: Independent, Mediated, and Global computation. Our analysis of protocols focuses in particular on features of the Mediated computation phase, which provides the facility to execute non-trivial program logic on private inputs from multiple users. Specifically, we compare implementations in different protocols for private limit order auctions, which we find to be a representative application which is common and relatively simple, but which exhibits adversarial dynamics which demonstrate the capabilities of a non-trivial Mediated computation mechanism. In our analysis, we identify four protocols representative of different high-level approaches used to implement Mediated computations. We compare protocols according to the degree and flexibility of programmability, the privacy properties achieved, and the security assumptions required for correct operation. We conclude by offering recommendations and best practices for future programmable privacy designs.
Last updated:  2024-06-18
Hadamard Product Arguments and Their Applications
Kyeongtae Lee, Donghwan Oh, Hankyung Ko, Jihye Kim, and Hyunok Oh
This paper introduces transparent and efficient arguments for Hadamard products between committed vectors from two source groups. For vectors of length $n$, the proofs consist of $\mathcal{O}(\log n)$ target group elements and $\mathcal{O}(1)$ additional elements. The verifier's workload is dominated by $\mathcal{O}(\log n)$ multi-exponentiations in the target group and $\mathcal{O}(1)$ pairings. We prove our security under the standard SXDH assumption. Additionally, we propose an aggregator for Groth16 pairing-based zk-SNARKs and a proof aggregation technique for the general case of the KZG pairing-based polynomial commitment scheme using our Hadamard product arguments. Both applications support logarithmic-sized aggregated proofs without requiring an additional trusted setup, significantly reducing the verifier’s pairing operations to $\mathcal{O}(1)$.
Last updated:  2024-06-18
FaultyGarble: Fault Attack on Secure Multiparty Neural Network Inference
Mohammad Hashemi, Dev Mehta, Kyle Mitard, Shahin Tajik, and Fatemeh Ganji
The success of deep learning across a variety of applications, including inference on edge devices, has led to increased concerns about the privacy of users’ data and deep learning models. Secure multiparty computation allows parties to remedy this concern, resulting in a growth in the number of such proposals and improvements in their efficiency. The majority of secure inference protocols relying on multiparty computation assume that the client does not deviate from the protocol and passively attempts to extract information. Yet clients, driven by different incentives, can act maliciously to actively deviate from the protocol and disclose the deep learning model owner’s private information. Interestingly, faults are well understood in multiparty computation-related literature, although fault attacks have not been explored. Our paper introduces the very first fault attack against secure inference implementations relying on garbled circuits as a prime example of multiparty computation schemes. In this regard, laser fault injection coupled with a model-extraction attack is successfully mounted against existing solutions that have been assumed to be secure against active attacks. Notably, the number of queries required for the attack is equal to that of the best model extraction attack mounted against the secure inference engines under the semi-honest scenario.
Last updated:  2024-06-18
Volatile and Persistent Memory for zkSNARKs via Algebraic Interactive Proofs
Alex Ozdemir, Evan Laufer, and Dan Boneh
In verifiable outsourcing, an untrusted server runs an expensive computation and produces a succinct proof (called a SNARK) of the results. In many scenarios, the computation accesses a RAM that the server maintains a commitment to (persistent RAM) or that is initially zero (volatile RAM). But, SNARKs for such scenarios are limited by the high overheads associated with existing techniques for RAM checking. We develop new proofs about volatile, persistent, and sparse persistent RAM that reduce SNARK proving times. Our results include both asymptotic and concrete improvements---including a proving time reduction of up to 51.3$\times$ for persistent RAM. Along the way, we apply two tools that may be of independent interest. First, we generalize an existing construction to convert any algebraic interactive proof (AIP) into a SNARK. An AIP is a public-coin, non-succinct, interactive proof with a verifier that is an arithmetic circuit. Second, we apply Bézout's identity for polynomials to construct new AIPs for uniqueness and disjointness. These are useful for showing the independence of accesses to different addresses.
Last updated:  2024-06-17
Distributed PIR: Scaling Private Messaging via the Users' Machines
Elkana Tovey, Jonathan Weiss, and Yossi Gilad
This paper presents a new architecture for metadata-private messaging that counters scalability challenges by offloading most computations to the clients. At the core of our design is a distributed private information retrieval (PIR) protocol, where the responder delegates its work to alleviate PIR's computational bottleneck and catches misbehaving delegates by efficiently verifying their results. We introduce DPIR, a messaging system that uses distributed PIR to let a server storing messages delegate the work to the system's clients, such that each client contributes proportional processing to the number of messages it reads. The server removes clients returning invalid results, which DPIR leverages to integrate an incentive mechanism for honest client behavior by conditioning messaging through DPIR on correctly processing PIR requests from other users. The result is a metadata-private messaging system that asymptotically improves scalability over prior work with the same threat model. We show through experiments on a prototype implementation that DPIR concretely improves performance by $3.25\times$ and $4.31\times$ over prior work and that the performance gap grows with the user base size.
Last updated:  2024-06-17
Improved Boomerang Attacks on 6-Round AES
Augustin Bariant, Orr Dunkelman, Nathan Keller, Gaëtan Leurent, and Victor Mollimard
The boomerang attack is a cryptanalytic technique which allows combining two short high-probability differentials into a distinguisher for a large number of rounds. Since its introduction by Wagner in 1999, it has been applied to many ciphers. One of the best-studied targets is a 6-round variant of AES, on which the boomerang attack is outperformed only by the dedicated Square attack. Recently, two new variants of the boomerang attack were presented: retracing boomerang (Eurocrypt'20) and truncated boomerang (Eurocrypt'23). These variants seem incompatible: the former achieves lower memory complexity by throwing away most of the data in order to force dependencies, while the latter achieves lower time complexity by using large structures, which inevitably leads to a large memory complexity. In this paper we show that elements of the two techniques can be combined to get `the best of the two worlds' – the practical memory complexity of the retracing attack and the lower time complexity of the truncated attack. We obtain an attack with data complexity of $2^{57}$ (compared to $2^{59}$ and $2^{55}$ of truncated and retracing boomerang, respectively), memory complexity of $2^{33}$ (compared to $2^{59}$ and $2^{31}$), and time complexity of $2^{61}$ (compared to $2^{61}$ and $2^{80}$). This is the second-best attack on 6-round AES, after the Square attack.
Last updated:  2024-06-17
PIR with Client-Side Preprocessing: Information-Theoretic Constructions and Lower Bounds
Yuval Ishai, Elaine Shi, and Daniel Wichs
It is well-known that classical Private Information Retrieval (PIR) schemes without preprocessing must suffer from linear server computation per query. Moreover, any such single-server PIR with sublinear bandwidth must rely on public-key cryptography. Several recent works showed that these barriers pertaining to classical PIR can be overcome by introducing a preprocessing phase where each client downloads a small hint that helps it make queries subsequently. Notably, the Piano PIR scheme (and subsequent improvements) showed that with such a client-side preprocessing, not only can we have PIR with sublinear computation and bandwidth per query, but somewhat surprisingly, we can also get it using only symmetric-key cryptography (i.e., one-way functions). In this paper, we take the question of minimizing cryptographic assumptions to an extreme. In particular, we are the first to explore the landscape of information theoretic single-server preprocessing PIR. We make contributions on both the upper- and lower-bounds fronts. First, we show new information-theoretic constructions with various non-trivial performance tradeoffs between server computation, client space and bandwidth. Second, we prove a (nearly) tight lower bound on the tradeoff between the client space and bandwidth in information-theoretic constructions. Finally, we prove that any computational scheme that overcomes the information-theoretic lower bound and satisfies a natural syntactic requirement (which is met by all known constructions) would imply a hard problem in the complexity class SZK. In particular, this shows that Piano achieves (nearly) optimal client space and bandwidth tradeoff subject to making a black-box use of a one-way function. Some of the techniques we use for the above results can be of independent interest.
Last updated:  2024-06-17
ZLR: a fast online authenticated encryption scheme achieving full security
Wonseok Choi, Seongha Hwang, Byeonghak Lee, and Jooyoung Lee
Online authenticated encryption has been considered of practical relevance in light-weight environments due to low latency and constant memory usage. In this paper, we propose a new tweakable block cipher-based online authenticated encryption scheme, dubbed ZLR, and its domain separation variant, dubbed DS-ZLR. ZLR and DS-ZLR follow the Encrypt-MixEncrypt paradigm. However, in contrast to existing schemes using the same paradigm such as ELmE and CoLM, ZLR and DS-ZLR enjoy n-bit security by using larger internal states with an efficient ZHash-like hashing algorithm. In this way, 2n-bit blocks are processed with only a single primitive call for hashing and two primitive calls for encryption and decryption, when they are based on an n-bit tweakable block cipher using n-bit (resp. 2n-bit) tweaks for ZLR (resp. DS-ZLR). Furthermore, they support pipelined computation as well as online nonce-misuse resistance. To the best of our knowledge, ZLR and DS-ZLR are the first pipelineable tweakable block cipher-based online authenticated encryption schemes of rate 2/3 that provide n-bit security with online nonce-misuse resistance.
Last updated:  2024-06-17
Towards Optimal Parallel Broadcast under a Dishonest Majority
Daniel Collins, Sisi Duan, Julian Loss, Charalampos Papamanthou, Giorgos Tsimos, and Haochen Wang
The parallel broadcast (PBC) problem generalises the classic Byzantine broadcast problem to the setting where all $n$ nodes broadcast a message and deliver $O(n)$ messages. PBC arises naturally in many settings including multi-party computation. Recently, Tsimos, Loss, and Papamanthou (CRYPTO 2022) showed PBC protocols with improved communication, against an adaptive adversary who can corrupt all but a constant fraction $\epsilon$ of nodes (i.e., $f < (1 - \epsilon)n$). However, their study is limited to single-bit messages, and their protocols have large polynomial overhead in the security parameter $\kappa$: their TrustedPBC protocol achieves $\tilde{O}(n^2 \kappa^4)$ communication and $O(\kappa\log n)$ rounds. Since these factors of $\kappa$ are in practice often close (or at least polynomially related) to $n$, they add a significant overhead. In this work, we propose three parallel broadcast protocols for $L$-bit messages, for any size $L$, that significantly improve the communication efficiency of the state-of-the-art. We first propose a new extension protocol that uses a $\kappa$-bit PBC as a black box and achieves i) communication complexity of $O(L n^2 + \mathcal{P}(\kappa))$, where $\mathcal{P}(\kappa)$ is the communication complexity of the $\kappa$-bit PBC, and ii) round complexity same as the $\kappa$-bit PBC. By comparison, the state-of-the-art extension protocol for regular broadcast (Nayak et al., DISC 2020) incurs $O(n)$ additional rounds of communication. Next, we propose a protocol that is secure against a static adversary, for $\kappa$-bit messages with $O(n^2 \kappa^{1+K} + n\kappa^3 + \kappa^4)$ communication and $O(\kappa)$ round complexity, where $K$ is an arbitrarily small constant such that $0<K<1$. Finally, we propose an adaptively-secure protocol for $\kappa$-bit messages with $\tilde{O}(n^2\kappa^2 + n\kappa^3)$ communication overhead and $O(\kappa \log{n})$ round complexity by modifying and improving the next-best protocol TrustedPBC in several key ways. Notably, our latter two protocols are $\tilde{O}(\kappa^{2 - K})$ and $O(\kappa^2)$ times more communication-efficient, respectively, than the state-of-the-art protocols while achieving the same round complexity.
Last updated:  2024-06-16
ICICLE v2: Polynomial API for Coding ZK Provers to Run on Specialized Hardware
Karthik Inbasekar, Yuval Shekel, and Michael Asa
Polynomials play a central role in cryptography. In the context of Zero Knowledge Proofs (ZKPs), protocols can be exclusively expressed using polynomials, making them a powerful abstraction tool, as demonstrated in most ZK research papers. Our first contribution is a high-level framework that enables practitioners to implement ZKPs in a more natural way, based solely on polynomial primitives. ZK provers are considered computationally intensive algorithms with a high degree of parallelization. These algorithms benefit significantly from hardware acceleration, and deployed ZK systems typically include specialized hardware to optimize the performance of the prover code. Our second contribution is leveraging our polynomial API to abstract away low-level hardware primitives and automate their memory management. This device-agnostic design allows ZK engineers to prototype and build solutions while taking advantage of the performance gains offered by specialized hardware, such as GPUs and FPGAs, without needing to understand the hardware implementation details. Finally, our polynomial API is integrated into version 2 of the ICICLE library and is running in production. This paper also serves as a comprehensive documentation for the ICICLE v2 polynomial API.
Last updated:  2024-06-16
Efficient Secure Communication Over Dynamic Incomplete Networks With Minimal Connectivity
Ivan Damgård, Divya Ravi, Lawrence Roy, Daniel Tschudi, and Sophia Yakoubov
We study the problem of implementing unconditionally secure reliable and private communication (and hence secure computation) in dynamic incomplete networks. Our model assumes that the network is always $k$-connected, for some $k$, but the concrete connection graph is adversarially chosen in each round of interaction. We show that, with $n$ players and $t$ malicious corruptions, perfectly secure communication is possible if and only if $k > 2t$. This disproves a conjecture from earlier work, that $k> 3t$ is necessary. Our new protocols are much more efficient than previous work; in particular, we improve the round and communication complexity by an exponential factor (in $n$) in both the semi-honest and the malicious corruption setting, leading to protocols with polynomial complexity.
Last updated:  2024-06-16
A Note on (2, 2)-isogenies via Theta Coordinates
Jianming Lin, Saiyu Wang, and Chang-An Zhao
In this paper, we revisit the algorithm for computing chains of $(2, 2)$-isogenies between products of elliptic curves via theta coordinates proposed by Dartois et al. For each fundamental block of this algorithm, we provide a explicit inversion-free version. Besides, we exploit a novel technique of $x$-only ladder to speed up the computation of gluing isogeny. Finally, we present a mixed optimal strategy, which combines the inversion-elimination tool with the original methods together to execute a chain of $(2, 2)$-isogenies. We make a cost analysis and present a concrete comparison between ours and the previously known methods for inversion elimination. Furthermore, we implement the mixed optimal strategy for benchmark. The results show that when computing $(2, 2)$-isogeny chains with lengths of 126, 208 and 632, compared to Dartois, Maino, Pope and Robert's original implementation, utilizing our techniques can reduce $30.8\%$, $20.3\%$ and $9.9\%$ multiplications over the base field $\mathbb{F}_p$, respectively. Even for the updated version which employs their inversion-free methods, our techniques still possess a slight advantage.
Last updated:  2024-06-16
Cryptography at the Crossroads: Ethical Responsibility, the Cypherpunk Movement and Institutions
Eric Blair
This paper explores the intersection of cryptographic work with ethical responsibility and political activism, inspired by the Cypherpunk Manifesto and Phillip Rogaway's analysis of the moral character of cryptography. The discussion encompasses the historical context of cryptographic development, the philosophical underpinnings of the cypherpunk ideology, and contemporary challenges posed by mass surveillance and privacy concerns. By examining these facets, the paper calls for a renewed commitment to developing cryptographic solutions that prioritize human rights and societal good.
Last updated:  2024-06-16
Analysis, modify and apply in IIOT form light-weight PSI in CM20
Zhuang Shan, Leyou Zhang, Qing Wu, and Qiqi Lai
Multi-party computation (\textsf{MPC}) is a major research interest in modern cryptography, and Privacy Set Intersection (\textsf{PSI}) is an important research topic within \textsf{MPC}. Its main function is to allow two parties to compute the intersection of their private sets without revealing any other information. Therefore, \textsf{PSI} can be applied to various real-world scenarios, such as the Industrial Internet of Things (\textsf{IIOT}). Chase and Miao presented a paper on ``Light-weight PSI'' at CRYPTO 2020, highlighting its convenient structure and optimal communication cost. However, the drawback is that this protocol is deterministically encrypted and it was discovered through simulation that it is not resistant to probabilistic attacks. Building upon the ideas from CM20, this paper introduces the concept of a {\em perturbed pseudorandom generator}, constructs and proves its security, and replaces one of the hash functions (originally there were two) from CM20. In order to demonstrate the security of the \textsf{PSI} protocol proposed in this paper, a dedicated definition of Chosen Plaintext Attack (\textsf{CPA}) security model for this \textsf{PSI} protocol is provided. The paper then proceeds to prove that the \textsf{PSI} protocol satisfies this defined security model. Efficiency analysis shows that the \textsf{PSI} in this paper is comparable to CM20's \textsf{PSI}, whether on PC, pad, or phone.
Last updated:  2024-06-20
Fast SNARK-based Non-Interactive Distributed Verifiable Random Function with Ethereum Compatibility
Jia Liu and Mark Manulis
Distributed randomness beacons (DRBs) are fundamental for various decentralised applications, such as consensus protocols, decentralised gaming and lotteries, and collective governance protocols. These applications are heavily used on modern blockchain platforms. This paper presents the so far most efficient direct construction and implementation of a non-interactive distributed verifiable random function (NI-DVRF) that is fully compatible with Ethereum. Our NI-DVRF scheme adopts pairings and combines techniques from secret sharing, SNARKs, and BLS signatures. The security properties of the resulting NI-DVRF scheme are formally modelled and proven in the random oracle model under standard pairing-based assumptions. To justify the efficiency and cost claims and more generally its adoption potential in practice, the proposed NI-DVRF scheme was implemented in Rust and Solidity. Our implementation is highly optimised and is currently being investigated for deployment on the multichain layer-2 scaling solution provided by Boba Network to power its DRB service zkRand. Our experimental analysis, therefore, also evaluates performance and scalability properties of the proposed NI-DVRF and its implementation.
Last updated:  2024-06-15
Consolidated Linear Masking (CLM): Generalized Randomized Isomorphic Representations, Powerful Degrees of Freedom and Low(er)-cost
Itamar Levi and Osnat Keren
Show abstract
Masking is a widely adopted countermeasure against side-channel analysis (SCA) that protects cryptographic implementations from information leakage. However, current masking schemes often incur significant overhead in terms of electronic cost. RAMBAM, a recently proposed masking technique that fits elegantly with the AES algorithm, offers ultra-low latency/area by utilizing redundant representations of finite field elements. This paper presents a comprehensive generalization of RAMBAM and various other masking schemes within a unified framework and a mathematical representation known as Consolidated Linear Masking (CLM), where masking schemes are formalized by their encoding. We establish a theoretical foundation for CLM linking randomized isomorphic (code) representations and the entropy provided by the redundancy to a revised notion of masking order. Our analysis reveals that RAMBAM is a specific instance of CLM as well as other masking constructions, thus paving the way for significant enhancements. For example, a $1^{st}$-order secure design can be achieved almost without increasing the size of the representation of the variables. This property scales up to any order and is versatile. We demonstrate how CLM enables: (1) randomized selection of the isomorphic field for improved security; (2) flexible choice of the randomization polynomial; (3) embedded mask-refreshing via the randomized isomorphic representation that reduces randomness requirements significantly as well as improves performance; (4) a wider range of isomorphic randomized mappings that significantly increases the available randomization space compared to RAMBAM; (5) considerable improvement in securing fault-injection attacks and inherent security against probing adversaries, i.e., more required probes. In addition, our framework addresses ways to improve the brute-force parameter choices in the original RAMBAM. By offering a unifying theoretical perspective for masking and practical enhancements, this work advances the design of efficient and secure masking countermeasures against SCA threats.
Last updated:  2024-06-15
Diffuse Some Noise: Diffusion Models for Measurement Noise Removal in Side-channel Analysis
Sengim Karayalcin, Guilherme Perin, and Stjepan Picek
Resilience against side-channel attacks is an important consideration for cryptographic implementations deployed in devices with physical access to the device. However, noise in side-channel measurements has a significant impact on the complexity of these attacks, especially when an implementation is protected with masking. Therefore, it is important to assess the ability of an attacker to deal with noise. While some previous works have considered approaches to remove (some) noise from measurements, these approaches generally require considerable expertise to be effectively employed or necessitate the ability of the attacker to capture a 'clean' set of traces without the noise. In this paper, we introduce a method for utilizing diffusion models to remove measurement noise from side-channel traces in a fully non-profiled setting. Denoising traces using our method considerably lowers the complexity of mounting attacks in both profiled and non-profiled settings. For instance, for a collision attack against the ASCADv2 dataset, we reduced the number of traces required to retrieve the key by 40%, and we showed similar improvements for ESHARD using a state-of-the-art MORE attack. Furthermore, we provide analyses into the scenarios where our method is useful and generate insights into how the diffusion networks denoise traces.
Last updated:  2024-06-15
Efficient and Secure Post-Quantum Certificateless Signcryption for Internet of Medical Things
Shiyuan Xu, Xue Chen, Yu Guo, Siu-Ming Yiu, Shang Gao, and Bin Xiao
Internet of Medical Things (IoMT) has gained significant research focus in both academic and medical institutions. Nevertheless, the sensitive data involved in IoMT raises concerns regarding user validation and data privacy. To address these concerns, certificateless signcryption (CLSC) has emerged as a promising solution, offering authenticity, confidentiality, and unforgeability. Unfortunately, most existing CLSC schemes are impractical for IoMT due to their heavy computational and storage requirements. Additionally, these schemes are vulnerable to quantum computing attacks. Therefore, research focusing on designing an efficient post-quantum CLSC scheme is still far-reaching. In this work, we propose PQ-CLSC, a novel post-quantum CLSC scheme that ensures quantum safety for IoMT. Our proposed design facilitates secure transmission of medical data between physicians and patients, effectively validating user legitimacy and minimizing the risk of private information leakage. To achieve this, we leverage lattice sampling algorithms and hash functions to generate the particial secret key and then employ the sign-then-encrypt method to obtain the ciphertext. We also formally and prove the security of our design, including indistinguishability against chosen-ciphertext attacks (IND-CCA2) and existential unforgeability against chosen-message attacks (EU-CMA) security. Finally, through comprehensive performance evaluation, our signcryption overhead is only 30%-55% compared to prior arts, while our computation overhead is just around 45% of other existing schemes. The evaluation results demonstrate that our solution is practical and efficient.
Last updated:  2024-06-18
Malicious Security for PIR (almost) for Free
Brett Falk, Pratyush Mishra, and Matan Shtepel
Private Information Retrieval (PIR) enables a client to retrieve a database element from a semi-honest server while hiding the element being queried from the server. Maliciously-secure PIR (mPIR) [Colombo et al., USENIX Security '23] strengthens the guarantees of plain (i.e., semi-honest) PIR by ensuring that even a misbehaving server (a) cannot compromise client privacy via selective-failure attacks, and (b) must answer every query *consistently* (i.e., with respect to the same database). These additional security properties are crucial for many real-world applications. In this work we present a generic compiler that transforms any PIR scheme into an mPIR scheme in a black-box manner, minimal overhead, and without requiring additional cryptographic assumptions. Since mPIR trivially implies PIR, our compiler establishes the equivalence of mPIR and PIR. By instantiating our compiler with existing PIR schemes, we immediately obtain mPIR schemes with $O(N^\epsilon)$ communication cost. In fact, by applying our compiler to a recent doubly-efficient PIR [Lin et al., STOC '23], we are able to construct a *doubly-efficient* mPIR scheme that requires only $\text{polylog}(N)$ communication and server and client computation. In comparison, all prior work incur a $\Omega(\sqrt{N})$ cost in these metrics. Our compiler makes use of smooth locally-decodable codes (LDCs) that have a robust decoding procedure. We term these codes "subcode"-LDCs, because they are LDCs where the query responses are from an error-correcting code. This property is shared by Reed--Muller codes (whose query responses are Reed--Solomon codewords) and more generally lifted codes. Applying our compiler requires us to consider decoding in the face of *non-signaling adversaries*, for reasons analogous to the need for non-signaling PCPs in the succinct-argument literature. We show how to construct such decoders for Reed--Muller codes, and more generally for smooth locally-decodable codes that have a robust decoding procedure.
Last updated:  2024-06-14
Shared OT and Its Applications to Unconditional Secure Integer Equality, Comparison and Bit-Decomposition
Lucas Piske, Jeroen van de Graaf, Anderson C. A. Nascimento, and Ni Trieu
We present unconditionally perfectly secure protocols in the semi-honest setting for several functionalities: (1) private elementwise equality; (2) private bitwise integer comparison; and (3) bit-decomposition. These protocols are built upon a new concept called Shared Oblivious Transfer (Shared OT). Shared OT extends the one-out-of-N String OT by replacing strings with integers modulo $M$ and allowing additive secret-sharing of all inputs and outputs. These extensions can be implemented by simple local computations without incurring additional OT invocations. We believe our Shared OT may be of independent interest. Our protocols demonstrate the best round, communication, and computational complexities compared to all other protocols secure in a similar setting. Moreover, all of our protocols involve either 2 or 3 rounds.
Last updated:  2024-06-14
Secure Account Recovery for a Privacy-Preserving Web Service
Ryan Little, Lucy Qin, and Mayank Varia
If a web service is so secure that it does not even know—and does not want to know—the identity and contact info of its users, can it still offer account recovery if a user forgets their password? This paper is the culmination of the authors' work to design a cryptographic protocol for account recovery for use by a prominent secure matching system: a web-based service that allows survivors of sexual misconduct to become aware of other survivors harmed by the same perpetrator. In such a system, the list of account-holders must be safeguarded, even against the service provider itself. In this work, we design an account recovery system that, on the surface, appears to follow the typical workflow: the user types in their email address, receives an email containing a one-time link, and answers some security questions. Behind the scenes, the defining feature of our recovery system is that the service provider can perform email-based account validation without knowing, or being able to learn, a list of users' email addresses. Our construction uses standardized cryptography for most components, and it has been deployed in production at the secure matching system. As a building block toward our main construction, we design a new cryptographic primitive that may be of independent interest: an oblivious pseudorandom function that can either have a fully-private input or a partially-public input, and that reaches the same output either way. This primitive allows us to perform online rate limiting for account recovery attempts, without imposing a bound on the creation of new accounts. We provide an open-source implementation of this primitive and provide evaluation results showing that the end-to-end interaction time takes 8.4-60.4 ms in fully-private input mode and 3.1-41.2 ms in partially-public input mode.
Last updated:  2024-06-14
Efficient Execution Auditing for Blockchains under Byzantine Assumptions
Jeff Burdges, Alfonso Cevallos, Handan Kılınç Alper, Chen-Da Liu-Zhang, Fatemeh Shirazi, Alistair Stewart, Rob Habermeier, Robert Klotzner, and Andronik Ordian
Security of blockchain technologies primarily relies on decentralization making them resilient against a subset of entities being taken down or corrupt. Blockchain scaling, crucial to decentralisation, has been addressed by architectural changes: i.e., the load of the nodes is reduced by parallelisation, called sharding or by taking computation load off the main blockchain via rollups. Both sharding and rollups have limitations in terms of decentralization and security. A crucial component in these architectures is a layer that allows to efficiently check the validity of incoming blocks in the system. We provide the first formalization and analysis of ELVES, the auditing layer that is currently deployed in the Polkadot and Kusama blockchains. In this layer, “auditing committees” are formed independently for each block, and security relies on the fact that it is prohibitively expensive in expectation for an adversary to make ELVES to accept a block that is not valid. In addition, ELVES has the following characteristics: 1) Auditing committees wind up orders of magnitude smaller than pre-assigned committees. In fact, the size of the committees adapts automatically to network conditions but remains a low constant in expectation, in the order of tens or low hundreds; 2) Although synchronous per se, ELVES tolerates instant adaptive crashes, mirroring realistic network capabilities. Surprisingly, the committee-size analysis of our protocol is ’all but simple’ and involves a novel strengthening of Cantelli’s inequality, which may be of independent interest.
Last updated:  2024-06-14
Designs for practical SHE schemes based on Ring-LWR
Madalina Bolboceanu, Anamaria Costache, Erin Hales, Rachel Player, Miruna Rosca, and Radu Titiu
The Learning with Errors problem (LWE) and its variants are among the most popular assumptions underlying lattice-based cryptography. The Learning with Rounding problem (LWR) can be thought of as a deterministic variant of LWE. While lattice-based cryptography is known to enable many advanced constructions, constructing Fully Homomorphic Encryption schemes based on LWR remains an under-explored part of the literature. In this work, we present a thorough study of Somewhat Homomorphic Encryption schemes based on Ring-LWR that are the analogue of the Ring-LWE-based BFV scheme. Our main contribution is to present and analyse two new schemes, in the LPR and Regev paradigms. The Regev-type scheme can be seen as a generalisation of the only prior work in this direction (Costache-Smart, 2017). Both our schemes present several im- provements compared to this prior work, and in particular we resolve the “tangled modulus” issue in the Costache-Smart scheme that led to unmanageable noise growth. Our schemes inherit the many benefits of being based on LWR, including ease of implementation, avoiding the need for expensive Gaussian sampling, improved resistance to side channels, suitability for hardware, and improved ciphertext size. Indeed, we give a detailed comparison showing that the LPR and Regev-type schemes marginally outperform the BFV scheme in terms of ciphertext size. Moreover, we show that both our schemes support RNS variants, which would make their practical performance competitive with BFV.
Last updated:  2024-06-14
Flood and Submerse: Distributed Key Generation and Robust Threshold Signature from Lattices
Thomas Espitau, Guilhem Niot, and Thomas Prest
We propose a new framework based on random submersions — that is projection over a random subspace blinded by a small Gaussian noise — for constructing verifiable short secret sharing and showcase it to construct efficient threshold lattice-based signatures in the hash-and-sign paradigm, when based on noise flooding. This is, to our knowledge, the first hash-and-sign lattice-based threshold signature. Our threshold signature enjoys the very desirable property of robustness, including at key generation. In practice, we are able to construct a robust hash-and-sign threshold signature for threshold and provide a typical parameter set for threshold T = 16 and signature size 13kB. Our constructions are provably secure under standard MLWE assumption in the ROM and only require basic primitives as building blocks. In particular, we do not rely on FHE-type schemes.
Last updated:  2024-06-14
Signer Revocability for Threshold Ring Signatures
Da Teng and Yanqing Yao
t-out-of-n threshold ring signature (TRS) is a type of anonymous signature designed for t signers to jointly sign a message while hiding their identities among n parties that include themselves. However, can TRS address those needs if one of the signers wants to revoke his signature or, additively, sign separately later? Can non-signers be revoked without compromising anonymity? Previous research has only discussed opposing situations. The present study introduces a novel property for TRS- revocability- addressing the need for improved flexibility and privacy security in TRS. Our proposed revocable threshold ring signature (RTRS) scheme is innovative in several ways: (1) It allows a signer to non-interactively revoke their identity and update the signature from t-out-of-n to t − 1-out-of-n; (2) It is possible to reduce the ring size and clip non-signers along with revoked signers while maintaining the anonymity level. We analyze and define the boundaries for these operations and implement and evaluate our structure. With a sufficiently large ring size, we can optimize the signature size, resulting in better signing performance as compared to the extensible signature scheme.
Last updated:  2024-06-18
VRaaS: Verifiable Randomness as a Service on Blockchains
Jacob Gorman, Lucjan Hanzlik, Aniket Kate, Easwar Vivek Mangipudi, Pratyay Mukherjee, Pratik Sarkar, and Sri AravindaKrishnan Thyagarajan
Web3 applications, such as on-chain games, NFT minting, and leader elections necessitate access to unbiased, unpredictable, and publicly verifiable randomness. Despite its broad use cases and huge demand, there is a notable absence of comprehensive treatments of on-chain verifiable randomness services. To bridge this, we offer an extensive formal analysis of on-chain verifiable randomness services. We present the $first$ formalization of on-chain verifiable randomness in the blockchain setting by introducing the notion of Verifiable Randomness as a Service (VRaaS). We formally define VRaaS using an ideal functionality $\mathcal{F}_{\sf VRaaS}$ in the Universal Composability model. Our definition not only captures the core features of randomness services, such as unbiasability, unpredictability, and public verifiability, but also accounts for many other crucial nuances pertaining to different entities involved, such as smart contracts. Within our framework we study a generic design of Verifiable Random Function~(VRF)-based randomness service -- where the randomness requester provides an input on which the randomness is evaluated as VRF output. We show that it does satisfy our formal VRaaS definition. Furthermore, we show that the generic protocol captures many real-world randomness services like Chainlink VRF and Supra dVRF. We investigate whether our definition is minimalistic in terms of the desired security properties - towards that, we show that a couple of insecure constructions fall short of realizing our definition. Using our definition we also discover practical vulnerabilities in other designs such as Algorand beacon, Pyth VRF and Band VRF that offer on-chain verifiable randomness.
Last updated:  2024-06-14
SNARGs under LWE via Propositional Proofs
Zhengzhong Jin, Yael Tauman Kalai, Alex Lombardi, and Vinod Vaikuntanathan
We construct a succinct non-interactive argument (SNARG) system for every NP language $\mathcal{L}$ that has a propositional proof of non-membership for each $x\notin \mathcal{L}$. The soundness of our SNARG system relies on the hardness of the learning with errors (LWE) problem. The common reference string (CRS) in our construction grows with the space required to verify the propositional proof, and the size of the proof grows poly-logarithmically in the length of the propositional proof. Unlike most of the literature on SNARGs, our result implies SNARGs for languages $\mathcal L$ with proof length shorter than logarithmic in the deterministic time complexity of $\mathcal L$. Our SNARG improves over prior SNARGs for such ``hard'' NP languages (Sahai and Waters, STOC 2014, Jain and Jin, FOCS 2022) in several ways: - For languages with polynomial-length propositional proofs of non-membership, our SNARGs are based on a single, polynomial-time falsifiable assumption, namely LWE. - Our construction handles propositional proofs of super-polynomial length, as long as they have bounded space, under the subexponential LWE assumption. - Our SNARGs have a transparent setup, meaning that no private randomness is required to generate the CRS. Moreover, our approach departs dramatically from these prior works: we show how to design SNARGs for hard languages without publishing a program (in the CRS) that has the power to verify $\mathsf{NP}$ witnesses. The key new idea in our cryptographic construction is what we call a ``locally unsatisfiable extension'' of the $\mathsf{NP}$ verification circuit $\{C_x\}_x$. We say that an $\mathsf{NP}$ verifier has a locally unsatisfiable extension if for every $x\not\in \mathcal L$, there exists an extension $E_x$ of $C_x$ that is not even locally satisfiable in the sense of a local assignment generator [Paneth-Rothblum, TCC 2017]. Crucially, we allow $E_x$ to be depend arbitrarily on $x$ rather than being efficiently constructible. In this work, we show -- via a ``hash-and-BARG'' for a hidden, encrypted computation -- how to build SNARGs for all languages with locally unsatisfiable extensions. We additionally show that propositional proofs of unsatisfiability generically imply the existence of locally unsatisfiable extensions, which allows us to deduce our main results. As an illustrative example, our results imply a SNARG for the decisional Diffie-Hellman (DDH) language under the LWE assumption.
Last updated:  2024-06-14
ElectionGuard: a Cryptographic Toolkit to Enable Verifiable Elections
Josh Benaloh, Michael Naehrig, Olivier Pereira, and Dan S. Wallach
ElectionGuard is a flexible set of open-source tools that---when used with traditional election systems---can produce end-to-end verifiable elections whose integrity can be verified by observers, candidates, media, and even voters themselves. ElectionGuard has been integrated into a variety of systems and used in actual public U.S. elections in Wisconsin, California, Idaho, Utah, and Maryland as well as in caucus elections in the U.S. Congress. It has also been used for civic voting in the Paris suburb of Neuilly-sur-Seine and for an online election by a Switzerland/Denmark-based organization. The principal innovation of ElectionGuard is the separation of the cryptographic tools from the core mechanics and user interfaces of voting systems. This separation allows the cryptography to be designed and built by security experts without having to re-invent and replace the existing infrastructure. Indeed, in its preferred deployment, ElectionGuard does not replace the existing vote counting infrastructure but instead runs alongside and produces its own independently-verifiable tallies. Although much of the cryptography in ElectionGuard is, by design, not novel, some significant innovations are introduced which greatly simplify the process of verification. This paper describes the design of ElectionGuard, its innovations, and many of the learnings from its implementation and growing number of real-world deployments.
Last updated:  2024-06-17
Arithmetisation of computation via polynomial semantics for first-order logic
Murdoch J. Gabbay
We propose a compositional shallow translation from a first-order logic with equality, into polynomials; that is, we arithmetise the semantics of first-order logic. Using this, we can translate specifications of mathematically structured programming into polynomials, in a form amenable to succinct cryptographic verification. We give worked example applications, and we propose a proof-of-concept succinct verification scheme based on inner product arguments.
Last updated:  2024-06-14
MixBuy: Contingent Payment in the Presence of Coin Mixers
Diego Castejon-Molina, Dimitrios Vasilopoulos, and Pedro Moreno-Sanchez
A contingent payment protocol involves two mutually distrustful parties, a buyer and a seller, operating on the same blockchain, and a digital product, whose ownership is not tracked on a blockchain (e.g. a digital book, but not a NFT). The buyer holds coins on the blockchain and transfers them to the seller in exchange for the product. However, if the blockchain does not hide transaction details, any observer can learn that a buyer purchased some product from a seller. In this work, we take contingent payment a step further: we consider a buyer who wishes to buy a digital product from a seller routing the payment via an untrusted mixer. Crucially, we require that said payment is unlinkable, meaning that the mixer (or any other observer) does not learn which buyer is paying which seller. We refer to such setting as unlinkable contingent payment (UCP). We present MixBuy, a system that realizes UCP. Mixbuy relies on \emph{oracle-based unlinkable contingent payment} (O-UCP), a novel four-party cryptographic protocol where the mixer pays the seller and the seller provides the buyer with the product only if a semi-trusted notary attests that the buyer has paid the mixer. More specifically, we require four security notions: (i) mixer security that guarantees that if the mixer pays the seller, the intermediary must get paid from the buyer; (ii) seller security that guarantees that if the seller delivers the product to the buyer, the seller must get paid from the intermediary; (iii) buyer security that guarantees that if the buyer pays the intermediary, the buyer must obtain the product; and (iv) unlinkability that guarantees that given a set of buyers and sellers, the intermediary should not learn which buyer paid which seller. We present a provably secure and efficient cryptographic construction for O-UCP. Our construction can be readily used to realize UCP on most blockchains, as it has minimal functionality requirements (i.e., digital signatures and timelocks). To demonstrate the practicality of our construction, we provide a proof of concept for O-UCP and our benchmarks in commodity hardware show that the communication overhead is small (a few kB per message) and the running time is below one second.
Last updated:  2024-06-13
Communication Complexity vs Randomness Complexity in Interactive Proofs
Benny Applebaum, Kaartik Bhushan, and Manoj Prabhakaran
In this note, we study the interplay between the communication from a verifier in a general private-coin interactive protocol and the number of random bits it uses in the protocol. Under worst-case derandomization assumptions, we show that it is possible to transform any $I$-round interactive protocol that uses $\rho$ random bits into another one for the same problem with the additional property that the verifier's communication is bounded by $O(I\cdot \rho)$. Importantly, this is done with a minor, logarithmic, increase in the communication from the prover to the verifier and while preserving the randomness complexity. Along the way, we introduce a new compression game between computationally-bounded compressor and computationally-unbounded decompressor and a new notion of conditioned efficient distributions that may be of independent interest. Our solutions are based on a combination of perfect hashing and pseudorandom generators.
Last updated:  2024-06-13
Notes on (failed) attempts to instantiate TLR3
Alexander Maximov
In this short paper we share our experience on instantiating the width-extension construct TLR3, based on a variety of tweakable block cipher constructs. As many of our attempts failed, we highlight the complexity of getting a practical tweakable block cipher and the gap between theory and practice.
Last updated:  2024-06-13
DISCO: Dynamic Searchable Encryption with Constant State
Xiangfu Song, Yu Zheng, Jianli Bai, Changyu Dong, Zheli Liu, and Ee-Chien Chang
Dynamic searchable encryption (DSE) with forward and backward privacy reduces leakages in early-stage schemes. Security enhancement comes with a price -- maintaining updatable keyword-wise state information. State information, if stored locally, incurs significant client-side storage overhead for keyword-rich datasets, potentially hindering real-world deployments. We propose DISCO, a simple and efficient framework for designing DSE schemes using constant client state. DISCO combines range-constrained pseudorandom functions (RCPRFs) over a global counter and leverages nice properties from the underlying primitives and index structure to simultaneously achieve forward-and-backward privacy and constant client state. To configure DISCO concretely, we identify a set of RCPRF properties that are vital for the resulting DISCO instantiations. By configuring DISCO with different RCPRFs, we resolve efficiency and usability issues in existing schemes. We further optimize DISCO's concrete efficiency without downgrading security. We implement DISCO constructions and report performance, showing trade-offs from different DISCO constructions. Besides, we compare the practical efficiency of DISCO with existing non-constant-state DSE schemes, demonstrating DISCO's competitive efficiency.
Last updated:  2024-06-18
Efficient 2PC for Constant Round Secure Equality Testing and Comparison
Tianpei Lu, Xin Kang, Bingsheng Zhang, Zhuo Ma, Xiaoyuan Zhang, Yang Liu, and Kui Ren
Secure equality testing and comparison are two important primitives that have been widely used in many secure computation scenarios, such as privacy-preserving machine learning, private set intersection, secure data mining, etc. In this work, we propose new constant-round two-party computation (2PC) protocols for secure equality testing and secure comparison. Our protocols are designed in the online/offline paradigm. Theoretically, for 32-bit integers, the online communication for our equality testing is only 76 bits, and the cost for our secure comparison is only 384 bits.Our benchmarks show that (i) our equality is $9 \times$ faster than the Guo \emph{et al.} (EUROCRYPT 2023) and $15 \times$ of the garbled circuit scheme (EMP-toolkit). (ii) our secure comparison protocol is $3 \times$ faster than Guo et al.(EUROCRYPT 2023), $6 \times$ faster than both Rathee et al. (CCS 2020) and garbled circuit scheme.
Last updated:  2024-06-13
Return of the Kummer: a toolbox for genus 2 cryptography
Maria Corte-Real Santos and Krijn Reijnders
This work expands the machinery we have for isogeny-based cryptography in genus 2 by developing a toolbox of several essential algorithms for Kummer surfaces, the dimension 2 analogue of x-only arithmetic on elliptic curves. Kummer surfaces have been suggested in (hyper-)elliptic curve cryptography since at least the 1980s and recently these surfaces have reappeared to efficiently compute (2,2)-isogenies. We construct several essential analogues of techniques used in one-dimensional isogeny-based cryptography, such as pairings, deterministic point sampling and point compression and give an overview of (2,2)-isogenies on Kummer surfaces. We furthermore show how Scholten's construction can be used to transform isogeny-based cryptography over elliptic curves over $\mathbb{F}_{p^2}$ into protocols over Kummer surfaces over $\mathbb{F}_p$. As an example of this approach, we demonstrate that SQIsign verification can be performed completely on Kummer surfaces, and, therefore, that one-dimensional SQIsign verification can be viewed as a two-dimensional isogeny between products of elliptic curves. Curiously, the isogeny is then defined over $\mathbb{F}_p$ rather than $\mathbb{F}_{p^2}$. Contrary to expectation, the cost of SQIsign verification using Kummer surfaces does not explode: verification costs only 1.5 times more in terms of finite field operations than the SQIsign variant AprèsSQI, optimised for fast verification. Furthermore, as Kummer surfaces allow a much higher degree of parallelization, Kummer-based protocols over $\mathbb{F}_p$ could potentially outperform elliptic curve analogues over $\mathbb{F}_{p^2}$ in terms of clock cycles and actual performance.
Last updated:  2024-06-12
A Modular Approach to Registered ABE for Unbounded Predicates
Nuttapong Attrapadung and Junichi Tomida
Registered attribute-based encryption (Reg-ABE), introduced by Hohenberger et al. (Eurocrypt’23), emerges as a pivotal extension of attribute-based encryption (ABE), aimed at mitigating the key-escrow problem. Although several Reg-ABE schemes with black-box use of cryptography have been proposed so far, there remains a significant gap in the class of achievable predicates between vanilla ABE and Reg-ABE. To narrow this gap, we propose a modular framework for constructing Reg-ABE schemes for a broader class of predicates. Our framework is a Reg-ABE analog of the predicate transformation framework for ABE introduced by Attrapadung (Eurocrypt’19) and later refined by Attrapadung and Tomida (Asiacrypt’20) to function under the standard MDDH assumption. As immediate applications, our framework implies the following new Reg-ABE schemes under the standard MDDH assumption: – the first Reg-ABE scheme for (non-)monotone span programs with the traditional completely unbounded property. – the first Reg-ABE scheme for general non-monotone span programs (also with the completely unbounded property) as defined in the case of vanilla ABE by Attrapadung and Tomida (Asiacrypt’20). Here, the term “completely unbounded” signifies the absence of restrictions on attribute sets for users and policies associated with ciphertexts. From a technical standpoint, we first substantially modify pair encoding schemes (PES), originally devised for vanilla ABE by Attrapadung (Eurocrypt’14), to make them compatible with Reg-ABE. Subsequently, we present a series of predicate transformations through which we can construct complex predicates, particularly those with an “unbounded” characteristic, starting from simple ones. Finally, we define new properties of PES necessary for constructing Reg-ABE schemes and prove that these properties are preserved through the transformations. This immediately implies that we can obtain Reg-ABE schemes for any predicates derived via predicate transformations.
Last updated:  2024-06-12
Provably Secure Butterfly Key Expansion from the CRYSTALS Post-Quantum Schemes
Edward Eaton, Philippe Lamontagne, and Peter Matsakis
This work presents the first provably secure protocol for Butterfly Key Expansion (BKE) -- a tripartite protocol for provisioning users with pseudonymous certificates -- based on post-quantum cryptographic schemes. Our work builds upon the CRYSTALS family of post-quantum algorithms that have been selected for standardization by NIST. We extend those schemes by imbuing them with the additional functionality of public key expansion: a process by which pseudonymous public keys can be derived by a single public key. Our work is the most detailed analysis yet of BKE: we formally define desired properties of BKE -- unforgeability and unlinkability -- as cryptographic games, and prove that BKE implemented with our modified CRYSTALS schemes satisfy those properties. We implemented our scheme by modifying the Kyber and Dilithium algorithms from the LibOQS project, and we report on our parameter choices and the performance of the schemes.
Last updated:  2024-06-12
Quantum-Safe Public Key Blinding from MPC-in-the-Head Signature Schemes
Sathvika Balumuri, Edward Eaton, and Philippe Lamontagne
Key blinding produces pseudonymous digital identities by rerandomizing public keys of a digital signature scheme. It is used in anonymous networks to provide the seemingly contradictory goals of anonymity and authentication. Current key blinding schemes are based on the discrete log assumption. Eaton, Stebila and Stracovsky (LATINCRYPT 2021) proposed the first key blinding schemes from lattice assumptions. However, the large public keys and lack of QROM security means they are not ready to replace existing solutions. We present a new way to build key blinding schemes form any MPC-in-the-Head signature scheme. These schemes rely on well-studied symmetric cryptographic primitives and admit short public keys. We prove a general framework for constructing key blinding schemes and for proving their security in the quantum random oracle model (QROM). We instantiate our framework with the recent AES-based Helium signature scheme (Kales and Zaverucha, 2022). Blinding Helium only adds a minor overhead to the signature and verification time. Both Helium and the aforementioned lattice-based key blinding schemes were only proven secure in the ROM. This makes our results the first QROM proof of Helium and the first fully quantum-safe public key blinding scheme.
Last updated:  2024-06-12
Quantum CCA-Secure PKE, Revisited
Navid Alamati and Varun Maram
Security against chosen-ciphertext attacks (CCA) concerns privacy of messages even if the adversary has access to the decryption oracle. While the classical notion of CCA security seems to be strong enough to capture many attack scenarios, it falls short of preserving the privacy of messages in the presence of quantum decryption queries, i.e., when an adversary can query a superposition of ciphertexts. Boneh and Zhandry (CRYPTO 2013) defined the notion of quantum CCA (qCCA) security to guarantee privacy of messages in the presence of quantum decryption queries. However, their construction is based on an exotic cryptographic primitive (namely, identity-based encryption with security against quantum queries), for which only one instantiation is known. In this work, we comprehensively study qCCA security for public-key encryption (PKE) based on both generic cryptographic primitives and concrete assumptions, yielding the following results: * We show that key-dependent message secure encryption (along with PKE) is sufficient to realize qCCA-secure PKE. This yields the first construction of qCCA-secure PKE from the LPN assumption. * We prove that hash proof systems imply qCCA-secure PKE, which results in the first instantiation of PKE with qCCA security from (isogeny-based) group actions. * We extend the notion of adaptive TDFs (ATDFs) to the quantum setting by introducing quantum ATDFs, and we prove that quantum ATDFs are sufficient to realize qCCA-secure PKE. We also show how to instantiate quantum ATDFs from the LWE assumption. * We show that a single-bit qCCA-secure PKE is sufficient to realize a multi-bit qCCA-secure PKE by extending the completeness of bit encryption for CCA security to the quantum setting.
Last updated:  2024-06-12
Dual Polynomial Commitment Schemes and Applications to Commit-and-Prove SNARKs
Chaya Ganesh, Vineet Nair, and Ashish Sharma
We introduce a primitive called a dual polynomial commitment scheme that allows linking together a witness committed to using a univariate polynomial commitment scheme with a witness inside a multilinear polynomial commitment scheme. This yields commit-and-prove (CP) SNARKs with the flexibility of going back and forth between univariate and multilinear encodings of witnesses. This is in contrast to existing CP frameworks that assume compatible polynomial commitment schemes between different component proofs systems. In addition to application to CP, we also show that our notion yields a version of Spartan with better proof size and verification complexity, at the cost of a more expensive prover. We achieve this via a combination of the following technical contributions: (i) we construct a new univariate commitment scheme in the updatable SRS setting that has better prover complexity than KZG (ii) we construct a new multilinear commitment scheme in the updatable setting that is compatible for linking with our univariate scheme (iii) we construct an argument of knowledge to prove a given linear relationship between two witnesses committed using a two-tiered commitment scheme (Pedersen+AFG) using Dory as a black-box. These constructions are of independent interest. We implement our commitment schemes and report on performance. We also implement the version of Spartan with our dual polynomial commitment scheme and demonstrate that it outperforms Spartan in proof size and verification complexity.
Last updated:  2024-06-12
Let Them Drop: Scalable and Efficient Federated Learning Solutions Agnostic to Client Stragglers
Riccardo Taiello, Melek Önen, Clémentine Gritti, and Marco Lorenzi
Secure Aggregation (SA) stands as a crucial component in modern Federated Learning (FL) systems, facilitating collaborative training of a global machine learning model while protecting the privacy of individual clients' local datasets. Many existing SA protocols described in the FL literature operate synchronously, leading to notable runtime slowdowns due to the presence of stragglers (i.e. late-arriving clients). To address this challenge, one common approach is to consider stragglers as client failures and use SA solutions that are robust against dropouts. While this approach indeed seems to work, it unfortunately affects the performance of the protocol as its cost strongly depends on the dropout ratio and this ratio has increased significantly when taking stragglers into account. Another approach explored in the literature to address stragglers is to introduce asynchronicity into the FL system. Very few SA solutions exist in this setting and currently suffer from high overhead. In this paper, similar to related work, we propose to handle stragglers as client failures but design SA solutions that do not depend on the dropout ratio so that an unavoidable increase on this metric does not affect the performance of the solution. We first introduce Eagle, a synchronous SA scheme designed not to depend on the client failures but on the online users' inputs only. This approach offers better computation and communication costs compared to existing solutions under realistic settings where the number of stragglers is high. We then propose Owl, the first SA solution that is suitable for the asynchronous setting and once again considers online clients' contributions only. We implement both solutions and show that: (i) in a synchronous FL with realistic dropout rates (taking potential stragglers into account), Eagle outperforms the best SA solution, namely Flamingo, by X4; (ii) In the asynchronous setting, Owl exhibits the best performance compared to the state-of-the-art solution LightSecAgg.
Last updated:  2024-06-12
SmartZKCP: Towards Practical Data Exchange Marketplace Against Active Attacks
Xuanming Liu, Jiawen Zhang, Yinghao Wang, Xinpeng Yang, and Xiaohu Yang
The trading of data is becoming increasingly important as it holds substantial value. A blockchain-based data marketplace can provide a secure and transparent platform for data exchange. To facilitate this, developing a fair data exchange protocol for digital goods has garnered considerable attention in recent decades. The Zero Knowledge Contingent Payment (ZKCP) protocol enables trustless fair exchanges with the aid of blockchain and zero-knowledge proofs. However, applying this protocol in a practical data marketplace is not trivial. In this paper, several potential attacks are identified when applying the ZKCP protocol in a practical public data marketplace. To address these issues, we propose SmartZKCP, an enhanced solution that offers improved security measures and increased performance. The protocol is formalized to ensure fairness and secure against potential attacks. Moreover, SmartZKCP offers efficiency optimizations and minimized communication costs. Evaluation results show that SmartZKCP is both practical and efficient, making it applicable in a data exchange marketplace.
Last updated:  2024-06-12
Scalable Collaborative zk-SNARK and Its Application to Efficient Proof Outsourcing
Xuanming Liu, Zhelei Zhou, Yinghao Wang, Jinye He, Bingsheng Zhang, Xiaohu Yang, and Jiaheng Zhang
Collaborative zk-SNARK (USENIX'22) allows multiple parties to jointly create a zk-SNARK proof over distributed secrets (also known as the witness). It provides a promising approach to proof outsourcing, where a client wishes to delegate the tedious task of proof generation to many servers from different locations, while ensuring no corrupted server can learn its witness (USENIX'23). Unfortunately, existing work remains a significant efficiency problem, as the protocols rely heavily on a particularly powerful server, and thus face challenges in achieving scalability for complex applications. In this work, we address this problem by extending the existing zk-SNARKs Libra (Crypto'19) and HyperPlonk (Eurocrypt'23) into scalable collaborative zk-SNARKs. Crucially, our collaborative proof generation does not require a powerful server, and all servers take up roughly the same proportion of the total workload. In this way, we achieve privacy and scalability simultaneously for the first time in proof outsourcing. To achieve this, we develop an efficient MPC toolbox for a number of useful multivariate polynomial primitives, including sumcheck, productcheck, and multilinear polynomial commitment, which can also be applied to other applications as independent interests. For proof outsourcing purposes, when using $128$ servers to jointly generate a proof for a circuit size of $2^{24}$ gates, our benchmarks for these two collaborative proofs show a speedup of $21\times$ and $24\times$ compared to a local prover, respectively. Furthermore, we are able to handle enormously large circuits, making it practical for real-world applications.
Last updated:  2024-06-11
Two RSA-based Cryptosystems
A. Telveenus
The cryptosystem RSA is a very popular cryptosystem in the study of Cryptography. In this article, we explore how the idea of a primitive m th root of unity in a ring can be integrated into the Discrete Fourier Transform, leading to the development of new cryptosystems known as RSA-DFT and RSA-HGR.
Last updated:  2024-06-11
Certifying Private Probabilistic Mechanisms
Zoë Ruha Bell, Shafi Goldwasser, Michael P. Kim, and Jean-Luc Watson
In past years, entire research communities have arisen to address concerns of privacy and fairness in data analysis. At present, however, the public must trust that institutions will re-implement algorithms voluntarily to account for these social concerns. Due to additional cost, widespread adoption is unlikely without effective legal enforcement. A technical challenge for enforcement is that the methods proposed are often probabilistic mechanisms, whose output must be drawn according to precise, and sometimes secret, distributions. The Differential Privacy (DP) case is illustrative: if a cheating curator answers queries according to an overly-accurate mechanism, privacy violations could go undetected. The need for effective enforcement raises the central question of our paper: Can we efficiently certify the output of a probabilistic mechanism enacted by an untrusted party? To this end: (1) We introduce two new notions: Certified Probabilistic Mechanisms (CPM) and Random Variable Commitment Schemes (RVCS). A CPM is an interactive protocol that forces a prover to enact a given probabilistic mechanism or be caught; importantly, the interaction does not reveal secret parameters of the mechanism. An RVCS—a key primitive for constructing CPMs—is a commitment scheme where the verifier is convinced that the commitment is to an RV sampled according to an agreed-upon distribution, but learns nothing else. (2) We instantiate the general notion of CPM for the special case of Certifying DP. We build a lightweight, doubly-efficent interactive proof system to certify arbitrary-predicate counting queries released via the DP Binomial mechanism. The construction relies on a commitment scheme with perfect hiding and additive homomorphic properties that can be used to release a broad class of queries about a committed database, which we construct on top of Pedersen commitments. (3) Finally, we demonstrate the immediate feasibility of Certified DP via a highly-efficient and scalable prototype implementation to answer counting queries of arbitrary predicates. The mechanism is composed of an offline and online stage, where the online phase allows for non-interactive certification of queries. For example, we show that CDP queries over a US Census Public Use Microdata Sample (PUMS) ($n=7000$) can be completed in only 1.6 ms and verified in just 38 $\mu \text{s}$. Our implementation is available in open source at
Last updated:  2024-06-11
Distributed Point Function with Constraints, Revisited
Keyu Ji, Bingsheng Zhang, Hong-Sheng Zhou, and Kui Ren
Distributed Point Function (DPF) provides a way for a dealer to split a point function $f_{\alpha, \beta}$ into multiple succinctly described function-shares, where the function $f_{\alpha, \beta}$ for a special input $\alpha$, returns a special output value $\beta$, and returns a fixed value $0$ otherwise. As the security requirement, any strict subset of the function-shares reveals nothing about the function $f_{\alpha,\beta}$. However, each function-share can be individually evaluated on the common input $x$, and these evaluation results can then be merged together to reconstruct the value $f_{\alpha, \beta}(x)$. Recently, Servan-Schreiber et al. (S&P 2023) investigate the access control problem for DPF; namely, the DPF evaluators can ensure that the DPF dealer is authorized to share the given function with privacy assurance. In this work, we revisit this problem, introducing a new notion called DPF with constraints; meanwhile, we identify that there exists a subtle flaw in their privacy definition as well as a soundness issue in one of their proposed schemes due to the lack of validation of the special output value $\beta$. Next, we show how to reduce both the storage size of the constraint representation and the server's computational overhead from $O(N)$ to $O(\log N)$, where $N$ is the number of authorized function sets. In addition, we show how to achieve fine-grained private access control, that is, the wildcard-style constraint for the choice of the special output $\beta$. Our benchmarks show that the amortized running time of our logarithmic storage scheme is $2\times$ - $3\times$ faster than the state-of-the-art when $N=2^{15}$. Furthermore, we provide the first impossibility and feasibility results of the DPF with constraints where the evaluators do not need to communicate with each other.
Last updated:  2024-06-11
Willow: Secure Aggregation with One-Shot Clients
James Bell-Clark, Adrià Gascón, Baiyu Li, Mariana Raykova, and Phillipp Schoppmann
A common drawback of secure vector summation protocols in the single-server model is that they impose at least one synchronization point between all clients contributing to the aggregation. This results in clients waiting on each other to advance through the rounds of the protocol, leading to large latency even if the protocol is computationally efficient. In this paper we propose protocols in the single-server model where clients contributing data to the aggregation send a single message to the server in an asynchronous fashion, i.e., without the need for synchronizing their reporting time with any other clients. Our approach is based on a committee of parties, called decryptors, that aid in the computation. Decryptors run a setup phase before data collection starts, and a decryption phase once it ends. Unlike existing committee-based protocols such as Flamingo (S&P 2023), the cost for committee members can be made sub-linear in the number of clients, and does not depend on the size of the input data. Our experimental evaluation shows that our protocol, even while enabling asynchronous client contributions,is competitive with the state of the art protocols that do not have that feature in both computation and communication.
Last updated:  2024-06-11
MFKDF: Multiple Factors Knocked Down Flat
Matteo Scarlata, Matilda Backendal, and Miro Haller
Nair and Song (USENIX 2023) introduce the concept of a Multi-Factor Key Derivation Function (MFKDF), along with constructions and a security analysis. MFKDF integrates dynamic authentication factors, such as HOTP and hardware tokens, into password-based key derivation. The aim is to improve the security of password-derived keys, which can then be used for encryption or as an alternative to multi-factor authentication. The authors claim an exponential security improvement compared to traditional password-based key derivation functions (PBKDF). We show that the MFKDF constructions proposed by Nair and Song fall short of the stated security goals. Underspecified cryptographic primitives and the lack of integrity of the MFKDF state lead to several attacks, ranging from full key recovery when an HOTP factor is compromised, to bypassing factors entirely or severely reducing their entropy. We reflect on the different threat models of key-derivation and authentication, and conclude that MFKDF is always weaker than plain PBKDF and multi-factor authentication in each setting.
Last updated:  2024-06-11
An Explicit High-Moment Forking Lemma and its Applications to the Concrete Security of Multi-Signatures
Gil Segev and Liat Shapira
In this work we first present an explicit forking lemma that distills the information-theoretic essence of the high-moment technique introduced by Rotem and Segev (CRYPTO '21), who analyzed the security of identification protocols and Fiat-Shamir signature schemes. Whereas the technique of Rotem and Segev was particularly geared towards two specific cryptographic primitives, we present a stand-alone probabilistic lower bound, which does not involve any underlying primitive or idealized model. The key difference between our lemma and previous ones is that instead of focusing on the tradeoff between the worst-case or expected running time of the resulting forking algorithm and its success probability, we focus on the tradeoff between higher moments of its running time and its success probability. Equipped with our lemma, we then establish concrete security bounds for the BN and BLS multi-signature schemes that are significantly tighter than the concrete security bounds established by Bellare and Neven (CCS '06) and Boneh, Drijvers and Neven (ASIACRYPT '18), respectively. Our analysis does not limit adversaries to any idealized algebraic model, such as the algebraic group model in which all algorithms are assumed to provide an algebraic justification for each group element they produce. Our bounds are derived in the random-oracle model based on the standard-model second-moment hardness of the discrete logarithm problem (for the BN scheme) and the computational co-Diffie-Hellman problem (for the BLS scheme). Such second-moment assumptions, asking that the success probability of any algorithm in solving the underlying computational problems is dominated by the second moment of the algorithm's running time, are particularly plausible in any group where no better-than-generic algorithms are currently known.
Last updated:  2024-06-11
A Pure Indistinguishability Obfuscation Approach to Adaptively-Sound SNARGs for NP
Brent Waters and David J. Wu
We construct an adaptively-sound succinct non-interactive argument (SNARG) for NP in the CRS model from sub-exponentially-secure indistinguishability obfuscation ($i\mathcal{O}$) and sub-exponentially-secure one-way functions. Previously, Waters and Wu (STOC 2024), and subsequently, Waters and Zhandry (CRYPTO 2024) showed how to construct adaptively-sound SNARGs for NP by relying on sub-exponentially-secure indistinguishability obfuscation, one-way functions, and an additional algebraic assumption (i.e., discrete log, factoring, or learning with errors). In this work, we show that no additional algebraic assumption is needed and vanilla (sub-exponentially-secure) one-way functions already suffice in combination with $i\mathcal{O}$. We first give a direct construction of an adaptively-sound SNARG for NP assuming (sub-exponentially-secure) $i\mathcal{O}$ and an injective one-way function. Then, we show that it suffices to have an injective one-way function that has an inefficient sampler (i.e., sampling a challenge for the one-way function requires super-polynomial time). Because we rely on the existence of injective one-way functions only in the security proof and not in the actual construction, having an inefficient sampling procedure does not impact correctness. We then show that injective one-way functions with an inefficient sampler can be built generically from any vanilla one-way function. Our approach may be independently useful in other settings to replace injective one-way functions with standard one-way functions in applications of $i\mathcal{O}$.
Last updated:  2024-06-11
CISELeaks: Information Leakage Assessment of Cryptographic Instruction Set Extension Prototypes
Aruna Jayasena, Richard Bachmann, and Prabhat Mishra
Software based cryptographic implementations provide flexibility but they face performance limitations. In contrast, hardware based cryptographic accelerators utilize application-specific customization to provide real-time security solutions. Cryptographic instruction-set extensions (CISE) combine the advantages of both hardware and software based solutions to provide higher performance combined with the flexibility of atomic-level cryptographic operations. While CISE is widely used to develop security solutions, side-channel analysis of CISE-based devices is in its infancy. Specifically, it is important to evaluate whether the power usage and electromagnetic emissions of CISE-based devices have any correlation with its internal operations, which an adversary can exploit to deduce cryptographic secrets. In this paper, we propose a test vector leakage assessment framework to evaluate the pre-silicon prototypes at the early stages of the design life-cycle. Specifically, we first identify functional units with the potential for leaking information through power side-channel signatures and then evaluate them on system prototypes by generating the necessary firmware to maximize the side-channel signature. Our experimental results on two RISC-V based cryptographic extensions, RISCV-CRYPTO and XCRYPTO, demonstrated that seven out of eight prototype AES- and SHA-related functional units are vulnerable to leaking cryptographic secrets through their power side-channel signature even in full system mode with a statistical significance of $\alpha = 0.05$.
Last updated:  2024-06-10
Leveled Fully-Homomorphic Signatures from Batch Arguments
Abtin Afshar, Jiaqi Cheng, and Rishab Goyal
Fully homomorphic signatures are a significant strengthening of digital signatures, enabling computations on \emph{secretly} signed data. Today, we have multiple approaches to design fully homomorphic signatures such as from lattices, or succinct functional commitments, or indistinguishability obfuscation, or mutable batch arguments. Unfortunately, all existing constructions for homomorphic signatures suffer from one or more limitations. We do not have homomorphic signatures with features such as multi-hop evaluation, context hiding, and fast amortized verification, while relying on standard falsifiable assumptions. In this work, we design homomorphic signatures satisfying all above properties. We construct homomorphic signatures for polynomial-sized circuits from a variety of standard assumptions such as sub-exponential DDH, standard pairing-based assumptions, or learning with errors. We also discuss how our constructions can be easily extended to the multi-key setting.
Last updated:  2024-06-10
Information-Theoretic Single-Server PIR in the Shuffle Model
Yuval Ishai, Mahimna Kelkar, Daniel Lee, and Yiping Ma
We revisit the problem of private information retrieval (PIR) in the shuffle model, where queries can be made anonymously by multiple clients. We present the first single-server PIR protocol in this model that has sublinear per-client communication and information-theoretic security. Moreover, following one-time preprocessing on the server side, our protocol only requires sublinear per-client computation. Concretely, for every $\gamma>0$, the protocol has $O(n^{\gamma})$ communication and computation costs per (stateless) client, with $1/\text{poly}(n)$ statistical security, assuming that a size-$n$ database is simultaneously accessed by $\text{poly}(n)$ clients. This should be contrasted with the recent breakthrough result of Lin, Mook, and Wichs (STOC 2023) on doubly efficient PIR in the standard model, which is (inherently) limited to computational security.
Last updated:  2024-06-10
Combining Outputs of a Random Permutation: New Constructions and Tight Security Bounds by Fourier Analysis
Itai Dinur
We consider constructions that combine outputs of a single permutation $\pi:\{0,1\}^n \rightarrow \{0,1\}^n$ using a public function. These are popular constructions for achieving security beyond the birthday bound when implementing a pseudorandom function using a block cipher (i.e., a pseudorandom permutation). One of the best-known constructions (denoted SXoP$[2,n]$) XORs the outputs of 2 domain-separated calls to $\pi$. Modeling $\pi$ as a uniformly chosen permutation, several previous works proved a tight information-theoretic indistinguishability bound for SXoP$[2,n]$ of about $q/2^{n}$, where $q$ is the number of queries. On the other hand, tight bounds are unknown for the generalized variant (denoted SXoP$[r,n]$) which XORs the outputs of $r>2$ domain-separated calls to a uniform permutation. In this paper, we obtain two results. Our first result improves the known bounds for SXoP$[r,n]$ for all (constant) $r \geq 3$ (assuming $q \leq O(2^n/r)$ is not too large) in both the single-user and multi-user settings. In particular, for $q=3$, our bound is about $\sqrt{u}q_{\max}/2^{2.5n}$ (where $u$ is the number of users and $q_{\max}$ is the maximal number of queries per user), improving the best-known previous result by a factor of at least $2^n$. For odd $r$, our bounds are tight for $q > 2^{n/2}$, as they match known attacks. For even $r$, we prove that our single-user bounds are tight by providing matching attacks. Our second and main result is divided into two parts. First, we devise a family of constructions that output $n$ bits by efficiently combining outputs of 2 calls to a permutation on $\{0,1\}^n$, and achieve multi-user security of about $\sqrt{u} q_{\max}/2^{1.5n}$. Then, inspired by the CENC construction of Iwata [FSE'06], we further extend this family to output $2n$ bits by efficiently combining outputs of 3 calls to a permutation on $\{0,1\}^n$. The extended construction has similar multi-user security of $\sqrt{u} q_{\max}/2^{1.5n}$. The new single-user ($u=1$) bounds of $q/2^{1.5n}$ for both families should be contrasted with the previously best-known bounds of $q/2^n$, obtained by the comparable constructions of SXoP$[2,n]$ and CENC. All of our bounds are proved by Fourier analysis, extending the provable security toolkit in this domain in multiple ways.
Last updated:  2024-06-12
The Committing Security of MACs with Applications to Generic Composition
Ritam Bhaumik, Bishwajit Chakraborty, Wonseok Choi, Avijit Dutta, Jérôme Govinden, and Yaobin Shen
Message Authentication Codes (MACs) are ubiquitous primitives deployed in multiple flavors through standards such as HMAC, CMAC, GMAC, LightMAC, and many others. Its versatility makes it an essential building block in applications necessitating message authentication and integrity checks, in authentication protocols, authenticated encryption schemes, or as a pseudorandom or key derivation function. Its usage in this variety of settings makes it susceptible to a broad range of attack scenarios. The latest attack trends leverage a lack of commitment or context-discovery security in AEAD schemes and these attacks are mainly due to the weakness in the underlying MAC part. However, these new attack models have been scarcely analyzed for MACs themselves. This paper provides a thorough treatment of MACs committing and context-discovery security. We reveal that commitment and context-discovery security of MACs have their own interest by highlighting real-world vulnerable scenarios. We formalize the required security notions for MACs, and analyze the security of standardized MACs for these notions. Additionally, as a constructive application, we analyze generic AEAD composition and provide simple and efficient ways to build committing and context-discovery secure AEADs.
Last updated:  2024-06-12
Anjali C B
The current cryptographic frameworks like RSA, ECC, and AES are potentially under quantum threat. Quantum cryptographic and post-quantum cryptography are being extensively researched for securing future information. The quantum computer and quantum algorithms are still in the early developmental stage and thus lack scalability for practical application. As a result of these challenges, most researched PQC methods are lattice-based, code-based, ECC isogeny, hash-based, and multivariate crypto schemes. In this paper, we explore other athematical topics such as stereographic projection, Mobius transformation, change of basis, Apollonian circle, Binary Quadratic form equivalence, Gauss composition law, and its conjunctions. It fulfills preliminary conditions like bijection, primality, and np-hard problems, and the feasibility of one-way functions along with its interconnection. Thus allowing the exploration of new realms of mathematics for the development of secure protocols for future communication.
Last updated:  2024-06-10
Verifiable and Private Vote-by-Mail
Henri Devillez, Olivier Pereira, and Thomas Peters
Vote-by-mail is increasingly used in Europe and worldwide for government elections. Nevertheless, very few attempts have been made towards the design of verifiable vote-by-mail, and none of them come with a rigorous security analysis. Furthermore, the ballot privacy of the currently deployed (non-verifiable) vote-by-mail systems relies on procedural means that a single malicious operator can bypass. We propose a verifiable vote-by-mail system that can accommodate the constraints of many of the large ballots that are common in Europe. Verifiability and privacy hold unless multiple system components collude to cheat on top of the postal channel. These security notions are expressed and analyzed in the simplified UC security framework. Our vote-by-mail system only makes limited requirements on the voters: voters can verify their vote by copying and comparing short strings and verifying the computation of a single hash on a short input, and they can vote normally if they want to ignore the verification steps completely. Our system also relies on common cryptographic components, all available in the ElectionGuard verifiable voting SDK for instance, which limits the risks of errors in the implementation of the cryptographic aspects of the system.
Last updated:  2024-06-10
Time Sharing - A Novel Approach to Low-Latency Masking
Dilip Kumar S. V., Siemen Dhooghe, Josep Balasch, Benedikt Gierlichs, and Ingrid Verbauwhede
We present a novel approach to small area and low-latency first-order masking in hardware. The core idea is to separate the processing of shares in time in order to achieve non-completeness. Resulting circuits are proven first-order glitch-extended PINI secure. This means the method can be straightforwardly applied to mask arbitrary functions without constraints which the designer must take care of. Furthermore we show that an implementation can benefit from optimization through EDA tools without sacrificing security. We provide concrete results of several case studies. Our low-latency implementation of a complete PRINCE core shows a 32% area improvement (44% with optimization) over the state-of-the-art. Our PRINCE S-Box passes formal verification with a tool and the complete core on FPGA shows no first-order leakage in TVLA with 100 million traces. Our low-latency implementation of the AES S-Box costs roughly one third (one quarter with optimization) of the area of state-of-the-art implementations. It shows no first-order leakage in TVLA with 250 million traces.
Last updated:  2024-06-10
Climbing and descending tall volcanos
Steven Galbraith
We revisit the question of relating the elliptic curve discrete logarithm problem (ECDLP) between ordinary elliptic curves over finite fields with the same number of points. This problem was considered in 1999 by Galbraith and in 2005 by Jao, Miller, and Venkatesan. We apply recent results from isogeny cryptography and cryptanalysis, especially the Kani construction, to this problem. We improve the worst case bound in Galbraith's 1999 paper from $\tilde{O}( q^{1.5} )$ to (heuristically) $\tilde{O}( q^{0.4} )$ operations. The two cases of main interest for discrete logarithm cryptography are random curves (flat volcanoes) and pairing-based crypto (tall volcanoes with crater of constant or polynomial size). In both cases we show a rigorous $\tO( q^{1/4})$ algorithm to compute an isogeny between any two curves in the isogeny class. We stress that this paper is motivated by pre-quantum elliptic curve cryptography using ordinary elliptic curves, which is not yet obsolete.
Last updated:  2024-06-10
On Orchestrating Parallel Broadcasts for Distributed Ledgers
Peiyao Sheng, Chenyuan Wu, Dahlia Malkhi, Michael K. Reiter, Chrysoula Stathakopoulou, Michael Wei, and Maofan Yin
This paper introduces and develops the concept of ``ticketing'', through which atomic broadcasts are orchestrated by nodes in a distributed system. The paper studies different ticketing regimes that allow parallelism, yet prevent slow nodes from hampering overall progress. It introduces a hybrid scheme which combines managed and unmanaged ticketing regimes, striking a balance between adaptivity and resilience. The performance evaluation demonstrates how managed and unmanaged ticketing regimes benefit throughput in systems with heterogeneous resources both in static and dynamic scenarios, with the managed ticketing regime performing better among the two as it adapts better. Finally, it demonstrates how using the hybrid ticketing regime performance can enjoy both the adaptivity of the managed regime and the liveness guarantees of the unmanaged regime.
Last updated:  2024-06-13
Scalable Private Set Union, with Stronger Security
Yanxue Jia, Shi-Feng Sun, Hong-Sheng Zhou, and Dawu Gu
Private Set Union (PSU) protocol allows parties, each holding an input set, to jointly compute the union of the sets without revealing anything else. In the literature, scalable PSU protocols follow the “split-execute-assemble” paradigm (Kolesnikov et al., ASIACRYPT 2019); in addition, those fast protocols often use Oblivious Transfer as building blocks. Kolesnikov et al. (ASIACRYPT 2019) and Jia et al. (USENIX Security 2022), pointed out that certain security issues can be introduced in the “split-execute-assemble” paradigm. In this work, surprisingly, we observe that the typical way of invoking Oblivious Transfer also causes unnecessary leakage, and only the PSU protocols based on additively homomorphic encryption (AHE) can avoid the leakage. However, the AHE-based PSU protocols are far from being practical. To bridge the gap, we also design a new PSU protocol that can avoid the unnecessary leakage. Unlike the AHE-based PSU protocols, our new construction only relies on symmetric-key operations other than base OTs, thereby being much more scalable. The experimental results demonstrate that our protocol can obtain at least 873.74× speedup over the best-performing AHE-based scheme. Moreover, our performance is comparable to that of the state-of-the-art PSU protocol (Chen et al., USENIX Security 2023), which also suffers from the unnecessary leakage.
Last updated:  2024-06-09
Simple Logarithmic-size LSAG signature
Edsger Hughes
A number of existing cryptosystems use the well-known LSAG signature and its extensions. This article presents a simple logarithmic-size signature scheme LS-LSAG which, despite a radical reduction in size, retains the basic code block of the LSAG signature. Therefore, substituting LS-LSAG for LSAG requires minimal changes to almost any existing coded LSAG extension, making it logarithmic instead of linear.
Last updated:  2024-06-09
Leveraging Small Message Spaces for CCA1 Security in Additively Homomorphic and BGN-type Encryption
Benoit Libert
We show that the smallness of message spaces can be used as a checksum allowing to hedge against CCA1 attacks in additively homomorphic encryption schemes. We first show that the additively homomorphic variant of Damgård's Elgamal provides IND-CCA1 security under the standard DDH assumption. Earlier proofs either required non-standard assumptions or only applied to hybrid versions of Damgård's Elgamal, which are not additively homomorphic. Our security proof builds on hash proof systems and exploits the fact that encrypted messages must be contained in a polynomial-size interval in order to enable decryption. With $3$ group elements per ciphertext, this positions Damgård's Elgamal as the most efficient/compact DDH-based additively homomorphic CCA1 cryptosystem. Under the same assumption, the best candidate so far was the lite Cramer-Shoup cryptosystem, where ciphertexts consist of $4$ group elements. We extend this observation to build an IND-CCA1 variant of the Boneh-Goh-Nissim encryption scheme, which allows evaluating 2-DNF formulas on encrypted data. By computing tensor products of Damgård's Elgamal ciphertexts, we obtain product ciphertexts consisting of $9$ group elements (instead of $16$ elements if we were tensoring lite Cramer-Shoup ciphertexts) in the target group of a bilinear map. Using similar ideas, we also obtain a CCA1 variant of the Elgamal-Paillier cryptosystem by forcing $\lambda$ plaintext bits to be zeroes, which yields CCA1 security almost for free. In particular, the message space remains exponentially large and ciphertexts are as short as in the IND-CPA scheme. We finally adapt the technique to the Castagnos-Laguillaumie system.
Last updated:  2024-06-09
Multi-Input Functional Encryption for Unbounded Inner Products
Bishnu Charan Behera and Somindu C. Ramanna
In this work, we propose a construction for $ Multi~Input~Inner ~Product ~Encryption$ (MIPFE) that can handle vectors of variable length in different encryption slots. This construction is the first of its kind, as all existing MIPFE schemes allow only equal length vectors. The scheme is constructed in the private key setting, providing privacy for both message as well as the function, thereby achieving the so-called $full-hiding$ security. Our MIPFE scheme uses bilinear groups of prime order and achieves security under well studied cryptographic assumptions, namely, the symmetric external Diffie-Hellman assumption.
Last updated:  2024-06-09
Cryptographic Analysis of Delta Chat
Yuanming Song, Lenka Mareková, and Kenneth G. Paterson
We analyse the cryptographic protocols underlying Delta Chat, a decentralised messaging application which uses e-mail infrastructure for message delivery. It provides end-to-end encryption by implementing the Autocrypt standard and the SecureJoin protocols, both making use of the OpenPGP standard. Delta Chat's adoption by categories of high-risk users such as journalists and activists, but also more generally users in regions affected by Internet censorship, makes it a target for powerful adversaries. Yet, the security of its protocols has not been studied to date. We describe five new attacks on Delta Chat in its own threat model, exploiting cross-protocol interactions between its implementation of SecureJoin and Autocrypt, as well as bugs in rPGP, its OpenPGP library. The findings have been disclosed to the Delta Chat team, who implemented fixes.
Last updated:  2024-06-09
Unbounded Non-Zero Inner Product Encryption
Bishnu Charan Behera and Somindu C. Ramanna
In a non-zero inner product encryption (NIPE) scheme, ciphertexts and keys are associated with vectors from some inner-product space. Decryption of a ciphertext for $\vec{x}$ is allowed by a key for $\vec{y}$ if and only if the inner product $\langle{\vec{x}},{\vec{y}}\rangle \neq 0$. Existing constructions of NIPE assume the length of the vectors are fixed apriori. We present the first constructions of $ unbounded $ non-zero inner product encryption (UNIPE) with constant sized keys. Unbounded here refers to the size of vectors not being pre-fixed during setup. Both constructions, based on bilinear maps, are proven selectively secure under the decisional bilinear Diffie-Hellman (DBDH) assumption. Our constructions are obtained by transforming the unbounded inner product functional encryption (IPFE) schemes of Dufour-Sans and Pointcheval (ACNS 2019), one in the $strict ~ domain$ setting and the other in the $permissive ~ domain$ setting. Interestingly, in the latter case, we prove security from DBDH, a static assumption while the original IPE scheme relied on an interactive parameterised assumption. In terms of efficiency, features of the IPE constructions are retrained after transformation to NIPE. Notably, the public key and decryption keys have constant size.
Last updated:  2024-06-08
Polymath: Groth16 Is Not The Limit
Helger Lipmaa
Shortening the argument (three group elements or 1536 / 3072 bits over the BLS12-381/BLS24-509 curves) of the Groth16 zk-SNARK for R1CS is a long-standing open problem. We propose a zk-SNARK Polymath for the Square Arithmetic Programming constraint system using the KZG polynomial commitment scheme. Polymath has a shorter argument (1408 / 1792 bits over the same curves) than Groth16. At 192-bit security, Polymath's argument is nearly half the size, making it highly competitive for high-security future applications. Notably, we handle public inputs in a simple way. We optimized Polymath's prover through an exhaustive parameter search. Polymath's prover does not output $\mathbb{G}_{2}$ elements, aiding in batch verification, SNARK aggregation, and recursion. Polymath's properties make it highly suitable to be the final SNARK in SNARK compositions.
Last updated:  2024-06-07
REACTIVE: Rethinking Effective Approaches Concerning Trustees in Verifiable Elections
Josh Benaloh, Michael Naehrig, and Olivier Pereira
For more than forty years, two principal questions have been asked when designing verifiable election systems: how will the integrity of the results be demonstrated and how will the privacy of votes be preserved? Many approaches have been taken towards answering the first question such as use of MixNets and homomorphic tallying. But in the academic literature, the second question has always been answered in the same way: decryption capabilities are divided amongst multiple independent “trustees” so that a collusion is required to compromise privacy. In practice, however, this approach can be fairly challenging to deploy. Human trustees rarely have a clear understanding of their responsibilities, and they typically all use identical software for their tasks. Rather than exercising independent judgment to maintain privacy, trustees are often reduced to automata who just push the buttons they are told to when they are told to, doing little towards protecting voter privacy. This paper looks at several aspects of the trustee experience. It begins by discussing various cryptographic protocols that have been used for key generation in elections, explores their impact on the role of trustees, and notes that even the theory of proper use of trustees is more challenging than it might seem. This is illustrated by showing that one of the only references defining a full threshold distributed key generation (DKG) for elections defines an insecure protocol. Belenios claims to rely on that reference for its DKG and security proof. Fortunately, it does not inherit the same vulnerability. We offer a security proof for the Belenios DKG. The paper then discusses various practical contexts, in terms of humans, software, and hardware, and their impact on the practical deployment of a trustee-based privacy model.
Last updated:  2024-06-07
Compact Key Storage: A Modern Approach to Key Backup and Delegation
Yevgeniy Dodis, Daniel Jost, and Antonio Marcedone
End-to-End (E2E) encrypted messaging, which prevents even the service provider from learning communication contents, is gaining popularity. Since users care about maintaining access to their data even if their devices are lost or broken or just replaced, these systems are often paired with cloud backup solutions: Typically, the user will encrypt their messages with a fixed key, and upload the ciphertexts to the server. Unfortunately, this naive solution has many drawbacks. First, it often undermines the fancy security guarantees of the core application, such as forward secrecy (FS) and post-compromise security (PCS), in case the single backup key is compromised. Second, they are wasteful for backing up conversations in large groups, where many users are interested in backing up the same sequence of messages. Instead, we formalize a new primitive called Compact Key Storage (CKS) as the "right" solution to this problem. Such CKS scheme allows a mutable set of parties to delegate to a server storage of an increasing set of keys, while each client maintains only a small state. Clients update their state as they learn new keys (maintaining PCS), or whenever they want to forget keys (achieving FS), often without the need to interact with the server. Moreover, access to the keys (or some subset of them) can be efficiently delegated to new group members, who all efficiently share the same server's storage. We carefully define syntax, correctness, privacy, and integrity of CKS schemes, and build two efficient schemes provably satisfying these notions. Our line scheme covers the most basic "all-or-nothing" flavor of CKS, where one wishes to compactly store and delegate the entire history of past secrets. Thus, new users enjoy the efficiency and compactness properties of the CKS only after being granted access to the entire history of keys. In contrast, our interval scheme is only slightly less efficient but allows for finer-grained access, delegation, and deletion of past keys.
Last updated:  2024-06-08
SoK: Model Reverse Engineering Threats for Neural Network Hardware
Seetal Potluri and Farinaz Koushanfar
There has been significant progress over the past seven years in model reverse engineering (RE) for neural network (NN) hardware. Although there has been systematization of knowledge (SoK) in an overall sense, however, the treatment from the hardware perspective has been far from adequate. To bridge this gap, this paper systematically categorizes the types of NN hardware used prevalently by the industry/academia, and also the model RE attacks/defenses published in each category. Further, we sub-categorize existing NN model RE attacks based on different criteria including the degree of hardware parallelism, threat vectors like side channels, fault-injection, scan-chain attacks, system-level attacks, type of asset under attack, the type of NN, exact versus approximate recovery, etc. We make important technical observations and identify key open research directions. Subsequently, we discuss the state-of-the-art defenses against NN model RE, identify certain categorization criteria, and compare the existing works based on these criteria. We note significant qualitative gaps for defenses, and suggest recommendations for important open research directions for protection of NN models. Finally, we discuss limitations of existing work in terms of the types of models where security evaluation or defenses were proposed, and suggest open problems in terms of protecting practically expensive model IPs.
Last updated:  2024-06-07
Quantum Evolving Secret Sharing for General Access Structures
Efrat Cohen and Anat Paskin-Cherniavsky
In the useful and well studied model of secret-sharing schemes, there are $n$ parties and a dealer, which holds a secret. The dealer applies some randomized algorithm to the secret, resulting in $n$ strings, called shares; it gives the $i$'th share to the $i$'th party. There are two requirements. (1) correctness: some predefined subsets of the parties can jointly reconstruct the secret from their shares, and (2) security: any other set gets no information on the secret. The collection of predefined qualified sets is called an access structure (AS). This model assumes that the number of parties is known when preparing the shares and giving the shares to the parties; furthermore, the sharing algorithm and the share size are determined by the number of parties, e.g. in the best-known secret-sharing scheme for an arbitrary $n$-party access structure the share size is $1.5^{n}$ by Appelbaum and Nir. The assumption that the number of parties is known in advance is problematic in many scenarios. Of course, one can take some upper bound on the number of parties. On one hand, if this bound is big, then the share size will be large even if only few parties actually participate in the scheme. On the other hand, if this bound is small, then there is a risk that too many parties will arrive and no further shares can be produced; this will require an expensive re-sharing of the secret and updating all shares (which can be impossible if some parties are temporally off-line). Thus, we need to consider models with an unbounded number of parties. To address these concrens, Komargodski, Naor, and Yogev defined \emph{evolving secret-sharing schemes} with an unbounded number of parties. In a nutshell, evolving AS's are defined as a monotone collection of finite qualified sets, such that at any time $t$ a set $A\subseteq [t]$ is either qualified or not, depending only on $A$ itself, and not on $t$ (a `global' monotonicity notion). Quantum secret sharing (QSS) in the standard $n$-party setting, where the secret is an arbitrary quantum state (say, qbit), rather than classical data. In face of recent advancements in quantum computing, this is a natural notion to consider, and has been studied before. In this work, we explore the natural notion of quantum evolving secret sharing (QESS). While this notion has been studied by Samadder 20', we make several new contributions. (1) The notion of QESS was only implicit in the above work. We formalize this notion (as well as AS's for which it is applicable), and in particular argue that the variant implied by the above work did not require `global monotonicity' of the AS, which was the standard in the evolving secret sharing literature, and appears to be useful for QESS as well. (2) Discuss the applicability and limitations of the notion in the quantum setting that follow from the no-cloning theorem, and make its usability more limited. Yet, we argue that fundamental advantages of the evovling setting, such as keeping parties' shares independent of the total number of parties that arrive can be mantainted in the quantum setting. (3) We characterize the AS's ammenable to construction of QSSS - so called `no cloning' evolving AS's, and point out that this class is not severly restricted relatively to the class of all evolving AS's. On the positive side, our construction combines the compiler of [Smith 00'] with ideas of hybrid secret sharing of [Goyal et. al 23'], to obtain a construction with share size comparable to the best classical linear share complexity of the scheme.
Last updated:  2024-06-10
Generalized Indifferentiable Sponge and its Application to Polygon Miden VM
Tomer Ashur and Amit Singh Bhati
Cryptographic hash functions are said to be the work-horses of modern cryptography. One of the strongest approaches to assess a cryptographic hash function's security is indifferentiability. Informally, indifferentiability measures to what degree the function resembles a random oracle when instantiated with an ideal underlying primitive. However, proving the indifferentiability security of hash functions has been challenging due to complex simulator designs and proof arguments. The Sponge construction is one of the prevalent hashing method used in various systems. The Sponge has been shown to be indifferentiable from a random oracle when initialized with a random permutation. In this work, we first introduce $\mathsf{GSponge}$, a generalized form of the Sponge construction offering enhanced flexibility in input chaining, field sizes, and padding types. $\mathsf{GSponge}$ not only captures all existing sponge variants but also unveils new, efficient ones. The generic structure of $\mathsf{GSponge}$ facilitates the discovery of two micro-optimizations for already deployed sponges. Firstly, it allows a new padding rule based on zero-padding and domain-separated inputs, saving one full permutation call in certain cases without increasing the generation time of zero-knowledge proofs. Secondly, it allows to absorb up to $\mathsf{c}/2$ more elements (that can save another permutation call for certain message lengths) without compromising the indifferentiability security. These optimizations enhance hashing time for practical use cases such as Merkle-tree hashing and short message processing. We then propose a new efficient instantiation of $\mathsf{GSponge}$ called $\mathsf{Sponge2}$ capturing these micro-optimizations and provide a formal indifferentiability proof to establish both $\mathsf{Sponge2}$ and $\mathsf{GSponge}$'s security. This proof, simpler than the original for Sponges, offers clarity and ease of understanding for real-world practitioners. Additionally, it is demonstrated that $\mathsf{GSponge}$ can be safely instantiated with permutations defined over large prime fields, a result not previously formally proven.
Last updated:  2024-06-07
A Tight Security Proof for $\mathrm{SPHINCS^{+}}$, Formally Verified
Manuel Barbosa, François Dupressoir, Andreas Hülsing, Matthias Meijers, and Pierre-Yves Strub
$\mathrm{SPHINCS^{+}}$ is a post-quantum signature scheme that, at the time of writing, is being standardized as $\mathrm{SLH\text{-}DSA}$. It is the most conservative option for post-quantum signatures, but the original tight proofs of security were flawed—as reported by Kudinov, Kiktenko and Fedorov in 2020. In this work, we formally prove a tight security bound for $\mathrm{SPHINCS^{+}}$ using the EasyCrypt proof assistant, establishing greater confidence in the general security of the scheme and that of the parameter sets considered for standardization. To this end, we reconstruct the tight security proof presented by Hülsing and Kudinov (in 2022) in a modular way. A small but important part of this effort involves a complex argument relating four different games at once, of a form not yet formalized in EasyCrypt (to the best of our knowledge). We describe our approach to overcoming this major challenge, and develop a general formal verification technique aimed at this type of reasoning. Enhancing the set of reusable EasyCrypt artifacts previously produced in the formal verification of stateful hash-based cryptographic constructions, we (1) improve and extend the existing libraries for hash functions and (2) develop new libraries for fundamental concepts related to hash-based cryptographic constructions, including Merkle trees. These enhancements, along with the formal verification technique we develop, further ease future formal verification endeavors in EasyCrypt, especially those concerning hash-based cryptographic constructions.
Last updated:  2024-06-07
Approximate CRT-Based Gadget Decomposition and Application to TFHE Blind Rotation
Olivier Bernard and Marc Joye
One of the main issues to deal with for fully homomorphic encryption is the noise growth when operating on ciphertexts. To some extent, this can be controlled thanks to a so-called gadget decomposition. A gadget decomposition typically relies on radix- or CRT-based representations to split elements as vectors of smaller chunks whose inner products with the corresponding gadget vector rebuilds (an approximation of) the original elements. Radix-based gadget decompositions present the advantage of also supporting the approximate setting: for most homomorphic operations, this has a minor impact on the noise propagation but leads to substantial savings in bandwidth, memory requirements and computational costs. A typical use-case is the blind rotation as used for example in the bootstrapping of the TFHE scheme. On the other hand, CRT-based representations are convenient when machine words are too small for directly accommodating the arithmetic on large operands. This arises in two typical cases: (i) in the hardware case with multipliers of restricted size, e.g., 17 bits; (ii) in the software case for ciphertext moduli above, e.g., 128 bits. This paper presents new CRT-based gadget decompositions for the approximate setting, which combines the advantages of non-exact decompositions with those of CRT-based decompositions. Significantly, it enables certain hardware or software realizations otherwise hardly supported like the two aforementioned cases. In particular, we show that our new gadget decompositions provide implementations of the (programmable) bootstrapping in TFHE relying solely on native arithmetic and offering extra degrees of parallelism.
Last updated:  2024-06-07
Preliminary Analysis of Ascon-Xof and Ascon-Hash
Christoph Dobraunig, Maria Eichlseder, Florian Mendel, and Martin Schläffer
In this note, we present additional preliminary analysis dedicated to Ascon-Xof and Ascon-Hash [DEMS19].
Last updated:  2024-06-06
Reducing the Number of Qubits in Quantum Information Set Decoding
Clémence Chevignard, Pierre-Alain Fouque, and André Schrottenloher
This paper presents an optimization of the memory cost of the quantum Information Set Decoding (ISD) algorithm proposed by Bernstein (PQCrypto 2010), obtained by combining Prange's ISD with Grover's quantum search. When the code has constant rate and length $n$, this algorithm essentially performs a quantum search which, at each iterate, solves a linear system of dimension $\mathcal{O}(n)$. The typical code lengths used in post-quantum public-key cryptosystems range from $10^3$ to $10^5$. Gaussian elimination, which was used in previous works, needs $\mathcal{O}(n^2)$ space to represent the matrix, resulting in millions or billions of (logical) qubits for these schemes. In this paper, we propose instead to use the algorithm for sparse matrix inversion of Wiedemann (IEEE Trans. inf. theory 1986). The interest of Wiedemann's method is that one relies only on the implementation of a matrix-vector product, where the matrix can be represented in an implicit way. This is the case here. We propose two main trade-offs, which we have fully implemented, tested on small instances, and benchmarked for larger instances. The first one is a quantum circuit using $\mathcal{O}(n)$ qubits, $\mathcal{O}(n^3)$ Toffoli gates like Gaussian elimination, and depth $\mathcal{O}(n^2 \log n)$. The second one is a quantum circuit using $\mathcal{O}(n \log^2 n)$ qubits, $\mathcal{O}(n^3)$ gates in total but only $\mathcal{O}( n^2 \log^2 n)$ Toffoli gates, which relies on a different representation of the search space. As an example, for the smallest Classic McEliece parameters we estimate that the Quantum Prange's algorithm can run with 18098 qubits, while previous works would have required at least half a million qubits.
Last updated:  2024-06-06
Are Your Keys Protected? Time will Tell
Yoav Ben-Dov, Liron David, Moni Naor, and Elad Tzalik
Side channel attacks, and in particular timing attacks, are a fundamental obstacle to obtaining secure implementation of algorithms and cryptographic protocols, and have been widely researched for decades. While cryptographic definitions for the security of cryptographic systems have been well established for decades, none of these accepted definitions take into account the running time information leaked from executing the system. In this work, we give the foundation of new cryptographic definitions for cryptographic systems that take into account information about their leaked running time, focusing mainly on keyed functions such as signature and encryption schemes. Specifically, (1) We define several cryptographic properties to express the claim that the timing information does not help an adversary to extract sensitive information, e.g. the key or the queries made. We highlight the definition of key-obliviousness, which means that an adversary cannot tell whether it received the timing of the queries with the actual key or the timing of the same queries with a random key. (2) We present a construction of key-oblivious pseudorandom permutations on a small or medium-sized domain. This construction is not ``fixed-time,'' and at the same time is secure against any number of queries even in case the adversary knows the running time exactly. Our construction, which we call Janus Sometimes Recurse, is a variant of the ``Sometimes Recurse'' shuffle by Morris and Rogaway. (3) We suggest a new security notion for keyed functions, called noticeable security, and prove that cryptographic schemes that have noticeable security remain secure even when the exact timings are leaked, provided the implementation is key-oblivious. We show that our notion applies to cryptographic signatures, private key encryption and PRPs.
Last updated:  2024-06-06
On the Semidirect Discrete Logarithm Problem in Finite Groups
Christopher Battarbee, Giacomo Borin, Ryann Cartor, Nadia Heninger, David Jao, Laura Maddison, Edoardo Persichetti, Angela Robinson, Daniel Smith-Tone, and Rainer Steinwandt
We present an efficient quantum algorithm for solving the semidirect discrete logarithm problem (SDLP) in any finite group. The believed hardness of the semidirect discrete logarithm problem underlies more than a decade of works constructing candidate post-quantum cryptographic algorithms from nonabelian groups. We use a series of reduction results to show that it suffices to consider SDLP in finite simple groups. We then apply the celebrated Classification of Finite Simple Groups to consider each family. The infinite families of finite simple groups admit, in a fairly general setting, linear algebraic attacks providing a reduction to the classical discrete logarithm problem. For the sporadic simple groups, we show that their inherent properties render them unsuitable for cryptographically hard SDLP instances, which we illustrate via a Baby-Step Giant-Step style attack against SDLP in the Monster Group. Our quantum SDLP algorithm is fully constructive for all but three remaining cases that appear to be gaps in the literature on constructive recognition of groups; for these cases SDLP is no harder than finding a linear representation. We conclude that SDLP is not a suitable post-quantum hardness assumption for any choice of finite group.
Last updated:  2024-06-06
On round elimination for special-sound multi-round identification and the generality of the hypercube for MPCitH
Andreas Hülsing, David Joseph, Christian Majenz, and Anand Kumar Narayanan
A popular way to build post-quantum signature schemes is by first constructing an identification scheme (IDS) and applying the Fiat-Shamir transform to it. In this work we tackle two open questions related to the general applicability of techniques around this approach that together allow for efficient post-quantum signatures with optimal security bounds in the QROM. First we consider a recent work by Aguilar-Melchor, Hülsing, Joseph, Majenz, Ronen, and Yue (Asiacrypt'23) that showed that an optimal bound for three-round commit & open IDS by Don, Fehr, Majenz, and Schaffner (Crypto'22) can be applied to the five-round Syndrome-Decoding in the Head (SDitH) IDS. For this, they first applied a transform that replaced the first three rounds by one. They left it as an open problem if the same approach applies to other schemes beyond SDitH. We answer this question in the affirmative, generalizing their round-elimination technique and giving a generic security proof for it. Our result applies to any IDS with $2n+1$ rounds for $n>1$. However, a scheme has to be suitable for the resulting bound to not be trivial. We find that IDS are suitable when they have a certain form of special-soundness which many commit & open IDS have. Second, we consider the hypercube technique by Aguilar-Melchor, Gama, Howe, Hülsing, Joseph, and Yue (Eurocrypt'23). An optimization that was proposed in the context of SDitH and is now used by several of the contenders in the NIST signature on-ramp. It was conjectured that the technique applies generically for the MPC-in-the-Head (MPCitH) technique that is used in the design of many post-quantum IDS if they use an additive secret sharing scheme but this was never proven. In this work we show that the technique generalizes to MPCitH IDS that use an additively homomorphic MPC protocol, and we prove that security is preserved. We demonstrate the application of our results to the identification scheme of RYDE, a contender in the recent NIST signature on-ramp. While RYDE was already specified with the hypercube technique applied, this gives the first QROM proof for RYDE with an optimally tight bound.
Last updated:  2024-06-14
Nopenena Untraceable Payments: Defeating Graph Analysis with Small Decoy Sets
Jayamine Alupotha, Mathieu Gestin, and Christian Cachin
Decentralized payments have evolved from using pseudonymous identifiers to much more elaborate mechanisms to ensure privacy. They can shield the amounts in payments and achieve untraceability, e.g., decoy-based untraceable payments use decoys to obfuscate the actual asset sender or asset receiver. There are two types of decoy-based payments: full decoy set payments that use all other available users as decoys, e.g., Zerocoin, Zerocash, and ZCash, and user-defined decoy set payments where the users select small decoy sets from available users, e.g., Monero, Zether, and QuisQuis. Existing decoy-based payments face at least two of the following problems: (1) degrading untraceability due to the possibility of payment-graph analysis in user-defined decoy payments, (2) trusted setup, (3) availability issues due to expiring transactions in full decoy sets and epochs, and (4) an ever-growing set of unspent outputs since transactions keep generating outputs without saying which ones are spent. QuisQuis is the first one to solve all these problems; however, QuisQuis requires large cryptographic proofs for validity. We introduce Nopenena (means ``cannot see''): account-based, confidential, and user-defined decoy set payment protocol, that has short proofs and also avoids these four issues. Additionally, Nopenena can be integrated with zero-knowledge contracts like Zether's $\Sigma-$Bullets and Confidential Integer Processing (CIP) to build decentralized applications. Nopenena payments are about 80% smaller than QuisQuis payments due to Nopenena's novel cryptographic protocol. Therefore, decentralized systems benefit from Nopenena's untraceability and efficiency.
Last updated:  2024-06-06
Access Structure Hiding Verifiable Tensor Designs
Anandarup Roy, Bimal Kumar Roy, Kouichi Sakurai, and Suprita Talnikar
The field of verifiable secret sharing schemes was introduced by Verheul et al. and has evolved over time, including well-known examples by Feldman and Pedersen. Stinson made advancements in combinatorial design-based secret sharing schemes in 2004. Desmedt et al. introduced the concept of frameproofness in 2021, while recent research by Sehrawat et al. in 2021 focuses on LWE-based access structure hiding verifiable secret sharing with malicious-majority settings. Furthermore, Roy et al. combined the concepts of reparable threshold schemes by Stinson et al. and frameproofness by Desmedt et al. in 2023, to develop extendable tensor designs built from balanced incomplete block designs, and also presented a frameproof version of their design. This paper explores ramp-type verifiable secret sharing schemes, and the application of hidden access structures in such cryptographic protocols. Inspired by Sehrawat et al.'s access structure hiding scheme, we develop an $\epsilon$-almost access structure hiding scheme, which is verifiable as well as frameproof. We detail how the concept $\epsilon$-almost hiding is important for incorporating ramp schemes, thus making a fundamental generalisation of this concept.
Last updated:  2024-06-06
Practical Committing Attacks against Rocca-S
Ryunosuke Takeuchi, Yosuke Todo, and Tetsu Iwata
This note shows practical committing attacks against Rocca-S, an authenticated encryption with associated data scheme designed for 6G applications. Previously, the best complexity of the attack was $2^{64}$ by Derbez et al. in ToSC 2024(1)/FSE 2024. We show that the committing attack against Rocca by Takeuchi et al. in ToSC 2024(2)/FSE 2025 can be applied to Rocca-S, where Rocca is an earlier version of Rocca-S. We show a concrete test vector of our attack. We also point out a committing attack that exploits equivalent keys.
Last updated:  2024-06-06
Breaktooth: Breaking Bluetooth Sessions Abusing Power-Saving Mode
Keiichiro Kimura, Hiroki Kuzuno, Yoshiaki Shiraishi, and Masakatu Morii
With the increasing demand for Bluetooth devices, various Bluetooth devices support a power-saving mode to reduce power consumption. One of the features of the power-saving mode is that the Bluetooth sessions among devices are temporarily disconnected or close to being disconnected. Prior works have analyzed that the power-saving mode is vulnerable to denial of sleep (DoSL) attacks that interfere with the transition to the power-saving mode of Bluetooth devices, thereby increasing its power consumption. However, to the best of our knowledge, no prior work has analyzed vulnerabilities or attacks on the state after transitioning to the power-saving mode. To address this issue, we present an attack that abuses two novel vulnerabilities in sleep mode, which is one of the Bluetooth power-saving modes, to break Bluetooth sessions. We name the attack Breaktooth. The attack is the first to abuse the vulnerabilities as an entry point to hijack Bluetooth sessions between victims. The attack also allows overwriting the link key between the victims using the hijacked session, enabling arbitrary command injection on the victims. Furthermore, while many prior attacks assume that attackers can forcibly disconnect the Bluetooth session using methods such as jamming to launch their attacks, our attack does not require such assumptions, making it more realistic. In this paper, we present the root causes of the Breaktooth attack and their impact. We also provide the technical details of how attackers can secretly detect the sleep mode of their victims. The attackers can easily recognize the state of the victim's Bluetooth session remotely using a standard Linux command. Additionally, we develop a low-cost toolkit to perform our attack and confirm the effectiveness of our attack. Then, we evaluate the attack on 13 types of commodity Bluetooth keyboards and mice that support the sleep mode and show that the attack poses a serious threat to Bluetooth devices supporting the sleep mode. To fix our attack, we present defenses and its proof-of-concept. We responsibly disclosed our findings to the Bluetooth SIG.
Last updated:  2024-06-05
Monotone-Policy Aggregate Signatures
Maya Farber Brodsky, Arka Rai Choudhuri, Abhishek Jain, and Omer Paneth
The notion of aggregate signatures allows for combining signatures from different parties into a short certificate that attests that *all* parties signed a message. In this work, we lift this notion to capture different, more expressive signing policies. For example, we can certify that a message was signed by a (weighted) threshold of signers. We present the first constructions of aggregate signatures for monotone policies based on standard polynomial-time cryptographic assumptions. The aggregate signatures in our schemes are succinct, i.e., their size is *independent* of the number of signers. Moreover, verification is also succinct if all parties sign the same message (or if the messages have a succinct representation). All prior work requires either interaction between the parties or non-standard assumptions (that imply SNARKs for NP). Our signature schemes are based on non-interactive batch arguments (BARGs) for monotone policies [Brakerski-Brodsky-Kalai-Lombardi-Paneth, Crypto'23]. In contrast to previous constructions, our BARGs satisfy a new notion of *adaptive* security which is instrumental to our application. Our new BARGs for monotone policies can be constructed from standard BARGs and other standard assumptions.
Last updated:  2024-06-05
Edit Distance Robust Watermarks for Language Models
Noah Golowich and Ankur Moitra
Motivated by the problem of detecting AI-generated text, we consider the problem of watermarking the output of language models with provable guarantees. We aim for watermarks which satisfy: (a) undetectability, a cryptographic notion introduced by Christ, Gunn & Zamir (2024) which stipulates that it is computationally hard to distinguish watermarked language model outputs from the model's actual output distribution; and (b) robustness to channels which introduce a constant fraction of adversarial insertions, substitutions, and deletions to the watermarked text. Earlier schemes could only handle stochastic substitutions and deletions, and thus we are aiming for a more natural and appealing robustness guarantee that holds with respect to edit distance. Our main result is a watermarking scheme which achieves both undetectability and robustness to edits when the alphabet size for the language model is allowed to grow as a polynomial in the security parameter. To derive such a scheme, we follow an approach introduced by Christ & Gunn (2024), which proceeds via first constructing pseudorandom codes satisfying undetectability and robustness properties analogous to those above; our key idea is to handle adversarial insertions and deletions by interpreting the symbols as indices into the codeword, which we call indexing pseudorandom codes. Additionally, our codes rely on weaker computational assumptions than used in previous work. Then we show that there is a generic transformation from such codes over large alphabets to watermarking schemes for arbitrary language models.
Last updated:  2024-06-05
Laconic Function Evaluation and ABE for RAMs from (Ring-)LWE
Fangqi Dong, Zihan Hao, Ethan Mook, Hoeteck Wee, and Daniel Wichs
Laconic function evaluation (LFE) allows us to compress a circuit $f$ into a short digest. Anybody can use this digest as a public-key to efficiently encrypt some input $x$. Decrypting the resulting ciphertext reveals the output $f(x)$, while hiding everything else about $x$. In this work we consider LFE for Random-Access Machines (RAM-LFE) where, instead of a circuit $f$, we have a RAM program $f_{\mathsf{DB}}$ that potentially contains some large hard-coded data $\mathsf{DB}$. The decryption run-time to recover $f_{\mathsf{DB}}(x)$ from the ciphertext should be roughly the same as a plain evaluation of $f_{\mathsf{DB}}(x)$ in the RAM model, which can be sublinear in the size of $\mathsf{DB}$. Prior works constructed LFE for circuits under LWE, and RAM-LFE under indisitinguishability obfuscation (iO) and Ring-LWE. In this work, we construct RAM-LFE with essentially optimal encryption and decryption run-times from just Ring-LWE and a standard circular security assumption, without iO. RAM-LFE directly yields 1-key succinct functional encryption and reusable garbling for RAMs with similar parameters. If we only want an attribute-based LFE for RAMs (RAM-AB-LFE), then we can replace Ring-LWE with plain LWE in the above. Orthogonally, if we only want leveled schemes, where the encryption/decryption efficiency can scale with the depth of the RAM computation, then we can remove the need for a circular-security. Lastly, we also get a leveled many-key attribute-based encryption for RAMs (RAM-ABE), from LWE.
Last updated:  2024-06-05
Dynamic-FROST: Schnorr Threshold Signatures with a Flexible Committee
Annalisa Cimatti, Francesco De Sclavis, Giuseppe Galano, Sara Giammusso, Michela Iezzi, Antonio Muci, Matteo Nardelli, and Marco Pedicini
Threshold signatures enable any subgroup of predefined cardinality $t$ out of a committee of $n$ participants to generate a valid, aggregated signature. Although several $(t,n)$-threshold signature schemes exist, most of them assume that the threshold $t$ and the set of participants do not change over time. Practical applications of threshold signatures might benefit from the possibility of updating the threshold or the committee of participants. Examples of such applications are consensus algorithms and blockchain wallets. In this paper, we present Dynamic-FROST (D-FROST, for short) that combines FROST, a Schnorr threshold signature scheme, with CHURP, a dynamic proactive secret sharing scheme. The resulting protocol is the first Schnorr threshold signature scheme that accommodates changes in both the committee and the threshold value without relying on a trusted third party. Besides detailing the protocol, we present a proof of its security: as the original signing scheme, D-FROST preserves the property of Existential Unforgeability under Chosen-Message Attack.
Last updated:  2024-06-05
Fully-Succinct Multi-Key Homomorphic Signatures from Standard Assumptions
Gaspard Anthoine, David Balbás, and Dario Fiore
Multi-Key Homomorphic Signatures (MKHS) allow one to evaluate a function on data signed by distinct users while producing a succinct and publicly-verifiable certificate of the correctness of the result. All the constructions of MKHS in the state of the art achieve a weak level of succinctness where signatures are succinct in the total number of inputs but grow linearly with the number of users involved in the computation. The only exception is a SNARK-based construction which relies on a strong notion of knowledge soundness in the presence of signing oracles that not only requires non-falsifiable assumptions but also encounters some impossibility results. In this work, we present the first construction of MKHS that are fully succinct (also with respect to the number of users) while achieving adaptive security under standard falsifiable assumptions. Our result is achieved through a novel combination of batch arguments for NP (BARGs) and functional commitments (FCs), and yields diverse MKHS instantiations for circuits of unbounded depth based on either pairing or lattice assumptions. Additionally, our schemes support efficient verification with pre-processing, and they can easily be extended to achieve multi-hop evaluation and context-hiding.
Last updated:  2024-06-05
Quantum Algorithms for Fast Correlation Attacks on LFSR-Based Stream Ciphers
Akinori Hosoyamada
This paper presents quantum algorithms for fast correlation attacks, one of the most powerful techniques for cryptanalysis on LFSR-based stream ciphers in the classical setting. Typical fast correlation attacks recover a value related to the initial state of the underlying LFSR by solving a decoding problem on a binary linear code with the Fast Walsh-Hadamard Transform (FWHT). Applying the FWHT on a function in the classical setting is mathematically equivalent to applying the Hadamard transform on the corresponding state in quantum computation. While the classical FWHT on a function with $\ell$-bit inputs requires $O(\ell 2^\ell)$ operations, the Hadamard transform on $\ell$-qubit states requires only a parallel application of $O(\ell)$ basic gates. This difference leads to the exponential speed-up by some quantum algorithms, including Simon's period finding algorithm. Given these facts, the question naturally arises of whether a quantum speedup can also be achieved for fast correlations by replacing the classical FWHT with the quantum Hadamard transform. We show quantum algorithms achieving speed-up in such a way, introducing a new attack model in the Q2 setting. The new model endows adversaries with a quite strong power, but we demonstrate its feasibility by showing that certain members of the ChaCha and Salsa20 families will likely be secure in the new model. Our attack exploits the link between LFSRs' state update and multiplication in a fine field to apply Shor's algorithm for the discrete logarithm problem. We apply our attacks on SNOW 2.0, SNOW 3G, and Sosemanuk, observing a large speed-up from classical attacks.
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