Previously [4], Orbis Labs presented a method for compiling (“arithmetizing”) relations, expressed as Σ¹₁ formulas in the language of rings, into Halo 2 [1, 2, 3] arithmetic circuits. In this research, we extend this method to support polynomial quantifier bounds, in addition to constant quantifier bounds. This allows for more efficient usage of rows in the resulting circuit.

Zero Knowledge Set Membership Proofs (zkSMPs) allow efficiently, i.e. sublinearly in the size of the set, proving membership of a value in a set in zero knowledge with respect to the value. They have been used to construct anonymous cryptocurrencies such as ZCash, which uses a zero knowledge Merkle proof to show that the inputs of a transaction belong to the Transaction Output (TXO) set. Using a Merkle tree instantiated with a pair of Pedersen hash functions between an amicable cycle of elliptic curves, similarly to Curve Trees, and the Weil Elliptic Curve Inner Product (ECIPs) proofs, I design a set membership protocol with substantially smaller witness sizes than other Merkle zkSMPs. This protocol uses a pair of communicating Bulletproofs, one over each curve, whose total proof size I am able to reduce by proving portions of each verifier inside the other proof. Using these techniques, along with an adaptation of the Bulletproofs++ confidential transaction protocol, I design an anonymous transaction protocol for a decentralized cryptocurrency, whose security argument is reducible to the discrete log problem over a pair of elliptic curves and that does not require a trusted setup. Over a $256$ bit field, these transactions are $1349 + 64n + 32 \lceil \log_2 c \rceil$ bytes for $n$ inputs, $m$ outputs, $d$ depth, and $c$ proof capacity, which is bounded by a linear function of $n d$, $n$, and $m$ and is equal to $1$ for up to $m < 1000$ or $n < 37$ when $d = 48$. Proving complexity is quasilinear and verifier complexity is linear in both $n d$ and $m$, and in practice verification will be dominated by the cost of two Bulletproof verifications of length $1536$ and $1744$ for $c=1$. $\mu$Cash support efficient batch verification, user defined assets and multi-asset confidential transactions, privacy preserving multi-party proving, adaptor signatures, absolute and relative time locks, and a multiphase transaction structure to support scriptless scripts for private atomic swaps and payment channels. This protocol is likely compatible with the Halo accumulation scheme, although I do not investigate this.

Although the supersingular isogeny Diffie-Hellman (SIDH) protocol is one of the most promising post-quantum cryptosystems, it is significantly slower than its main counterparts due to the underlying large smooth-degree isogeny computation. In this work, we address the problem of evaluating and constructing a strategy for computing the large smooth-degree isogeny in the multi-processor setting by formulating them as scheduling problems with dependencies. The contribution of this work is two-fold. For the strategy evaluation, we transform strategies into task dependency graphs and apply precedence-constrained scheduling algorithms to them in order to find their costs. For the strategy construction, we construct strategies from smaller parts that are optimal solutions of integer programming representing the problem. We show via experiments that the proposed two techniques together offer more than 13% reduction in the strategy costs compared to the best current results by Hutchinson and Karabina presented at Indocrypt 2018.

Assume that Alice can do only classical probabilistic polynomial-time computing while Bob can do quantum polynomial-time computing. Alice and Bob communicate over only classical channels, and finally Bob gets a state $|x_0\rangle+|x_1\rangle$ with some bit strings $x_0$ and $x_1$. Is it possible that Alice can know $\{x_0,x_1\}$ but Bob cannot? Such a task, called {\it remote state preparations}, is indeed possible under some complexity assumptions, and is bases of many quantum cryptographic primitives such as proofs of quantumness, (classical-client) blind quantum computing, (classical) verifications of quantum computing, and quantum money. A typical technique to realize remote state preparations is to use 2-to-1 trapdoor collision resistant hash functions: Alice sends a 2-to-1 trapdoor collision resistant hash function $f$ to Bob, and Bob evaluates it coherently, i.e., Bob generates $\sum_x|x\rangle|f(x)\rangle$. Bob measures the second register to get the measurement result $y$, and sends $y$ to Alice. Bob's post-measurement state is $|x_0\rangle+|x_1\rangle$, where $f(x_0)=f(x_1)=y$. With the trapdoor, Alice can learn $\{x_0,x_1\}$ from $y$, but due to the collision resistance, Bob cannot. This Alice's advantage can be leveraged to realize the quantum cryptographic primitives listed above. It seems that the collision resistance is essential here. In this paper, surprisingly, we show that the collision resistance is not necessary for a restricted case: we show that (non-verifiable) remote state preparations of $|x_0\rangle+|x_1\rangle$ secure against {\it classical} probabilistic polynomial-time Bob can be constructed from classically-secure (full-domain) trapdoor permutations. Trapdoor permutations are not likely to imply the collision resistance, because black-box reductions from collision-resistant hash functions to trapdoor permutations are known to be impossible. As an application of our result, we construct proofs of quantumness from classically-secure (full-domain) trapdoor permutations.

Weak coin flipping is an important cryptographic primitive, as it is the strongest known secure two-party computation primitive, that classically becomes secure only when certain assumptions are made (e.g. computational hardness), while quantumly there exist protocols that achieve arbitrarily close to perfect security. This breakthrough result was established by C. Mochon in 2007 [arXiv:0711.4114], however, his proof of existence was partially non-constructive, thus, setting back the proposal of explicit protocols. In this work, we report three different solutions to the quantum weak coin flipping problem. In particular, we propose different methods that result---either analytically or numerically---in the operators needed to construct weak coin flipping protocols with different levels of security, including nearly perfect security. In order to develop these methods, we study the quantum weak coin flipping problem from both an algebraic and a geometric perspective. We also analytically construct illustrative examples of weak coin flipping protocols achieving different levels of security.

We construct non-malleable codes in the split-state model with codeword length $m + 3\lambda$ or $m+5\lambda$, where $m$ is the message size and $\lambda$ is the security parameter, depending on how conservative one is. Our scheme is very simple and involves a single call to a block cipher meeting a new security notion which we dub entropic fixed-related-key security, which essentially means that the block cipher behaves like a pseudorandom permutation when queried upon inputs sampled from a distribution with sufficient min-entropy, even under related-key attacks with respect to an arbitrary but fixed key relation. Importantly, indistinguishability only holds with respect to the original secret key (and not with respect to the tampered secret key). In a previous work, Fehr, Karpman, and Mennink (ToSC 2018) used a related assumption (where the block cipher inputs can be chosen by the adversary, and where indistinguishability holds even with respect to the tampered key) to construct a non-malleable code in the split-state model with codeword length $m + 2\lambda$. Unfortunately, no block cipher (even an ideal one) satisfies their assumption when the tampering function is allowed to be cipher-dependent. In contrast, we are able to show that entropic fixed-related-key security holds in the ideal cipher model with respect to a large class of cipher-dependent tampering attacks (including those which break the assumption of Fehr, Karpman, and Mennink).

Arithmetic to Boolean masking (A2B) conversion is a crucial technique in the masking of lattice-based post-quantum cryptography. It is also a crucial part of building a masked comparison which is one of the hardest to mask building blocks for active secure lattice-based encryption. We first present a new method, called one-hot conversion, to efficiently convert from higher-order arithmetic masking to Boolean masking using a variant of the higher-order table-based conversion of Coron et al. Secondly, we specialize our method to perform arithmetic to 1-bit Boolean functions. Our one-hot function can be applied to masking lattice-based encryption building blocks such as masked comparison or to determine the most significant bit of an arithmetically masked variable. In our benchmarks, a speedup of 40 to 66 times is achieved over state-of-the-art table-based A2B conversions, bringing table-based A2B conversions in the performance range of the Boolean circuit-based A2B conversions by only a slowdown of factor 1.2 to 2.

Cryptanalysis of block ciphers is an active and important research area with an extensive volume of literature. For this work, we focus on SBox-based ciphers, as they are widely used and cover a large class of block ciphers. While there have been prior works that have consolidated attacks on block ciphers, they usually focus on describing and listing the attacks. Moreover, the methods for evaluating a cipher's security are often ad hoc, differing from cipher to cipher, as attacks and evaluation techniques are developed along the way. As such, we aim to organise the attack literature, as well as the work on security evaluation. In this work, we present a systematization of cryptanalysis of SBox-based block ciphers focusing on three main areas: (1) Evaluation of block ciphers against standard cryptanalytic attacks; (2) Organisation and relationships between various attacks; (3) Comparison of the evaluation and attacks on existing ciphers.

The tweakable Even-Mansour construction yields a tweakable block cipher from a public random permutation. We prove post-quantum security of tweakable Even-Mansour when attackers have quantum access to the random permutation but only classical access to the secretly-keyed construction, the relevant setting for most real-world applications. We then use our results to prove post-quantum security—in the same model—of the symmetric-key schemes Chaskey (an ISO-standardized MAC), Elephant (an AEAD finalist of NIST's lightweight cryptography standardization effort), and a variant of Minalpher (an AEAD second-round candidate of the CAESAR competition).

Searchable Symmetric Encryption (SSE) supports efficient yet secure query processing over outsourced symmetrically encrypted databases without the need for decryption. A longstanding open question has been the following: can we design a fast, scalable, linear storage and low-leakage SSE scheme that efficiently supports arbitrary Boolean queries over encrypted databases? In this paper, we present the design, analysis and prototype implementation of the first SSE scheme that efficiently supports conjunctive, disjunctive and more general Boolean queries (in both the conjunctive and disjunctive normal forms) while scaling smoothly to extremely large encrypted databases, and while incurring linear storage overheads and supporting extremely fast query processing in practice. We quantify the leakage of our proposal via a rigorous cryptographic analysis and argue that it achieves security against a well-known class of leakage-abuse and volume analysis attacks. Finally, we demonstrate the storage-efficiency and scalability of our proposed scheme by presenting experimental results of a prototype implementation of our scheme over large real-world databases.

Shor's algorithm solves Elliptic Curve Discrete Logarithm Problem(ECDLP) in polynomial time. To optimize Shor's algorithm for binary elliptic curve, reducing the cost for binary field multiplication is essential because it is most cost-critical basic arithmetic. In this paper, we propose Toffoli gate count optimized space-efficient quantum circuits for binary field $(\mathbb{F}_{2^{n}})$ multiplication. To do so, we take advantage of Karatsuba-like formula and show that its application can be provided without ancillary qubits and optimized them in terms of CNOT gate and depth. Based on the Karatsuba-like formula, we drive a space-efficient CRT-based multiplication with two types of out-of-place multiplication algorithm to reduce CNOT gate cost. Our quantum circuits do not use ancillary qubits and have extremely low TOF gates count $O(n2^{\log_{2}^{\ast}n})$ where $\log_{2}^{\ast}$ is a function named iterative logarithm that grows very slowly. Compared to recent Karatsuba-based space-efficient quantum circuit, our circuit requires only $(12 \sim 24 \% )$ of Toffoli gate count with comparable depth for cryptographic field sizes $(n = 233 \sim 571)$. To the best of our knowledge, this is the first result that utilizes Karatsuba-like formula and CRT-based multiplication in quantum circuits.

This work considers the problem of mitigating information leakage between communication and sensing in systems jointly performing both operations. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to convey information, while simultaneously performing channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to part of the transmitted information. The model abstracts the challenges behind security for joint communication and sensing if one views the channel state as a sensitive attribute, e.g., location. For independent and identically distributed states, perfect output feedback, and when part of the transmitted message should be kept secret, a partial characterization of the secrecy-distortion region is developed. The characterization is exact when the broadcast channel is either physically-degraded or reversely-physically-degraded. The partial characterization is also extended to the situation in which the entire transmitted message should be kept secret. The benefits of a joint approach compared to separation-based secure communication and state-sensing methods are illustrated with binary joint communication and sensing models.

CRYSTALS-Kyber (Kyber) was recently chosen as the first quantum resistant Key Encapsulation Mechanism (KEM) scheme for standardisation, after three rounds of the National Institute of Standards and Technology (NIST) initiated PQC competition which begin in 2016 and search of the best quantum resistant KEMs and digital signatures. Kyber is based on the Module-Learning with Errors (M-LWE) class of Lattice-based Cryptography, that is known to manifest efficiently on FPGAs. This work explores several architectural optimizations and proposes a high-performance and area-time (AT) product efficient hardware accelerator for Kyber. The proposed architectural optimizations include inter-module and intra-module pipelining, that are designed and balanced via FIFO based buffering to ensure maximum parallelisation. The implementation results show that compared to state-of-the-art designs, the proposed architecture delivers 25-51% speedups for Kyber's three different security levels on Artix-7 and Zynq UltraScale+ devices, and a 50-75\% reduction in DSPs at comparable security level. Consequently, the proposed design achieve higher AT product efficiencies of 19-33%.

NTRU-ν-um is a fully homomorphic encryption schemes making use of NTRU as a building block. NTRU-ν-um comes originally in two versions: a first instantiation working with polynomials modulo $X^N - 1$ with $N$ a prime [cyclic version] and a second instantiation working with polynomials modulo $X^N + 1$ with $N$ a power of two [negacyclic version]. The cyclic version is now deprecated. This work shows that the cyclic version of NTRU-ν-um is not secure. Specifically, it does not provide indistinguishability of encryptions. More critically, the scheme leaks the underlying private LWE keys. Source code for mounting the attacks is provided. The attacks were practically validated on the given parameter sets.

It has been forty years since the TCP/IP protocol blueprint, which is the core of modern worldwide Internet, was published. Over this long period, technology has made rapid progress. These advancements are slowly putting pressure and placing new demands on the underlying network architecture design. Therefore, there was a need for innovations that can handle the increasing demands of new technologies like IoT while ensuring secrecy and privacy. It is how Named Data Networking (NDN) came into the picture. NDN enables robust data distribution with interest-based content retrieval and leave-copy-everywhere caching policy. Even though NDN has surfaced as a future envisioned and decisive machinery for data distribution in IoT, it suffers from new data security challenges like content poisoning attacks. In this attack, an attacker attempts to introduce poisoned content with an invalid signature into the network. Given the circumstances, there is a need for a cost-effective signature scheme, requiring inexpensive computing resources and fast when implemented. An identity-based signature scheme (IBS) seems to be the natural choice to address this problem. Herein, we present an IBS, namely Mul-IBS relying on multivariate public key cryptography (MPKC), which leads the race among the post-quantum cryptography contenders. A 5-pass identification scheme accompanying a safe and secure signature scheme based on MPKC works as key ingredients of our design. Our Mul-IBS attains optimal master public key size, master secret key size, and user’s secret key size in the context of multivariate identity-based signatures. The proposed scheme Mul-IBS is proven to be secure in the model “existential unforgeability under chosen-message and chosen identity attack (uf-cma)” contingent upon the fact that Multivariate Quadratic (MQ) problem is NP-hard. The proposed design Mul-IBS can be utilized as a crucial cryptographic building block to build a robust and resilient IoT-based NDN architecture.

Post-Compromise Security (PCS) is a property of secure-channel establishment schemes, which limits the security breach of an adversary that has compromised one of the endpoint to a certain number of messages, after which the channel heals. An attractive property, especially in view of Snowden's revelation of mass-surveillance, PCS was pioneered by the Signal messaging protocol, and is present in OTR. In this paper, we introduce a framework for quantifying and comparing PCS security, with respect to a broad taxonomy of adversaries. The generality and flexibility of our approach allows us to model the healing speed of a broad class of protocols, including Signal, but also an identity-based messaging protocol named SAID, and even a composition of 5G handover protocols.

Databases often require the flexibility to control which entities can access specific database records. Such access control is absent in works that provide private access to databases, namely private information retrieval (PIR) systems. In this paper, we show how to address this shortcoming by introducing Pirmission, the first practical single-server PIR system that allows the enforcement of access control policies. Pirmission’s mechanism does not even reveal whether the client passed or failed the access control check—instead the client receives random data if they are not authorized to access a database record. To demonstrate the usefulness and practicality of Pirmission, we use it to build a private contact discovery platform that allows users to only be discoverable by their friends (who have permission). Compared to state-of- the-art single-server PIR protocols that do not provide access control, Pirmission increases the server’s response time by around 2.8X (much less for databases with large records), and requires only one additional ciphertext to be sent by the client.

Determining bounds on the differential probability of differential trails and the squared correlation contribution of linear trails forms an important part of the security evaluation of a permutation. For Xoodoo, such bounds were proven using the trail core tree search technique, with a dedicated tool (XooTools) that scans the space of all r-round trails with weight below a given threshold $T_r$. The search space grows exponentially with the value of $T_r$ and XooTools appeared to have reached its limit, requiring huge amounts of CPU time to push the bounds a little further. The bottleneck was the phase called trail extension where short trails are extended to more rounds, especially in the backward direction. In this work, we present a number of techniques that allowed us to make extension much more efficient and as such to increase the bounds significantly. Notably, we prove that the minimum weight of any 4-round trail is 80, the minimum weight of any 6-round trail is at least 132 and the minimum weight of any 12-round trail is at least 264, both for differential and linear trails. As a byproduct we found families of trails that have predictable weight once extended to more rounds and use them to compute upper bounds for the minimum weight of trails for arbitrary numbers of rounds.

Deep neural networks have proven effective for second-order profiling side-channel attacks, even in a black-box setting with no prior knowledge of masks and implementation details. While such attacks have been successful, no explanations were provided for understanding why a variety of deep neural networks can (or cannot) learn high-order leakages and what the limitations are. In other words, we lack the explainability on neural network layers combining (or not) unknown and random secret shares, which is a necessary step to defeat, e.g., Boolean masking countermeasures. In this paper, we use information-theoretic metrics to explain the internal activities of deep neural network layers. We propose a novel methodology for the explainability of deep learning-based profiling side-channel analysis (denoted ExDL-SCA) to understand the processing of secret masks. Inspired by the Information Bottleneck theory, our explainability methodology uses perceived information to explain and detect the different phenomena that occur in deep neural networks, such as fitting, compression, and generalization. We provide experimental results on masked AES datasets showing what relevant features deep neural networks use, and where in the networks relevant features are learned and irrelevant features are compressed. Using our method, evaluators can determine what secret masks are being exploited by the network, which allows for more detailed feedback on the implementations. This paper opens new perspectives for understanding the role of different neural network layers in profiling side-channel attacks.

Quantum computers pose a threat to the security of communications over the internet. This imminent risk has led to the standardization of cryptographic schemes for protection in a post-quantum scenario. We present a design methodology for future implementations of such algorithms. This is manifested using the NIST selected digital signature scheme CRYSTALS-Dilithium and key encapsulation scheme CRYSTALS-Kyber. A unified architecture, \crystal, is proposed that can perform key generation, encapsulation, decapsulation, signature generation, and signature verification for all the security levels of CRYSTALS-Dilithium, and CRYSTALS-Kyber. A unified yet flexible polynomial arithmetic unit is designed that can processes Kyber operations twice as fast as Dilithium operations. Efficient memory management is proposed to achieve optimal latency. \crystal is explicitly tailored for ASIC platforms using multiple clock domains. On ASIC 28nm/65nm technology, it occupies 0.263/1.107 mm$^2$ and achieves a clock frequency of 2GHz/560MHz for the fast clock used for memory unit. On Xilinx Zynq Ultrascale+ZCU102 FPGA, the proposed architecture uses 23,277 LUTs, 9,758 DFFs, 4 DSPs, and 24 BRAMs, at 270 MHz clock frequency. \crystal performs better than the standalone implementations of either of the two schemes. This is the first work to provide a unified design in hardware for both schemes.

The overhead of non-linear functions dominates the performance of the secure multiparty computation (MPC) based privacy-preserving machine learning (PPML). This work introduces a family of novel secure three-party computation (3PC) protocols, Bicoptor, which improve the efficiency of evaluating non-linear functions. The basis of Bicopter is a new sign determination protocol, which relies on a clever use of the truncation protocol proposed in SecureML (S\&P 2017). Our 3PC sign determination protocol only requires two communication rounds, and does not involve any preprocessing. Such sign determination protocol is well-suited for computing non-linear functions in PPML, e.g. the activation function ReLU, Maxpool, and their variants. We develop suitable protocols for these non-linear functions, which form a family of GPU-friendly protocols, Bicopter. All Bicoptor protocols only require two communication rounds without preprocessing. We evaluate Bicoptor under a 3-party LAN network over a public cloud, and achieve 90,000 DReLU/ReLU or 3,200 Maxpool (find the maximum value of nine inputs) operations per second. Under the same settings and environment, our ReLU protocol has a one or even two order(s) of magnitude improvement to the state-of-the-art works, Edabits (CRYPTO 2020) or Falcon (PETS 2021), respectively without batch processing.

The highly transmissible COVID-19 disease is a serious threat to people’s health and life. To automate tracing those who have been in close physical contact with newly infected people and/or to analyse tracing-related data, researchers have proposed various ad-hoc programs that require being executed on users’ smartphones. Nevertheless, the existing solutions have two primary limitations: (1) lack of generality: for each type of analytic task, a certain kind of data needs to be sent to an analyst; (2) lack of transparency: parties who provide data to an analyst are not necessarily infected individuals; therefore, infected individuals’ data can be shared with others (e.g., the analyst) without their fine-grained and direct consent. In this work, we present Glass-Vault, a protocol that addresses both limitations simultaneously. It allows an analyst to run authorised programs over the collected data of infectious users, without learning the input data. Glass-Vault relies on a new variant of generic Functional Encryption that we propose in this work. This new variant, called DD-Steel, offers these two additional properties: dynamic and decentralised. We illustrate the security of both Glass-Vault and DD-Steel in the Universal Composability setting. Glass-Vault is the first UC-secure protocol that allows analysing the data of Exposure Notification users in a privacy-preserving manner. As a sample application, we indicate how it can be used to generate “infection heatmaps”.

Imagine that a privacy-conscious client would like to query a key-value store residing on an untrusted server equipped with a secure processor. To protect the privacy of the client's queries as well as the database, one approach is to implement an {\it oblivious map} inside a secure enclave. Indeed, earlier works demonstrated numerous applications of an enclaved-based oblivious map, including private contact discovery, key transparency, and secure outsourced databases. Our work is motivated by the observation that the previous enclave implementations of oblivious algorithms are sub-optimal both asymptotically and concretely. We make the key observation that for enclave applications, the {\it number of page swaps} should be a primary performance metric. We therefore adopt techniques from the {\it external-memory} algorithms literature, and we are the first to implement such algorithms inside hardware enclaves. We also devise asymptotically better algorithms for ensuring a strong notion of obliviousness that resists cache-timing attacks. We complement our algorithmic improvements with various concrete optimizations that save constant factors in practice. The resulting system, called Enigmap, achieves 15$\times$ speedup over Signal's linear scan implementation, and 53$\times$ speedup over the %state-of-the-art prior best oblivious algorithm implementation, at a realistic database size of 256 million and a batch size of 1000. The speedup is asymptotical in nature and will be even greater as Signal's user base grows.

Private Information Retrieval (PIR) addresses the cryptographic problem of hiding sensitive database queries from database operators. In practice, PIR schemes face the challenges of either high computational costs or restrictive security assumptions, resulting in a barrier to deployment. In this work, we introduce Assisted Private Information Retrieval (APIR), a new PIR framework for keyword-value databases generalizing multi-server PIR and relaxing its database consistency assumption. We propose the construction of Synchronized APIR, an efficient hybrid APIR scheme combining black-box single-server PIR and non-black-box multi-server PIR. To evaluate the scheme, we apply it to a proof-of-concept privacy-preserving DNS application. The experiment results demonstrate that Synchronized APIR outperforms the baseline single-server PIR protocol in communication and computational cost after the initial one-time cost.

Modern-day mobile communications allow users to connect from any place, at any time. However, this ubiquitous access comes at the expense of their privacy. Currently, the operators providing mobile service to users learn call-and SMS-metadata, and even the contents of those exchanges. A main reason behind this is the Lawful-Interception (LI) requirement, by which serving networks must provide this (meta-)data to authorities, given a warrant. At ESORICS 2021, Arfaoui et al. pioneered a primitive called Lawful-Interception Key-Exchange, which achieves the best of both worlds: (provably) privacy-enhanced communications, and finegrained fine-grained, limited access to user data. Their work had two important shortcomings. First, their protocol required pairings which, while sufficiently efficient, might not always be available in the mobile setting. More importantly, that scheme was only applicable in a domestic setting, where the concerned users (Alice and Bob) were subject to the same LI authorities. The case of roaming was left as an open question. In this paper we answer that open question. We extend the framework of Arfaoui et al. to allow Alice and Bob (now subject to potentially two sets of authorities) to establish a secure channel that guarantees the strong properties afforded by the LIKE schemes of ESORICS 2021. Our construction is pairing-free, faster than that of Arfaoui et al., and its security relies on standard assumptions.

With the rapid development of Internet of Things (IoT), designing a secure two-factor authentication scheme for these network is increasingly demanding. Recently, historical bigdata has gained interest as a novel authentication factor in this area. In this paper, we focus on a recent authentication scheme using bigdata (Liu et al.’s scheme) which claims to provide additional security properties such as Perfect Forward Secrecy (PFS), Key Compromise Impersonation (KCI) resilience and Server Compromise Impersonation (SCI) resilience. However, assuming a real strong attacker, rather than a weak one. we show that their scheme not only fails to provide KCI and SCI, but also doesn’t provide real two-factor security, revocability and suffers inside attack. Then we propose our novel scheme which can indeed provide two-factor security, PFS , KCI and inside attack resilience and revocability of the client. Further, our performance analysis shows that our scheme has reduced modular exponentiation operation and multiplication for both client and server compared to Liu et al.’s scheme which reduces the execution time by one third i.e. 6 ms and 30 ms (0.3 ms and 4 ms) for IoT device (server) for security levels of λ = 128, λ = 256 respectively

Proving discrete log equality for groups of the same order is addressed by Chaum and Pedersen's seminal work. However, there has not been a lot of work in proving discrete log equality for groups of different orders. This paper presents an efficient solution, which leverages a technique we call delegated Schnorr. The discovery of this technique is guided by a design methodology that we call the inspection model, and we find it useful for protocol designs. We show two applications of this technique on the Findora blockchain: **Maxwell-Zerocash switching:** There are two privacy-preserving transfer protocols on the Findora blockchain, one follows the Maxwell construction and uses Pedersen commitments over Ristretto, one follows the Zerocash construction and uses Rescue over BLS12-381. We present an efficient protocol to convert assets between these two constructions while preserving the privacy. **Zerocash with secp256k1 keys:** Bitcoin, Ethereum, and many other chains do signatures on secp256k1. There is a strong need for ZK applications to not depend on special curves like Jubjub, but be compatible with secp256k1. Due to FFT unfriendliness of secp256k1, many proof systems (e.g., Groth16, Plonk, FRI) are infeasible. We present a solution using Bulletproofs over curve secq256k1 ("q") and delegated Schnorr which connects Bulletproofs to TurboPlonk over BLS12-381. We conclude the paper with (im)possibility results about Zerocash with only access to a deterministic ECDSA signing oracle, which is the case when working with MetaMask. This result shows the limitations of the techniques in this paper. This paper is under a bug bounty program through a grant from Findora Foundation.

Hash chains are a simple way to generate pseudorandom data, but are inefficient in situations that require long chains. This can cause unnecessary overhead for use cases including logical clocks, synchronizing the heads of a pseudorandom stream, or non-interactive key agreement. This paper presents the “skip ratchet”, a novel pseudorandom function that can be efficiently incremented by arbitrary intervals.

Multiplicative Complexity (MC) is defined as the minimum number of AND gates required to implement a function with a circuit over the basis AND, XOR, NOT. This complexity measure is relevant for many advanced cryptographic protocols such as fully homomorphic encryption, multi-party computation, and zero-knowledge proofs, where processing AND gates is more expensive than processing XOR gates. Although there is no known asymptotically efficient technique to compute the MC of a random Boolean function, bounds on the MC of Boolean functions are successfully used to to show existence of Boolean functions with a particular MC. In 2000, Boyar et al. showed that, for all $n\geq 0$, at most $2^{k^2+2k+2kn+n+1}$ $n$-variable Boolean functions can be computed with $k$ AND gates. This bound is used to prove the existence of a 8-variable Boolean functions with MC greater than 7. In this paper, we improve the Boyar et al. bound.

This work addresses expressive queries over encrypted data by presenting the first systematic study of multi-attribute range search on a symmetrically encrypted database outsourced to an honest-but-curious server. Prior work includes a thorough analysis of single-attribute range search schemes (e.g. Demertzis et al. 2016) and a proposed high-level approach for multi-attribute schemes (De Capitani di Vimercati et al. 2021). We first introduce a flexible framework for building secure range search schemes over multiple attributes (dimensions) by adapting a broad class of geometric search data structures to operate on encrypted data. Our framework encompasses widely used data structures such as multi-dimensional range trees and quadtrees, and has strong security properties that we formally prove. We then develop six concrete highly parallelizable range search schemes within our framework that offer a sliding scale of efficiency and security tradeoffs to suit the needs of the application. We evaluate our schemes with a formal complexity and security analysis, a prototype implementation, and an experimental evaluation on real-world datasets.

We address the problem of privately evaluating a branching program on encrypted data. This scenario is a 2-party protocol consisting of a server and a client. The server privately holds a branching program which is a representation of a boolean function using a directed acyclic graph. The client holds a secret input to the branching program. The goal of the computation is to evaluate the client's input on the server program such that only the result is revealed to the client, and nothing is revealed to the server. To solve this problem Ishai-Paskin introduced a public-key encryption scheme that is based on Damgård-Jurik additively homomorphic encryption and has the property, that given a branching program $P$ and an encryption $c$ of an input $y$, it is possible to efficiently compute a succinct ciphertext $c'$ corresponding to $P(y)$. The entire computation is done by the server relying on the fact that Damgård-Jurik scheme has length-flexible ciphertexts which allows multiplications between ciphertexts of different sizes under the same encryption key. Although the decryption of the Damgård-Jurik scheme is theoretically efficient, the size of $c'$ and the decoding time depend on the depth of the branching program. In this paper, we propose a new scheme where the input is instead encrypted using fully homomorphic encryption and discuss different variants and optimizations. The entire computation is also done by the server but the size of the resulting ciphertext is independent of the depth of the program. We implement Ishai-Paskin and our scheme and show that the running time of our scheme is an order of magnitude smaller.

The qINDqCPA security notion for public-key encryption schemes by Gagliardoni et al. (PQCrypto'21) models security against adversaries which are able to obtain ciphertexts in superposition. Defining this security notion requires a special type of quantum operator. Known constructions differ in which keys are necessary to construct this operator, depending on properties of the encryption scheme. We argue—for the typical setting of securing communication between Alice and Bob—that in order to apply the notion, the quantum operator should be realizable for challengers knowing only the public key. This is already known to be the case for a wide range of public-key encryption schemes, in particular, those exhibiting the so-called recoverability property which allows to recover the message from a ciphertext using the randomness instead of the secret key. The open question is whether there are real-world public-key encryption schemes for which the notion is not applicable, considering the aforementioned observation on the keys known by the challenger. We answer this question in the affirmative by showing that applying the qINDqCPA security notion to the OAEP construction requires the challenger to know the secret key. We conclude that the qINDqCPA security notion might need to be refined to eventually yield a universally applicable PKE notion of quantum security with a quantum indistinguishability phase.

This work addresses the security flaw in the original VeriFL protocol and proposes a patched protocol. The patched protocol is secure against any static malicious adversary with a certain threshold and only introduces moderate modifications to the original protocol.

SNARK is a well-known family of cryptographic tools that is increasingly used in the field of computation integrity at scale. In this area, multiple works have introduced SNARK-friendly cryptographic primitives: hashing, but also encryption and signature verification. Despite all the efforts to create cryptographic primitives that can be proved faster, it remains a major performance hole in practice. In this paper, we present a recursive technique that can improve the efficiency of the prover by an order of magnitude compared to proving MiMC hashes (a SNARK-friendly hash function, Albrecht et al. 2016) with a Groth16 (Eurocrypt 2016) proof. We use GKR (a well-known public-coin argument system by Goldwasser et al., STOC 2008) to prove the integrity of hash computations and embed the GKR verifier inside a SNARK circuit. The challenge comes from the fact that GKR is a public-coin interactive protocol, and applying Fiat-Shamir naively may result in worse performance than applying existing techniques directly. This is because Fiat-Shamir itself is involved with hash computation over a large string. We take advantage of a property that SNARK schemes commonly have, to build a protocol in which the Fiat-Shamir hashes have very short inputs. The technique we present is generic and can be applied over any SNARK-friendly hash, most known SNARK schemes, and any (one-round) public-coin argument system in place of GKR. We emphasize that while our general compiler is secure in the random oracle model, our concrete instantiation (i.e., GKR plus outer SNARK) is only proved to be heuristically secure. This is due to the fact we first need to convert the GKR protocol to a one-round protocol. Thus, the random oracle of GKR, starting from the second round, is replaced with a concrete hash inside the outer layer SNARK which makes the security-proof heuristic.

This paper presents results of performance evaluation of NIST Lightweight Cryptography standardization finalists which are implemented by us. Our implementation method puts on the target to reduce RAM consumption on embedded devices. Our target microcontrollers are AVR ATmega 128 and ARM Cortex-M3. We apply our implementation method to five AEAD schemes which include four finalists of the NIST lightweight cryptography standardization and demonstrate the performance evaluation on target microcontrollers. From our performance evaluation of the RAM size, we have achieved 117-byte TinyJAMBU-128 on ATmega 128 and 140-byte TinyJAMBU-128 on ARM Cortex-M3. Our implementation of TinyJAMBU-128 has the smallest RAM of all the target AEAD schemes.

Unique ring signatures (URS) were introduced by Franklin and Zhang (FC 2012) as a unification of linkable and traceable ring signatures. In URS, each member within a ring can only produce, on behalf of the ring, at most one signature for a message. Applications of URS potentially are e-voting systems and e–token systems. In blockchain technology, URS has been implemented for mixing contracts. However, existing URS schemes are based on the Discrete Logarithm Problem, which is insecure in the post-quantum setting. In this paper, we design a new lattice-based URS scheme where the signature size is logarithmic in the number of ring members. The proposed URS exploits a Merkle tree-based accumulator as a building block in the lattice setting. Our scheme is secure under the Short Integer Solution and Learning With Rounding assumptions in the random oracle model.

Analysis of advanced Physical Unclonable Function (PUF) applications and protocols rely on assuming that a PUF behaves like a random oracle, that is, upon receiving a challenge, a uniform random response with replacement is selected, measurement noise is added, and the resulting response is returned. In order to justify such an assumption, we need to rely on digital interface computation that to some extent remains confidential -- otherwise, information about PUF challenge response pairs leak with which the adversary can train a prediction model for the PUF. We introduce a theoretical framework that allows the adversary to have a prediction model (with a typical accuracy of 75\% for predicting response bits for state-of-the-art silicon PUF designs). We do not require any confidential digital computing or digital secrets while we can still prove rigorous statements about the bit security of a system that interfaces with the PUF. In particular, we prove the bit security of a PUF-based random oracle construction; this merges the PUF framework with fuzzy extractors.

Let 𝑓 ∶ 𝐸 → 𝐸′ be an N-isogeny between elliptic curves (or abelian varieties) over a finite field 𝔽_𝑞. We show that there always exist an efficient representation of 𝑓 that takes polylogarithmic 𝑂(log^𝑂(1) 𝑁 log 𝑞) space and which can evaluate 𝑓 at any point 𝑃 ∈ 𝐸(𝔽_{𝑞^𝑘}) in polylogarithmic 𝑂(log^𝑂(1) 𝑁) arithmetic operations in 𝔽_{𝑞^𝑘}. Furthermore, this efficient representation can be computed by evaluating 𝑓 on 𝑂(log 𝑁) points defined over extensions of degree 𝑂(log 𝑁) over 𝔽_𝑞. In particular, if 𝑓 is represented by the equation 𝐻(𝑥) = 0 of its kernel 𝐾, then using Vélu’s formula the efficient representation can be computed in time 𝑂 ̃(𝑁 log 𝑞 + log^2 𝑞).

Lattice enumeration is a linear-space algorithm for solving the shortest lattice vector problem(SVP). Extreme pruning is a practical technique for accelerating lattice enumeration, which has mature theoretical analysis and practical implementation. However, these works are still remain to be done for discrete pruning. In this paper, we improve the discrete pruned enumeration (DP enumeration), and give a solution to the problem proposed by Leo Ducas et Damien Stehle about the cost estimation of discrete pruning. Our contribution is on the following three aspects: First, we refine the algorithm both from theoretical and practical aspects. Discrete pruning using natural number representation lies on a randomness assumption of lattice point distribution, which has an obvious paradox in the original analysis. We rectify this assumption to fix the problem, and correspondingly modify some details of DP enumeration. We also improve the binary search algorithm for cell enumeration radius with polynomial time complexity, and refine the cell decoding algorithm. Besides, we propose to use a truncated lattice reduction algorithm -- k-tours-BKZ as reprocessing method when a round of enumeration failed. Second, we propose a cost estimation simulator for DP enumeration. Based on the investigation of lattice basis stability during reprocessing, we give a method to simulate the squared length of Gram-Schmidt orthogonalization basis quickly, and give the fitted cost estimation formulae of sub-algorithms in CPU-cycles through intensive experiments. The success probability model is also modified based on the rectified assumption. We verify the cost estimation simulator on middle size SVP challenge instances, and the simulation results are very close to the actual performance of DP enumeration. Third, we give a method to calculate the optimal parameter setting to minimize the running time of DP enumeration. We compare the efficiency of our optimized DP enumeration with extreme pruning enumeration in solving SVP challenge instances. The experimental results in medium dimension and simulation results in high dimension both show that the discrete pruning method could outperform extreme pruning. An open-source implementation of DP enumeration with its simulator is also provided.

While blockchain systems are quickly gaining popularity, front-running remains a major obstacle to fair exchange. In this paper, we show how to apply identity-based encryption (IBE) to prevent front-running with minimal bandwidth overheads. In our approach, to decrypt a block of N transactions, the number of messages sent across the network only grows linearly with the size of decrypting committees, S. That is, to decrypt a set of N transactions sequenced at a specific block, a committee only needs to exchange S decryption shares (independent of N ). In comparison, previous solutions are based on threshold decryption schemes, where each transaction in a block must be decrypted separately by the committee, resulting in bandwidth overhead of N × S. Along the way, we present a model for fair block processing and build a prototype implementation. We show that on a sample of 1000 messages with 1000 validators our system saves 42.53 MB of bandwidth which is 99.6% less compared with the standard threshold decryption paradigm.

Differential cryptanalysis is one of the most effective methods for evaluating the security level of block ciphers. For this, an attacker tries to find a differential or a characteristic with a high probability that distinguishes a block cipher from a random permutation to obtain the secret key. Although it is theoretically possible to compute the probability of a differential for a block cipher, there are two problems to compute it practically. The first problem is that it is computationally impossible to compute differential probability by trying all plaintext pairs. The second problem is that the probability of a differential over all choices of the plaintext and key might be different from the probability of the differential over all plaintexts for a fixed key. Thus, to evaluate the security against the differential cryptanalysis, one must assume both the hypothesis of stochastic equivalence and the Markov model. However, the hypothesis of stochastic equivalence does not hold in general. Indeed, we show on simple ciphers that the hypothesis of stochastic equivalence does not hold. Moreover, we observe that the differential probability is not equal to the expected differential probability. For these results, we study plateau characteristics for a 4-bit cipher and a 16-bit super box. As a result, when considering differential cryptanalysis, one must be careful about the gap between the theoretical and the practical security of block ciphers.

Resistance to key misuse attacks is a vital property for key encapsulation mechanisms（KEMs）in NIST-PQC standardization process. In key mismatch attack, the adversary recovers reused secret key with the help of an oracle $\mathcal{O}$ that indicates whether the shared key matches or not. Key mismatch attack is more powerful when fewer oracle queries are required. A series of works tried to reduce query times, Qin et al. [AISACRYPT 2021] gave a systematic approach to finding lower bound of oracle queries for a category of KEMs, including NIST’s third-round candidate Kyber and Saber. In this paper, we found the aforementioned bound can be bypassed by combining Qin et al. (AISACRYPT 2021)’s key mismatch attack with a standard lattice attack. In particular, we explicitly build the relationship between the number of queries to the oracle and the bit security of the lattice-based KEMs. Our attack is inspired by the fact that each oracle query reveals partial information of reused secrets, and affects the mean and the covariance parameter of secrets, making the attack on lattice easier. In addition, We quantify such effect in theory and estimate the security loss for all NIST second-round candidate KEMs.Specifically, Our improved attack reduces the number of queries for Kyber512 by 34% from 1312 queries with bit security 107 to 865 with bit security 32. For Kyber768 and Kyber1024, our improved attack reduces the number of queries by 29% and 27% with bit security is 32.

Cross-chain trading is fundamental to blockchains and Decentralized Finance (DeFi). A way to achieve such trading in a truly decentralized manner, i.e., without trusted third parties, is by using atomic swaps. However, recent works revealed that Hashed Time-Lock Contract, a key building block of the existing atomic swaps, is entirely insecure in the presence of user-miner collusion. Specifically, a user can bribe the miners of the blockchain to help it cheat. In this work, we give the first and rigorous formal treatment of fair trading on blockchains, where users and miners may enter arbitrary binding contracts on the side. We propose Rapidash, a new atomic swap protocol, and prove its incentive-compatibility in the presence of user-miner collusion. Specifically, we show that Rapidash satisfies a coalition-resistant Nash equilibrium absent external incentives. We give instantiations of Rapidash that are compatible with Bitcoin and Ethereum, and incur only minimal overheads in terms of costs for the users.

The time sequence-based outsourcing makes new demands for related access control continue to grow increasingly in cloud computing. In this paper, we propose a practical password-based access control framework for such media cloudization relying on content control based on the time-sequence attribute, which is designed over prime-order groups. First, the scheme supports multi-keyword search simultaneously in any monotonic boolean formulas, and enables media owner to control content encryption key for different time-periods using an updatable password; Second, the scheme supports the key self-retrievability of content encryption key, which is more suitable for the cloud-based media applications with massive users. Then, we show that the proposed scheme is provably secure in the standard model. Finally, the detailed result of performance evaluation shows the proposed scheme is efficient and practical for cloud-based media applications.

SPHINCS$^+$ is a stateless hash-based signature scheme that has been selected for standardization as part of the NIST post-quantum cryptography (PQC) standardization process. Its security proof relies on the distinct-function multi-target second-preimage resistance (DM-SPR) of the underlying keyed hash function. The SPHINCS$^+$ submission offered several instantiations of this keyed hash function, including one based on SHA-256. A recent observation by Sydney Antonov on the PQC mailing list demonstrated that the construction based on SHA-256 did not have DM-SPR at NIST category five, for several of the parameter sets submitted to NIST; however, it remained an open question whether this observation leads to a forgery attack. We answer this question in the affirmative by giving a complete forgery attack that reduces the concrete classical security of these parameter sets by approximately 40 bits of security. Our attack works by applying Antonov's technique to the {WOTS$^+$} public keys in {\SPHINCS}, leading to a new one-time key that can sign a very limited set of hash values. From that key, we construct a slightly altered version of the original hypertree with which we can sign arbitrary messages, yielding signatures that appear valid.

A distributed point function (DPF) is a cryptographic primitive that enables compressed additive sharing of a secret unit vector across two or more parties. Despite growing ubiquity within applications and notable research efforts, the best 2-party DPF construction to date remains the tree-based construction from (Boyle et al, CCS'16), with no significantly new approaches since. We present a new framework for 2-party DPF construction, which applies in the setting of feasible (polynomial-size) domains. This captures in particular all DPF applications in which the keys are expanded to the full domain. Our approach is motivated by a strengthened notion we put forth, of programmable DPF (PDPF): in which a short, input-independent "offline" key can be reused for sharing many point functions. * PDPF from OWF: We construct a PDPF for feasible domains from the minimal assumption that one-way functions exist, where the second "online" key size is polylogarithmic in the domain size $N$. Our approach offers multiple new efficiency features and applications: * Privately puncturable PRFs: Our PDPF gives the first OWF-based privately puncturable PRFs (for feasible domains) with sublinear keys. * $O(1)$-round distributed DPF Gen: We obtain a (standard) DPF with polylog-size keys that admits an analog of Doerner-shelat (CCS'17) distributed key generation, requiring only $O(1)$ rounds (versus $\log N$). * PCG with 1 short key: Compressing useful correlations for secure computation, where one key is of minimal size. This provides up to exponential communication savings in some application scenarios.

We describe how any function over a finite field $\mathbb{F}_{p^n}$ can be represented in terms of the values of its derivatives. In particular, we observe that a function of algebraic degree $d$ can be represented uniquely through the values of its derivatives of order $(d-1)$ up to the addition of terms of algebraic degree strictly less than $d$. We identify a set of elements of the finite field, which we call the degree $d$ extension of the basis, which has the property that for any choice of values for the elements in this set, there exists a function of algebraic degree $d$ whose values match the given ones. We discuss how to reconstruct a function from the values of its derivatives, and discuss the complexity involved in transitioning between the truth table of the function and its derivative representation. We then specialize to the case of quadratic functions, and show how to directly convert between the univariate and derivative representation without going through the truth table. We thus generalize the matrix representation of qaudratic vectorial Boolean functions due to Yu et al. to the case of arbitrary characteristic. We also show how to characterize quadratic planar functions using the derivative representation. Based on this, we adapt the method of Yu et al. for searching for quadratic APN functions with prime field coefficients to the case of planar DO functions. We use this method to find all such functions (up to CCZ-equivalence) over $\mathbb{F}_{3^n}$ for $n \le 7$. We conclude that the currently known planar DO polynomials cover all possible cases for $n \le 7$. We find representatives simpler than the known ones for the Zhou-Pott, Dickson, and Lunardon-Marino-Polverino-Trombetti-Bierbrauer families for $n = 6$. Finally, we discuss the computational resources that would be needed to push this search to higher dimensions.

In this work, we evaluate the security of Merkle-Damgård (MD) hash functions and their combiners (XOR and concatenation combiners) in quantum settings. Two main quantum scenarios are considered, including the scenario where a substantial amount of cheap quantum random access memory (qRAM) is available and where qRAM is limited and expensive to access. We present generic quantum attacks on the MD hash functions and hash combiners, and carefully analyze the complexities under both quantum scenarios. The considered securities are fundamental requirements for hash functions, including the resistance against collision and (second-)preimage. The results are consistent with the conclusions in the classical setting, that is, the considered resistances of the MD hash functions and their combiners are far less than ideal, despite the significant differences in the expected security bounds between the classical and quantum settings. Particularly, the generic attacks can be improved significantly using quantum computers under both scenarios. These results serve as an indication that classical hash constructions require careful security re-evaluation before being deployed to the post-quantum cryptography schemes.

In ToSC'20, a new approach combining Mix-Integer Linear Programming (MILP) tool and Constraint Programming (CP) tool to search for boomerang distinguishers is proposed and later used for rebound attack in ASIACRYPT'21 and CRYPTO'22. In this work, we extend these techniques to mount collision attacks on SKINNY-128-256 MMO hashing mode in classical and quantum settings. The first results of 17-round (and 15-round) free-start collision attack on this variant of SKINNY hashing mode are presented. Moreover, one more round of the inbound phase is covered leading to the best existing classical free-start collision attack of 19-round on the SKINNY-128-384 MMO hashing.

Interactive oracle proofs (IOPs) are a generalization of probabilistically checkable proofs that can be used to construct succinct arguments. Improvements in the efficiency of IOPs lead to improvements in the efficiency of succinct arguments. Key efficiency goals include achieving provers that run in linear time and verifiers that run in sublinear time, where the time complexity is with respect to the arithmetic complexity of proved computations over a finite field $\mathbb{F}$. We consider the problem of constructing IOPs for any given finite field $\mathbb{F}$ with a linear-time prover and polylogarithmic query complexity. Several previous works have achieved these efficiency requirements with $O(1)$ soundness error for NP-complete languages. However, constrained by the soundness error of the sumcheck protocol underlying these constructions, the IOPs achieve linear prover time only for instances in fields of size $\Omega(\log n)$. Recent work (Ron-Zewi and Rothblum, STOC 2022) overcomes this problem, but with linear verification time. We construct IOPs for the algebraic automata problem over any finite field $\mathbb{F}$ with a linear-time prover, polylogarithmic query complexity, and sublinear verification complexity. We additionally prove a similar result to Ron-Zewi and Rothblum for the NP-complete language R1CS using different techniques. The IOPs imply succinct arguments for (nondeterministic) arithmetic computations over any finite field with linear-time proving (given black-box access to a linear-time collision-resistant hash function). Inspired by recent constructions of reverse-multiplication-friendly embeddings, our IOP constructions embed problem instances over small fields into larger fields and adapt previous IOP constructions to the new instances. The IOP provers are modelled as random access machines and use precomputation techniques to achieve linear prover time. In this way, we avoid having to replace the sumcheck protocol.

Implementation-based attacks are major concerns for modern cryptography. For symmetric-key cryptography, a significant amount of exploration has taken place in this regard for primitives such as block ciphers. Concerning symmetric-key operating modes, such as Authenticated Encryption with Associated Data (AEAD), the state- of-the-art mainly addresses the passive Side-Channel Attacks (SCA) in the form of leakage resilient cryptography. So far, only a handful of work address Fault Attacks (FA) in the context of AEADs concerning the fundamental properties – integrity and confidentiality. In this paper, we address this gap by exploring mode-level issues arising due to FAs. We emphasize that FAs can be fatal even in cases where the adversary does not aim to extract the long-term secret, but rather tries to violate the basic security requirements (integrity and confidentiality). Notably, we show novel integrity attack examples on state-of-the-art AEAD constructions and even on a prior fault-resilient AEAD construction called SIV$. On the constructive side, we first present new security notions of fault-resilience, for PRF (frPRF), MAC (frMAC) and AEAD (frAE), the latter can be seen as an improved version of the notion introduced by Fischlin and Gunther at CT-RSA’20. Then, we propose new constructions to turn a frPRF into a fault-resilient MAC frMAC (hash-then-frPRF) and into a fault-resilient AEAD frAE (MAC-then-Encrypt-then-MAC or MEM).

We propose a countermeasure to the Castryck-Decru attack on SIDH. The attack heavily relies on the images of torsion points. The main input to our countermeasure consists in masking the torsion point images in SIDH in a way they are not exploitable in the attack, but can be used to complete the key exchange. This comes with a change in the form the field characteristic and a considerable increase in the parameter sizes.

The distributed source coding problem is extended by positing that noisy measurements of a remote source are the correlated random variables that should be reconstructed at another terminal. We consider a secure and private distributed lossy source coding problem with two encoders and one decoder such that (i) all terminals noncausally observe a noisy measurement of the remote source; (ii) a private key is available to each legitimate encoder and all private keys are available to the decoder; (iii) rate-limited noiseless communication links are available between each encoder and the decoder; (iv) the amount of information leakage to an eavesdropper about the correlated random variables is defined as secrecy leakage, and privacy leakage is measured with respect to the remote source; and (v) two passive attack scenarios are considered, where a strong eavesdropper can access both communication links and a weak eavesdropper can only choose one of the links to access. Inner and outer bounds on the rate regions defined under secrecy, privacy, communication, and distortion constraints are derived for both passive attack scenarios. When one or both sources should be reconstructed reliably, the rate region bounds are simplified.

Double-odd curves are curves with order equal to 2 modulo 4. A prime order group with complete formulas and a canonical encoding/decoding process could previously be built over a double-odd curve. In this paper, we reformulate such curves as a specific case of the Jacobi quartic. This allows using slightly faster formulas for point operations, as well as defining a more efficient encoding format, so that decoding and encoding have the same cost as classic point compression (decoding is one square root, encoding is one inversion). We define the prime-order groups jq255e and jq255s as the application of that modified encoding to the do255e and do255s groups. We furthermore define an optimized signature mechanism on these groups, that offers shorter signatures (48 bytes instead of the usual 64 bytes, for 128-bit security) and makes signature verification faster (down to less than 83000 cycles on an Intel x86 Coffee Lake core).

The verifiable encryption of bits is the main computational step that is needed to prepare ballots in many practical voting protocols. Its computational load can also be a practical bottleneck, preventing the deployment of some protocols or requiring the use of computing clusters. We investigate the question of producing many verifiably encrypted bits in an efficient and portable way, using as a baseline the protocol that is in use in essentially all modern voting systems and libraries supporting homomorphic voting, including ElectionGuard, a state-of-the-art open source voting SDK deployed in government elections. Combining fixed base exponentiation techniques and new encryption and ZK proof mechanisms, we obtain speed-ups by more than one order of magnitude against standard implementations. Our exploration requires balancing conflicting optimization strategies, and the use of asymptotically less efficient protocols that turn out to be very effective in practice. Several of our proposed improvements are now on the ElectionGuard roadmap.

SNARKs for some standard cryptographic primitives tend to be plenty designed with SNARK-unfriendly operations such as XOR. Previous protocols such as [GW20] worked around this problem by the introduction of lookup arguments. However, these protocols were only appliable over the same circuit. RapidUp is a protocol that solves this limitation by unfolding the grand-product polynomial into two (equivalent) polynomials of the same size. Morevoer, a generalization of previous protocols is presented by the introduction of selectors.

The Security Protocol and Data Model (SPDM) defines flows to authenticate hardware identity of a computing device. It also allows for establishing a secure session for confidential and integrity protected data communication between two devices. The present version of SPDM, namely version 1.2, relies on traditional asymmetric cryptographic algorithms that are known to be vulnerable to quantum attacks. This paper describes the means by which support for post-quantum (PQ) cryptography can be added to the SPDM protocol in order to enable SPDM for the upcoming world of quantum computing. We examine SPDM 1.2 protocol and discuss how to negotiate the use of post-quantum cryptography algorithms (PQC), how to support device identity reporting, means to authenticate the device, and how to establish a secure session when using PQC algorithms. We consider so called hybrid modes where both classical and PQC algorithms are used to achieve security properties as these modes are important during the transition period. We also share our experience with implementing PQ-SPDM and provide benchmarks for some of the winning NIST PQC algorithms.

We propose a practical sublinear-size zero-knowledge proof system for Rank-1 Constraint Satisfaction (R1CS) based on lattices. The proof size scales asymptotically with the square root of the witness size. Concretely, the size becomes $2$-$3$ times smaller than Ligero (ACM CCS 2017), which also exhibits square root scaling, for large instances of R1CS. At the core lies an interactive variant of the Schwartz-Zippel Lemma that might be of independent interest.

In this work, we study perfectly-secure multi-party computation (MPC) against general (non-threshold) adversaries. Known protocols in a synchronous network are secure against $Q^{(3)}$ adversary structures, while in an asynchronous network, known protocols are secure against $Q^{(4)}$ adversary structures. A natural question is whether there exists a single protocol which remains secure against $Q^{(3)}$ and $Q^{(4)}$ adversary structures in a synchronous and in an asynchronous network respectively, where the parties are not aware of the network type. We design the first such best-of-both-worlds protocol against general adversaries. Our result generalizes the result of Appan, Chandramouli and Choudhury (PODC 2022), which presents a best-of-both-worlds perfectly-secure protocol against threshold adversaries. To design our protocol, we present two important building blocks which are of independent interest. The first building block is a best-of-both-worlds perfectly-secure Byzantine agreement (BA) protocol for $Q^{(3)}$ adversary structures, which remains secure both in a synchronous, as well as an asynchronous network. The second building block is a best-of-both-worlds perfectly-secure verifiable secret-sharing (VSS) protocol, which remains secure against $Q^{(3)}$ and $Q^{(4)}$ adversary structures in a synchronous network and an asynchronous network respectively.

A multi-message multi-recipient PKE (mmPKE) encrypts a batch of messages, in one go, to a corresponding set of independently chosen receiver public keys. The resulting "multi-recipient ciphertext" can be then be reduced (by any 3rd party) to a shorter, receiver specific, "invidual ciphertext". Finally, to recover the $i$-th message in the batch from their indvidual ciphertext the $i$-th receiver only needs their own decryption key. A special case of mmPKE is multi-recipient PKE where all receivers are sent the same message. By treating (m)mPKE and their KEM counterparts as a stand-alone primitives we allow for more efficient constructions than trivially composing individual PKE/KEM instances. This is especially valuable in the post-quantum setting, where PKE/KEM ciphertexts and public keys tend to be far larger than their classic counterparts. In this work we describe a collection of new results around batched KEMs and PKE. We provide both classic and post-quantum proofs for all results. Our results are geared towards practical constructions and applications (for example in the domain of PQ-secure group messaging). Concretely, our results include a new non-adaptive to adaptive compiler for CPA-secure mKEMs resulting in public keys roughly half the size of the previous state-of-the-art [Hashimoto et.al., CCS'21]. We also prove their FO transform for mKEMs to be secure in the quantum random oracle model. We provide the first mKEM combiner as well as two mmPKE constructions. The first is an arbitrary message-length black-box construction from an mKEM (e.g. one produced by combining a PQ with a classic mKEM). The second is optimized for short messages and achieves hybrid PQ/classic security more directly. When encrypting $n$ short messages (e.g. as in several recent mmPKE applications) at 256-bits of security the mmPKE ciphertext are $144 n$ bytes shorter than the generic construction. Finally, we provide an optimized implementation of the (CCA secure) mKEM construction based on the NIST PQC winner Kyber and report benchmarks showing a significant speedup for batched encapsulation and up to 79% savings in ciphertext size compared to a naive solution.

Verifiable random functions (Micali et al., FOCS'99) allow a key-pair holder to verifiably evaluate a pseudorandom function under that particular key pair. These primitives enable fair and verifiable pseudorandom lotteries, essential in proof-of-stake blockchains such as Algorand and Cardano, and are being used to secure billions of dollars of capital. As a result, there is an ongoing IRTF effort to standardize VRFs, with a proposed ECVRF based on elliptic-curve cryptography appearing as the most promising candidate. In this work, towards understanding the general security of VRFs and in particular the ECVRF construction, we provide an ideal functionality in the Universal Composability (UC) framework (Canetti, FOCS'01) that captures VRF security, and show that ECVRF UC-realizes this functionality. We further show how the range of a VRF can generically be extended in a modular fashion based on the above functionality. This observation is particularly useful for protocols such as Ouroboros since it allows to reduce the number of VRF evaluations (per slot) and VRF verifications (per block) from two to one at the price of additional (but much faster) hash-function evaluations. Finally, we study batch verification in the context of VRFs. We provide a UC-functionality capturing a VRF with batch-verification capability, and propose modifications to ECVRF that allow for this feature. We again prove that our proposal UC-realizes the desired functionality. We provide a performance analysis showing that verification can yield a factor-two speedup for batches with 1024 proofs, at the cost of increasing the proof size from 80 to 128 bytes.

Many online applications, such as online file backup services, support the sharing of indexed data between a set of devices. These systems may offer client-side encryption of the data, so that the stored data is inaccessible to the online host. A potentially desirable goal in this setting would be to protect not just the contents of the backed-up files, but also their identifiers. However, as these identifiers are typically used for indexing, a deterministic consistent mapping across devices is necessary. Additionally, in a multi-device setting, it may be desirable to maintain an ability to revoke a device’s access—e.g. through rotating encryption keys for new data. We present a new primitive, called the Oblivious Revocable Function (ORF), which operates in the above setting and allows identifiers to be obliviously mapped to a consistent value across multiple devices, while enabling the server to permanently remove an individual device’s ability to map values. This permits a stronger threat model against metadata, in which metadata cannot be derived from identifiers by a revoked device colluding with the service provider, so long as the service provider was honest at the instant of revocation. We describe a simple Diffie- Hellman-based construction that achieves ORFs and provide a proof of security under the UC framework.

We present experimental findings on the decoding failure rate (DFR) of BIKE, a fourth-round candidate in the NIST Post-Quantum Standardization process, at the 20-bit security level. We select parameters according to BIKE design principles and conduct a series of experiments. We directly compute the average DFR on a range of BIKE block sizes and identify both the waterfall and error floor regions of the DFR curve. We then study the influence on the average DFR of three sets $\mathcal{C}$, $\mathcal{N}$, and $2\mathcal{N}$ of near-codewords --- vectors of low weight that induce syndromes of low weight --- defined by Vasseur in 2021. We find that error vectors leading to decoding failures have small maximum support intersection with elements of these sets; further, the distribution of intersections is quite similar to that of sampling random error vectors and counting the intersections with $\mathcal{C}$, $\mathcal{N}$, and $2\mathcal{N}$. Our results indicate that these three sets are not sufficient in classifying vectors expected to cause decoding failures. Finally, we study the role of syndrome weight on the decoding behavior and conclude that the set of error vectors that lead to decoding failures differ from random vectors by having low syndrome weight.

Lightweight cryptography is characterized by the need for low implementation cost, while still providing sufficient security. This requires careful analysis of building blocks and their composition. SKINNY is an ISO/IEC standardized family of tweakable block ciphers and is used in the NIST lightweight cryptography standardization process finalist Romulus. We present non-trivial linear approximations of two- round SKINNY that have correlation one or minus one and that hold for a large fraction of all round tweakeys. Moreover, we show how these could have been avoided.

This note discusses lattice-based cryptography over the field with $p= 2^{64} - 2^{32} + 1$ elements, with an eye to supporting lattice-based cryptography operations in virtual machines such as Miden VM that operate natively over this field. It discusses how to support Dilithium and Falcon, two lattice-based signature scheme recently selected by the NIST PQC project; and proposes parameters for efficient public key encryption and publicly re-randomizable commitments modulo $p$.

The emergence of distributed digital currencies has raised the need for a reliable consensus mechanism. In proof-of-stake cryptocur- rencies, the participants periodically choose a closed set of validators, who can vote and append transactions to the blockchain. Each valida- tor can become a leader with the probability proportional to its stake. Keeping the leader private yet unique until it publishes a new block can significantly reduce the attack vector of an adversary and improve the throughput of the network. The problem of Single Secret Leader Election (SSLE) was first formally defined by Boneh et al. in 2020. In this work, we propose a novel framework for constructing SSLE proto- cols, which relies on secure multi-party computation (MPC) and satisfies the desired security properties. Our framework does not use any shuffle or sort operations and has a computational cost for N parties as low as O(N) of basic MPC operations per party. We improve the state-of-the- art for SSLE protocols that do not assume a trusted setup. Moreover, our SSLE scheme efficiently handles weighted elections. That is, for a total weight S of N parties, the associated costs are only increased by a factor of logS. When the MPC layer is instantiated with techniques based on Shamir’s secret-sharing, our SSLE has a communication cost of O(N2) which is spread over O(log N) rounds, can tolerate up to t < N/2 of faulty nodes without restarting the protocol, and its security relies on DDH in the random oracle model. When the MPC layer is instantiated with more efficient techniques based on garbled circuits, our SSLE re- quires all parties to participate, up to N − 1 of which can be malicious, and its security is based on the random oracle model.

Can we hope to provide provable security against model extraction attacks? As a step towards a theoretical study of this question, we unify and abstract a wide range of "observational" model extraction defenses (OMEDs) --- roughly, those that attempt to detect model extraction by analyzing the distribution over the adversary's queries. To accompany the abstract OMED, we define the notion of complete OMEDs --- when benign clients can freely interact with the model --- and sound OMEDs --- when adversarial clients are caught and prevented from reverse engineering the model. Our formalism facilitates a simple argument for obtaining provable security against model extraction by complete and sound OMEDs, using (average-case) hardness assumptions for PAC-learning, in a way that abstracts current techniques in the prior literature. The main result of this work establishes a partial computational incompleteness theorem for the OMED: any efficient OMED for a machine learning model computable by a polynomial size decision tree that satisfies a basic form of completeness cannot satisfy soundness, unless the subexponential Learning Parity with Noise (LPN) assumption does not hold. To prove the incompleteness theorem, we introduce a class of model extraction attacks called natural Covert Learning attacks based on a connection to the Covert Learning model of Canetti and Karchmer (TCC '21), and show that such attacks circumvent any defense within our abstract mechanism in a black-box, nonadaptive way. As a further technical contribution, we extend the Covert Learning algorithm of Canetti and Karchmer to work over any "concise" product distribution (albeit for juntas of a logarithmic number of variables rather than polynomial size decision trees), by showing that the technique of learning with a distributional inverter of Binnendyk et al. (ALT '22) remains viable in the Covert Learning setting.

We show that we can break SIDH in classical polynomial time, even with a random starting curve $E_0$.

This work presents RPM, a scalable anonymous communication protocol suite using secure multiparty computation (MPC) with the offline-online model. We generate random, unknown permutation matrices in a secret-shared fashion and achieve improved (online) performance and the lightest communication and computation overhead for the clients compared to the state of art robust anonymous communication protocols. Using square-lattice shuffling, we make our protocol scale well as the number of clients increases. We provide three protocol variants, each targeting different input volumes and MPC frameworks/libraries. Besides, due to the modular design, our protocols can be easily generalized to support more MPC functionalities and security properties as they get developed. We also illustrate how to generalize our protocols to support two-way anonymous communication and secure sorting. We have implemented our protocols using the MP-SPDZ library suit and the benchmark illustrates that our protocols achieve unprecedented online phase performance with practical offline phases.

Multi-signatures are protocols that allow a group of signers to jointly produce a single signature on the same message. In recent years, a number of practical multi-signature schemes have been proposed in the discrete-log setting, such as MuSigT (CRYPTO'21) and DWMS (CRYPTO'21). The main technical challenge in constructing a multi-signature scheme is to achieve a set of several desirable properties, such as (1) security in the plain public-key (PPK) model, (2) concurrent security, (3) low online round complexity, and (4) key aggregation. However, previous lattice-based, post-quantum counterparts to Schnorr multi-signatures fail to satisfy these properties. In this paper, we introduce MuSigL, a lattice-based multi-signature scheme simultaneously achieving these design goals for the first time. Unlike the recent, round-efficient proposal of Damgård et al. (PKC'21), which had to rely on lattice-based trapdoor commitments, we do not require any additional primitive in the protocol, while being able to prove security from the standard module-SIS and LWE assumptions. The resulting output signature of our scheme therefore looks closer to the usual Fiat--Shamir-with-abort signatures.

Secure multiparty computation can often utilize a trusted source of correlated randomness to achieve better efficiency. A recent line of work, initiated by Boyle et al. (CCS 2018, Crypto 2019), showed how useful forms of correlated randomness can be generated using a cheap, one-time interaction, followed by only "silent" local computation. This is achieved via a pseudorandom correlation generator (PCG), a deterministic function that stretches short correlated seeds into long instances of a target correlation. Previous works constructed concretely efficient PCGs for simple but useful correlations, including random oblivious transfer and vector-OLE, together with efficient protocols to distribute the PCG seed generation. Most of these constructions were based on variants of the Learning Parity with Noise (LPN) assumption. PCGs for other useful correlations had poor asymptotic and concrete efficiency. In this work, we design a new class of efficient PCGs based on different flavors of the ring-LPN assumption. Our new PCGs can generate OLE correlations, authenticated multiplication triples, matrix product correlations, and other types of useful correlations over large fields. These PCGs are more efficient by orders of magnitude than the previous constructions and can be used to improve the preprocessing phase of many existing MPC protocols.

Impossible differential (ID) cryptanalysis is one of the most important attacks on block ciphers. The Mixed Integer Linear Programming (MILP) model is a popular method to determine whether a specific difference pair is an ID. Unfortunately, due to the huge search space (approximately $2^{2n}$ for a cipher with a block size $n$ bits), we cannot leverage this technique to exhaust all difference pairs, which is a well-known long-standing problem. In this paper, we propose a systematic method to find all IDs for SPN block ciphers. The idea is to partition the whole difference pair space into lots of small disjoint sets, each of which has a representative difference pair. All difference pairs in one small set are possible if its representative pair is possible, and this can be conveniently checked by the MILP model. In this way, the overall search space is drastically reduced to a practical size by excluding the sets containing no IDs. We then examine the remaining difference pairs to identify all IDs (if some IDs exist). If our method cannot find any ID, the target cipher is proved free of ID distinguishers. Our method works especially well for SPN ciphers with block size 64. We apply our method to SKINNY-64 and successfully find all 432 and 12 truncated IDs (we find all IDs but all of them can be assembled into certain truncated IDs) for 11 and 12 rounds, respectively. We also prove, for the first time, that 13-round SKINNY-64 is free of ID distinguishers even when considering the differential transitions through the Difference Distribution Table (DDT). Similarly, we find all 12 truncated IDs (all IDs are assembled into 12 truncated IDs) for 13-round CRAFT and prove there is no ID for 14 rounds. For SbPN cipher GIFT-64, we prove that there is no ID for 8 rounds. For SPN ciphers with larger block sizes, we show that our idea is also useful to strengthen the current search methods. For example, if we consider the Sbox to be ideal and only consider the branch number information of the diffusion matrix, we can find all 6,750 truncated IDs for 6-round Rijndael-192 in 1 second and prove that there is no truncated ID for 7 rounds. Previously, we need to solve approximately $2^{48}$ MILP models to achieve the same goal. For GIFT-128, we exhausted all difference patterns that have an active superbox in the plaintext and ciphertext and proved there is no ID of such patterns for 8 rounds. Although we have searched for a larger or even full space for IDs, no longer ID distinguishers have been found. This implies the reasonableness of the intuition that a small number (usually one or two) of active bits/words at the beginning and end of an ID will be the longest.

We give characterizations of IND\$-CPA security for a large, natural class of encryption schemes. Specifically, we consider encryption algorithms that invoke a block cipher and otherwise perform linear operations (e.g., XOR and multiplication by fixed field elements) on intermediate values. This class of algorithms corresponds to the Linicrypt model of Carmer & Rosulek (Crypto 2016). Our characterization for this class of encryption schemes is sound but not complete. We then focus on a smaller subclass of block cipher modes, which iterate over the blocks of the plaintext, repeatedly applying the same Linicrypt program. For these Linicrypt block cipher modes, we are able to give a sound and complete characterization of IND\$-CPA security. Our characterization is linear-algebraic in nature and is easy to check for a candidate mode. Interestingly, we prove that a Linicrypt block cipher mode is secure if and only if it is secure against adversaries who choose all-zeroes plaintexts.

We obtain a black-box construction of non-interactive CCA commitments against non-uniform adversaries. This makes black-box use of an appropriate base commitment scheme for small tag spaces, variants of sub-exponential hinting PRG (Koppula and Waters, Crypto 2019) and variants of keyless sub-exponentially collision-resistant hash function with security against non-uniform adversaries (Bitansky, Kalai and Paneth, STOC 2018 and Bitansky and Lin, TCC 2018). All prior works on non-interactive non-malleable or CCA commitments without setup first construct a "base" scheme for a relatively small identity/tag space, and then build a tag amplification compiler to obtain commitments for an exponential-sized space of identities. Prior black-box constructions either add multiple rounds of interaction (Goyal, Lee, Ostrovsky and Visconti, FOCS 2012) or only achieve security against uniform adversaries (Garg, Khurana, Lu and Waters, Eurocrypt 2021). Our key technical contribution is a novel tag amplification compiler for CCA commitments that replaces the non-interactive proof of consistency required in prior work. Our construction satisfies the strongest known definition of non-malleability, i.e., CCA2 (chosen commitment attack) security. In addition to only making black-box use of the base scheme, our construction replaces sub-exponential NIWIs with sub-exponential hinting PRGs, which can be obtained based on assumptions such as (sub-exponential) CDH or LWE.

The Rank Decoding problem (RD) is at the core of rank-based cryptography. Cryptosystems such as ROLLO and RQC, which made it to the second round of the NIST Post-Quantum Standardization Process, as well as the Durandal signature scheme, rely on it or its variants. This problem can also be seen as a structured version of MinRank, which is ubiquitous in multivariate cryptography. Recently, [1,2] proposed attacks based on two new algebraic modelings, namely the MaxMinors modeling which is specific to RD and the Support-Minors modeling which applies to MinRank in general. Both improved significantly the complexity of algebraic attacks on these two problems. In the case of RD and contrarily to what was believed up to now, these new attacks were shown to be able to outperform combinatorial attacks and this even for very small field sizes. However, we prove here that the analysis performed in [2] for one of these attacks which consists in mixing the MaxMinors modeling with the Support-Minors modeling to solve RD is too optimistic and leads to underestimate the overall complexity. This is done by exhibiting linear dependencies between these equations and by considering an Fqm version of these modelings which turns out to be instrumental for getting a better understanding of both systems. Moreover, by working over Fqm rather than over Fq, we are able to drastically reduce the number of variables in the system and we (i) still keep enough algebraic equations to be able to solve the system, (ii) are able to analyze rigorously the complexity of our approach. This new approach may improve the older MaxMinors approach on RD from [1,2] for certain parameters. We also introduce a new hybrid approach on the Support-Minors system whose impact is much more general since it applies to any MinRank problem. This technique improves significantly the complexity of the Support-Minors approach for small to moderate field sizes. References: [1] An Algebraic Attack on Rank Metric Code-Based Cryptosystems, Bardet, Briaud, Bros, Gaborit, Neiger, Ruatta, Tillich, EUROCRYPT 2020. [2] Improvements of Algebraic Attacks for solving the Rank Decoding and MinRank problems, Bardet, Bros, Cabarcas, Gaborit, Perlner, Smith-Tone, Tillich, Verbel, ASIACRYPT 2020.

We study the problem of biometric-based authentication with template confidentiality. Typical schemes addressing this problem, such as Fuzzy Vaults (FV) and Fuzzy Extractors (FE), allow a server, aka Authenticator, to store “random looking” Helper Data (HD) instead of biometric templates in clear. HD hides information about the corresponding biometric while still enabling secure biometric-based authentication. Even though these schemes reduce the risk of storing biometric data, their correspondent authentication procedures typically require sending the HD (stored by the Authenticator) to a client who claims a given identity. The premise here is that only the identity owner - i.e., the person whose biometric was sampled to originally generate the HD - is able to provide the same biometric to reconstruct the proper cryptographic key from HD. As a side effect, the ability to freely retrieve HD, by simply claiming a given identity, allows invested adversaries to perform offline statistical attacks (a biometric analog for dictionary attacks on hashed passwords) or re-usability attacks (if the FE scheme is not reusable) on the HD to eventually recover the user’s biometric. In this work we develop Oblivious Extractors: a new construction that allows an Authenticator to authenticate a user without requiring neither the user to send a biometric to the Authenticator, nor the server to send the HD to the client. Oblivious Extractors provide concrete security advantages for biometric-based authentication systems. From the perspective of secure storage, an oblivious extractor is as secure as its non-oblivious fuzzy extractor counterpart. In addition, it enhances security against aforementioned statistical and re-usability attacks. To demonstrate the construction’s practicality, we implement and evaluate a biometric-based authentication prototype using Oblivious Extractors.

The FIDO2 protocol is a globally used standard for passwordless authentication, building on an alliance between major players in the online authentication space. While already widely deployed, the standard is still under active development. Since version 2.1 of its CTAP sub-protocol, FIDO2 can potentially be instantiated with post-quantum secure primitives. We provide the first formal security analysis of FIDO2 with the CTAP 2.1 and WebAuthn 2 sub-protocols. Our security models build on work by Barbosa et al. for their analysis of FIDO2 with CTAP 2.0 and WebAuthn 1, which we extend in several ways. First, we provide a more fine-grained security model that allows us to prove more relevant protocol properties, such as guarantees about token binding agreement, the None attestation mode, and user verification. Second, we can prove post-quantum security for FIDO2 under certain conditions and minor protocol extensions. Finally, we show that for some threat models, the downgrade resilience of FIDO2 can be improved, and show how to achieve this with a simple modification.

Verifiable Data Streaming (VDS) enables a resource-limited client to continuously outsource data to an untrusted server in a sequential manner while supporting public integrity verification and efficient update. However, most existing VDS schemes require the client to generate all proofs in advance and store them at the server, which leads to a heavy computation burden on the client. In addition, all the previous VDS schemes can perform batch query (i.e., retrieving multiple data entries at once), but are subject to linear communication cost $l$, where $l$ is the number of queried data. In this paper, we first introduce a new cryptographic primitive named Double-trapdoor Chameleon Vector Commitment (DCVC), and then present an unbounded VDS scheme $\mathsf{VDS_1}$ with optimal communication cost in the random oracle model from aggregatable cross-commitment variant of DCVC. Furthermore, we propose, to our best knowledge, the first unbounded VDS scheme $\mathsf{VDS}_2$ with optimal communication and storage overhead in the standard model by integrating Double-trapdoor Chameleon Hash Function (DCH) and Key-Value Commitment (KVC). Both of our schemes enjoy constant-size public key. Finally, we demonstrate the efficiency of our two VDS schemes with a comprehensive performance evaluation.

The Massive Parallel Computing (MPC) model gained wide adoption over the last decade. By now, it is widely accepted as the right model for capturing the commonly used programming paradigms (such as MapReduce, Hadoop, and Spark) that utilize parallel computation power to manipulate and analyze huge amounts of data. Motivated by the need to perform large-scale data analytics in a privacy-preserving manner, several recent works have presented generic compilers that transform algorithms in the MPC model into secure counterparts, while preserving various efficiency parameters of the original algorithms. The first paper, due to Chan et al. (ITCS ’20), focused on the honest majority setting. Later, Fernando et al. (TCC ’20) considered the dishonest majority setting. The latter work presented a compiler that transforms generic MPC algorithms into ones which are secure against semi-honest attackers that may control all but one of the parties involved. The security of their resulting algorithm relied on the existence of a PKI and also on rather strong cryptographic assumptions: indistinguishability obfuscation and the circular security of certain LWE-based encryption systems. In this work, we focus on the dishonest majority setting, following Fernando et al. In this setting, the known compilers do not achieve the standard security notion called malicious security, where attackers can arbitrarily deviate from the prescribed protocol. In fact, we show that unless very strong setup assumptions as made (such as a programmable random oracle), it is provably impossible to withstand malicious attackers due to the stringent requirements on space and round complexity. As our main contribution, we complement the above negative result by designing the first general compiler for malicious attackers in the dishonest majority setting. The resulting protocols withstand all-but-one corruptions. Our compiler relies on a simple PKI and a (programmable) random oracle, and is proven secure assuming LWE and SNARKs. Interestingly, even with such strong assumptions, it is rather non-trivial to obtain a secure protocol.

We present an attack on SIDH which does not require any endomorphism information on the starting curve. Our attack has subexponential complexity thus significantly reducing the security of SIDH and SIKE; our analysis and preliminary implementation suggests that our algorithm will be feasible for the Microsoft challenge parameters $p = 2^{110}3^{67}-1$ on a regular computer. Our attack applies to any isogeny-based cryptosystem that publishes the images of points under the secret isogeny, for example Seta and B-SIDH. It does not apply to CSIDH, CSI-FiSh, or SQISign.

We present the first non-interactive delegation scheme for P with time-tight parallel prover efficiency based on standard hardness assumptions. More precisely, in a time-tight delegation scheme–which we refer to as a SPARG (succinct parallelizable argument)–the prover's parallel running time is t + polylog(t), while using only polylog(t) processors and where t is the length of the computation. (In other words, the proof is computed essentially in parallel with the computation, with only some minimal additive overhead in terms of time). Our main results show the existence of a publicly-verifiable, non-interactive, SPARG for P assuming polynomial hardness of LWE. Our SPARG construction relies on the elegant recent delegation construction of Choudhuri, Jain, and Jin (FOCS'21) and combines it with techniques from Ephraim et al (EuroCrypt'20). We next demonstrate how to make our SPARG time-independent–where the prover and verifier do not need to known the running-time t in advance; as far as we know, this yields the first construction of a time-tight delegation scheme with time-independence based on any hardness assumption. We finally present applications of SPARGs to the constructions of VDFs (Boneh et al, Crypto'18), resulting in the first VDF construction from standard polynomial hardness assumptions (namely LWE and the minimal assumption of a sequentially hard function).

Motivated by several new and natural applications, we initiate the study of multi-input predicate encryption (${\sf miPE}$) and further develop multi-input attribute based encryption (${\sf miABE}$). Our contributions are: 1. Formalizing Security: We provide definitions for ${\sf miABE}$ and ${\sf miPE}$ in the {symmetric} key setting and formalize security in the standard indistinguishability (IND) paradigm, against unbounded collusions. 2. Two-input ${\sf ABE}$ for ${\sf NC}_1$ from ${\sf LWE}$ and Pairings: We provide the first constructions for two-input key-policy ${\sf ABE}$ for ${\sf NC}_1$ from ${\sf LWE}$ and pairings. Our construction leverages a surprising connection between techniques recently developed by Agrawal and Yamada (Eurocrypt, 2020) in the context of succinct single-input ciphertext-policy ${\sf ABE}$, to the seemingly unrelated problem of two-input key-policy ${\sf ABE}$. Similarly to Agrawal-Yamada, our construction is proven secure in the bilinear generic group model. By leveraging inner product functional encryption and using (a variant of) the KOALA knowledge assumption, we obtain a construction in the standard model analogously to Agrawal, Wichs and Yamada (TCC, 2020). 3. Heuristic two-input ${\sf ABE}$ for ${\sf P}$ from Lattices: We show that techniques developed for succinct single-input ciphertext-policy ${\sf ABE}$ by Brakerski and Vaikuntanathan (ITCS 2022) can also be seen from the lens of ${\sf miABE}$ and obtain the first two-input key-policy ${\sf ABE}$ from lattices for ${\sf P}$. 4. Heuristic three-input ${\sf ABE}$ and ${\sf PE}$ for ${\sf NC}_1$ from Pairings and Lattices: We obtain the first three-input ${\sf ABE}$ for ${\sf NC}_1$ by harnessing the powers of both the Agrawal-Yamada and the Brakerski-Vaikuntanathan constructions. 5. Multi-input ${\sf ABE}$ to multi-input ${\sf PE}$ via Lockable Obfuscation: We provide a generic compiler that lifts multi-input ${\sf ABE}$ to multi-input ${\sf PE}$ by relying on the hiding properties of Lockable Obfuscation (${\sf LO}$) by Wichs-Zirdelis and Goyal-Koppula-Waters (FOCS 2018), which can be based on ${\sf LWE}$. Our compiler generalizes such a compiler for single-input setting to the much more challenging setting of multiple inputs. By instantiating our compiler with our new two and three-input ${\sf ABE}$ schemes, we obtain the first constructions of two and three-input ${\sf PE}$ schemes. Our constructions of multi-input ${\sf ABE}$ provide the first improvement to the compression factor of non-trivially exponentially efficient Witness Encryption defined by Brakerski et al. (SCN 2018) without relying on compact functional encryption or indistinguishability obfuscation. We believe that the unexpected connection between succinct single-input ciphertext-policy ${\sf ABE}$ and multi-input key-policy ${\sf ABE}$ may lead to a new pathway for witness encryption.

The offline-online model is a leading paradigm for practical secure multi-party computation (MPC) protocol design that has successfully reduced the overhead for several prevalent privacy-preserving computation functionalities common to diverse application domains. However, the prohibitive overheads associated with secure comparison -- one of these vital functionalities -- often bottlenecks current and envisioned MPC solutions. Indeed, an efficient secure comparison solution has the potential for significant real-world impact through its broad applications. This work identifies and presents SIM, a secure protocol for the functionality of interval membership testing. This security functionality, in particular, facilitates secure less-than-zero testing and, in turn, secure comparison. A key technical challenge is to support a fast online protocol for testing in large rings while keeping the precomputation tractable. Motivated by the map-reduce paradigm, this work introduces the innovation of (1) computing a sequence of intermediate functionalities on a partition of the input into input blocks and (2) securely aggregating the output from these intermediate outputs. This innovation allows controlling the size of the precomputation through a granularity parameter representing these input blocks' size -- enabling application-specific automated compiler optimizations. To demonstrate our protocols' efficiency, we implement and test their performance in a high-demand application: privacy-preserving machine learning. The benchmark results show that switching to our protocols yields significant performance improvement, which indicates that using our protocol in a plug-and-play fashion can improve the performance of various security applications. Our new paradigm of protocol design may be of independent interest because of its potential for extensions to other functionalities of practical interest.

The security of the post-quantum signature scheme Picnic is highly related to the difficulty of recovering the secret key of LowMC from a single plaintext-ciphertext pair. Since Picnic is one of the alternate third-round candidates in NIST post-quantum cryptography standardization process, it has become urgent and important to evaluate the security of LowMC in the Picnic setting. The best attacks on LowMC with full S-box layers used in Picnic3 were achieved with Dinur's algorithm. For LowMC with partial nonlinear layers, e.g. 10 S-boxes per round adopted in Picnic2, the best attacks on LowMC were published by Banik et al. with the meet-in-the-middle (MITM) method. In this paper, we improve the attacks on LowMC in a model where memory consumption is costly. First, a new attack on 3-round LowMC with full S-box layers with negligible memory complexity is found, which can outperform Bouillaguet et al.'s fast exhaustive search attack and can achieve better time-memory tradeoffs than Dinur's algorithm. Second, we extend the 3-round attack to 4 rounds to significantly reduce the memory complexity of Dinur's algorithm at the sacrifice of a small factor of time complexity. For LowMC instances with 1 S-box per round, our attacks are shown to be much faster than the MITM attacks. For LowMC instances with 10 S-boxes per round, we can reduce the memory complexity from 32GB ($2^{38}$ bits) to only 256KB ($2^{21}$ bits) using our new algebraic attacks rather than the MITM attacks, while the time complexity of our attacks is about $2^{3.2}\sim 2^{5}$ times higher than that of the MITM attacks. A notable feature of our new attacks (apart from the 4-round attack) is their simplicity. Specifically, only some basic linear algebra is required to understand them and they can be easily implemented.

For a group $\mathbb{G}$ of unknown order, a *Proof of Exponentiation* (PoE) allows a prover to convince a verifier that a tuple $(y,x,q,T)\in \mathbb{G}^2\times\mathbb{N}^2$ satisfies $y=x^{q^T}$. PoEs have recently found exciting applications in constructions of verifiable delay functions and succinct arguments of knowledge. The current PoEs that are practical in terms of proof-size only provide restricted soundness guarantees: Wesolowski's protocol (Journal of Cryptology 2020) is only computationally-sound (i.e., it is an argument), whereas Pietrzak's protocol (ITCS 2019) is statistically-sound only in groups that come with the promise of not having any small subgroups. On the other hand, the only statistically-sound PoE in *arbitrary* groups of unknown order is due to Block et al. (CRYPTO 2021), and it can be seen as an elaborate parallel repetition of Pietrzak's PoE. Therefore, to achieve $\lambda$ bits of security, say $\lambda=80$, the number of repetitions required -- and hence the (multiplicative) overhead incurred in proof-size -- is as large as $\lambda$. In this work, we propose a statistically-sound PoE for arbitrary groups for the case where the exponent $q$ is the product of all primes up to some bound $B$. For such a structured exponent, we show that it suffices to run only $\lambda/\log(B)$ parallel instances of Pietrzak's PoE. This reduces the concrete proof-size compared to Block et al. by an order of magnitude. Furthermore, we show that in the known applications where PoEs are used as a building block such structured exponents are viable. Finally, we also discuss batching of our PoE, showing that many proofs (for the same $\mathbb{G}$ and $q$ but different $x$ and $T$) can be batched by adding only a single element to the proof per additional statement.

We present an attack on Ethereum's consensus mechanism which can be used by miners to obtain consistently higher mining rewards compared to the honest protocol. This attack is novel in that it does not entail withholding blocks or any behavior which has a non-zero probability of earning less than mining honestly, in contrast with the existing literature. This risk-less attack relies instead on manipulating block timestamps, and carefully choosing whether and when to do so. We present this attack as an algorithm, which we then analyze to evaluate the revenue a miner obtains from it, and its effect on a miner's absolute and relative share of the main-chain blocks. The attack allows an attacker to replace competitors' main-chain blocks after the fact with a block of its own, thus causing the replaced block's miner to lose all transactions fees for the transactions contained within the block, which will be demoted from the main-chain. This block, although ``kicked-out'' of the main-chain, will still be eligible to be referred to by other main-chain blocks, thus becoming what is commonly called in Ethereum an uncle. We proceed by defining multiple variants of this attack, and assessing whether any of these attacks has been performed in the wild. Surprisingly, we find that this is indeed true, making this the first case of a confirmed consensus-level manipulation performed on a major cryptocurrency. Additionally, we implement a variant of this attack as a patch for geth, Ethereum's most popular client, making it the first consensus-level attack on Ethereum which is implemented as a patch. Finally, we suggest concrete fixes for Ethereum's protocol and implemented them as a patch for geth which can be adopted quickly and mitigate the attack and its variants.

Isogeny-based cryptography is one of the candidates for post-quantum cryptography. SIDH is a compact and efficient isogeny-based key exchange, and SIKE, which is the SIDH-based key encapsulation mechanism, remains the NIST PQC Round 4. However, by the brilliant attack provided by Castryck and Decru, the original SIDH is broken in polynomial time (with heuristics). To break the original SIDH, there are three important pieces of information in the public key: information about the endomorphism ring of a starting curve, some image points under a cyclic hidden isogeny, and the degree of the isogeny. In this paper, we proposed the new isogeny-based scheme named \textit{masked-degree SIDH}. This scheme is the variant of SIDH that masks most information about degrees of hidden isogenies, and the first trial against Castryck--Decru attack. The main idea to cover degrees is to use many primes to compute isogenies that allow the degree to be more flexible. Though the size of the prime $p$ for this scheme is slightly larger than that of SIDH, this scheme resists current attacks using degrees of isogenies like the attack of Castryck and Decru. The most effective attack for masked-degree SIDH has $\tilde{O}(p^{1/(8\log_2{(\log_2{p})})})$ time complexity with classical computers and $\tilde{O}(p^{1/(16\log_2{(\log_2{p})})})$ time complexity with quantum computers in our analysis.

In this work we propose time-deniable signatures (TDS), a new primitive that facilitates deniable authentication in protocols such as DKIM-signed email. As with traditional signatures, TDS provide strong authenticity for message content, at least for a sender-chosen period of time. Once this time period has elapsed, however, time-deniable signatures can be forged by any party who obtains a signature. This forgery property ensures that signatures serve a useful authentication purpose for a bounded time period, while also allowing signers to plausibly disavow the creation of older signed content. Most critically, and unlike many past proposals for deniable authentication, TDS do not require interaction with the receiver or the deployment of any persistent cryptographic infrastructure or services beyond the signing process (e.g., APIs to publish secrets or author timestamp certificates.) We first investigate the security definitions for time-deniability, demonstrating that past definitional attempts are insufficient (and indeed, allow for broken signature schemes.) We then propose an efficient construction of TDS based on well-studied assumptions.

We investigate how users of instant messaging (IM) services can acquire strong encryption keys to back up their messages and media with strong cryptographic guarantees. Many IM users regularly change their devices and use multiple devices simultaneously, ruling out any long-term secret storage. Extending the end-to-end encryption guarantees from just message communication to also incorporate backups has so far required either some trust in an IM or outsourced storage provider, or use of costly third-party encryption tools with unclear security guarantees. Recent works have proposed solutions for password-protected key material, however all require one or more servers to generate and/or store per-user information, inevitably invoking a cost to the users. We define distributed key acquisition (DKA) as the primitive for the task at hand, where a user interacts with one or more servers to acquire a strong cryptographic key, and both user and server are required to store as little as possible. We present a construction framework that we call PERKS---Password-based Establishment of Random Keys for Storage---providing efficient, modular and simple protocols that utilize Oblivious Pseudorandom Functions (OPRFs) in a distributed manner with minimal storage by the user (just the password) and servers (a single global key for all users). Along the way we introduce a formal treatment of DKA, and provide proofs of security for our constructions in their various flavours. Our approach enables key rotation by the OPRF servers, and for this we incorporate updatable encryption. Finally, we show how our constructions fit neatly with recent research on encrypted outsourced storage to provide strong security guarantees for the outsourced ciphertexts.

Public key encryption with keyword search (PEKS) inherently suffers from the inside keyword guessing attack. To resist against this attack, Huang et al. proposed the public key authenticated encryption with keyword search (PAEKS), where the sender not only encrypts a keyword, but also authenticates it. To further resist against quantum attacks, Liu et al. proposed a generic construction of PAEKS and the first quantum-resistant PAEKS instantiation based on lattices. Later, Emura pointed out some issues in Liu et al.'s construction and proposed a new generic construction of PAEKS. The basic construction methodology of Liu et al. and Emura is the same, i.e., each keyword is converted into an extended keyword using the shared key calculated by a word-independent smooth projective hash functions (SPHF), and PEKS is used for the extended keyword. In this paper, we first analyze the schemes of Liu et al. and Emura, and point out some issues regarding their construction and security model. In short, in their lattice-based instantiations, the sender and receiver use a lattice-based word independent SPHF to compute the same shared key to authenticate keywords, leading to a super-polynomial modulus $q$; their generic constructions need a trusted setup assumption or the designated-receiver setting; Liu et al. failed to provide convincing evidence that their scheme satisfies their claimed security. Then, we propose two new lattice-based PAEKS schemes with totally different construction methodology from Liu et al. and Emura. Specifically, in our PAEKS schemes, instead of using the shared key calculated by SPHF, the sender and receiver achieve keyword authentication by using their own secret key to sample a set of short vectors related to the keyword. In this way, the modulus $q$ in our schemes could be of polynomial size, which results in much smaller size of the public key, ciphertext and trapdoor. In addition, our schemes need neither a trusted setup assumption nor the designated-receiver setting. Finally, our schemes can be proven secure in stronger security model, and thus provide stronger security guarantee for both ciphertext privacy and trapdoor privacy.

In this paper, we provide new quantum cryptanalysis results on 5 rounds (balanced) Feistel schemes and on Benes schemes. More precisely, we give an attack on 5 rounds Feistel schemes in $\Theta(2^{2n/3})$ quantum complexity and an attack on Benes schemes in $\Theta(2^{2n/3})$ quantum complexity, where n is the number of bits of the internel random functions.

A pseudorandom correlation generator (PCG) is a recent tool for securely generating useful sources of correlated randomness, such as random oblivious transfers (OT) and vector oblivious linear evaluations (VOLE), with low communication cost. We introduce a simple new design for PCGs based on so-called expand-accumulate codes, which first apply a sparse random expander graph to replicate each message entry, and then accumulate the entries by computing the sum of each prefix. Our design offers the following advantages compared to state-of-the-art PCG constructions: - Competitive concrete efficiency backed by provable security against relevant classes of attacks; - An offline-online mode that combines near-optimal cache-friendliness with simple parallelization; - Concretely efficient extensions to pseudorandom correlation functions, which enable incremental generation of new correlation instances on demand, and to new kinds of correlated randomness that include circuit-dependent correlations. To further improve the concrete computational cost, we propose a method for speeding up a full-domain evaluation of a puncturable pseudorandom function (PPRF). This is independently motivated by other cryptographic applications of PPRFs.

In this article, we tackle for the first time the problem of dynamic memory-efficient Searchable Symmetric Encryption (SSE). In the term "memory-efficient" SSE, we encompass both the goals of local SSE, and page-efficient SSE. The centerpiece of our approach is a new connection between those two goals. We introduce a map, called the Generic Local Transform, which takes as input a page-efficient SSE scheme with certain special features, and outputs an SSE scheme with strong locality properties. We obtain several results. 1. First, we build a dynamic SSE scheme with storage efficiency $O(1)$ and page efficiency only $\tilde{O}(\log \log (N/p))$, where $p$ is the page size, called LayeredSSE. The main technique behind LayeredSSE is a new weighted extension of the two-choice allocation process, of independent interest. 2. Second, we introduce the Generic Local Transform, and combine it with LayeredSSE to build a dynamic SSE scheme with storage efficiency $O(1)$, locality $O(1)$, and read efficiency $\tilde{O}(\log\log N)$, under the condition that the longest list is of size $O(N^{1-1/\log \log \lambda})$. This matches, in every respect, the purely static construction of Asharov et al. from STOC 2016: dynamism comes at no extra cost. 3. Finally, by applying the Generic Local Transform to a variant of the Tethys scheme by Bossuat et al. from Crypto 2021, we build an unconditional static SSE with storage efficiency $O(1)$, locality $O(1)$, and read efficiency $O(\log^\varepsilon N)$, for an arbitrarily small constant $\varepsilon > 0$. To our knowledge, this is the construction that comes closest to the lower bound presented by Cash and Tessaro at Eurocrypt 2014.

We analyze nonce-misuse resilience (NMRL) security of Romulus-N and GIFT-COFB, the two finalists of NIST Lightweight Cryptography project for standardizing lightweight authenticated encryption. NMRL, introduced by Ashur et al. at CRYPTO 2017, is a relaxed security notion from a stronger, nonce-misuse resistance notion. We proved that Romulus-N and GIFT-COFB have nonce-misuse resilience. For Romulus-N, we showed the perfect privacy (NMRL-PRIV) and n/2-bit authenticity (NMRL-AUTH) with graceful degradation with respect to nonce repetition. For GIFT-COFB, we showed n/4-bit security for both NMRL-PRIV and NMRL-AUTH notions.

In two-party private set intersection (PSI), Alice holds a set $X$, Bob holds a set $Y$, and they learn (only) the contents of $X \cap Y$. We introduce structure-aware PSI protocols, which take advantage of situations where Alice's set $X$ is publicly known to have a certain structure. The goal of structure-aware PSI is to have communication that scales with the description size of Alice's set, rather its cardinality. We introduce a new generic paradigm for structure-aware PSI based on function secret-sharing (FSS). In short, if there exists compact FSS for a class of structured sets, then there exists a semi-honest PSI protocol that supports this class of input sets, with communication cost proportional only to the FSS share size. Several prior protocols for efficient (plain) PSI can be viewed as special cases of our new paradigm, with an implicit FSS for unstructured sets. Our PSI protocol can be instantiated from a significantly weaker flavor of FSS, which has not been previously studied. We develop several improved FSS techniques that take advantage of these relaxed requirements, and which are in some cases exponentially better than existing FSS. Finally, we explore in depth a natural application of structure-aware PSI. If Alice's set $X$ is the union of many radius-$\delta$ balls in some metric space, then an intersection between $X$ and $Y$ corresponds to fuzzy PSI, in which the parties learn which of their points are within distance $\delta$. In structure-aware PSI, the communication cost scales with the number of balls in Alice's set, rather than their total volume. Our techniques lead to efficient fuzzy PSI for $\ell_\infty$ and $\ell_1$ metrics (and approximations of $\ell_2$ metric) in high dimensions. We implemented this fuzzy PSI protocol for 2-dimensional $\ell_\infty$ metrics. For reasonable input sizes, our protocol requires 45--60% less time and 85% less communication than competing approaches that simply reduce the problem to plain PSI.

Zero-knowledge proof is a powerful cryptographic primitive that has found various applications in the real world. However, existing schemes with succinct proof size suffer from a high overhead on the proof generation time that is super-linear in the size of the statement represented as an arithmetic circuit, limiting their efficiency and scalability in practice. In this paper, we present Orion, a new zero-knowledge argument system that achieves $O(N)$ prover time of field operations and hash functions and $O(\log^2 N)$ proof size. Orion is concretely efficient and our implementation shows that the prover time is 3.09s and the proof size is 1.5MB for a circuit with $2^{20}$ multiplication gates. The prover time is the fastest among all existing succinct proof systems, and the proof size is an order of magnitude smaller than a recent scheme proposed in Golovnev et al. 2021. In particular, we develop two new techniques leading to the efficiency improvement. (1) We propose a new algorithm to test whether a random bipartite graph is a lossless expander graph or not based on the small set expansion problem. It allows us to sample lossless expanders with an overwhelming probability. The technique improves the efficiency and/or security of all existing zero-knowledge argument schemes with a linear prover time. (2) We develop an efficient proof composition scheme, code switching, to reduce the proof size from square root to polylogarithmic in the size of the computation. The scheme is built on the encoding circuit of a linear code and shows that the witness of a second zero-knowledge argument is the same as the message in the linear code. The proof composition only introduces a small overhead on the prover time.

Sponge hashing is a novel alternative to the popular Merkle-Damgård hashing design. The sponge construction has become increasingly popular in various applications, perhaps most notably, it underlies the SHA-3 hashing standard. Sponge hashing is parametrized by two numbers, $r$ and $c$ (bitrate and capacity, respectively), and by a fixed-size permutation on $r+c$ bits. In this work, we study the collision resistance of sponge hashing instantiated with a random permutation by adversaries with arbitrary $S$-bit auxiliary advice input about the random permutation that make $T$ online queries. Recent work by Coretti et al. (CRYPTO '18) showed that such adversaries can find collisions (with respect to a random $c$-bit initialization vector) with advantage $\Theta(ST^2/2^c + T^2/ 2^{r})$. Although the above attack formally breaks collision resistance in some range of parameters, its practical relevance is limited since the resulting collision is very long (on the order of $T$ blocks). Focusing on the task of finding short collisions, we study the complexity of finding a $B$-block collision for a given parameter $B\ge 1$. We give several new attacks and limitations. Most notably, we give a new attack that results in a single-block collision and has advantage $$ \Omega \left(\left(\frac{S^{2}T}{2^{2c}}\right)^{2/3} + \frac{T^2}{2^r}\right). $$ In certain range of parameters (e.g., $ST^2>2^c$), our attack outperforms the previously-known best attack. To the best of our knowledge, this is the first natural application for which sponge hashing is provably less secure than the corresponding instance of Merkle-Damgård hashing. Our attack relies on a novel connection between single-block collision finding in sponge hashing and the well-studied function inversion problem. We also give a general attack that works for any $B\ge 2$ and has advantage $\Omega({STB}/{2^{c}} + {T^2}/{2^{\min\{r,c\}}})$, adapting an idea of Akshima et al. (CRYPTO '20). We complement the above attacks with bounds on the best possible attacks. Specifically, we prove that there is a qualitative jump in the advantage of best possible attacks for finding unbounded-length collisions and those for finding very short collisions. Most notably, we prove (via a highly non-trivial compression argument) that the above attack is optimal for $B=2$ in some range of parameters.

We introduce Multimodal Private Signature (MPS) - an anonymous signature system that offers a novel accountability feature: it allows a designated opening authority to learn some partial information $\mathsf{op}$ about the signer's identity $\mathsf{id}$, and nothing beyond. Such partial information can flexibly be defined as $\mathsf{op} = \mathsf{id}$ (as in group signatures), or as $\mathsf{op} = \mathbf{0}$ (like in ring signatures), or more generally, as $\mathsf{op} = G_j(\mathsf{id})$, where $G_j(\cdot)$ is a certain disclosing function. Importantly, the value of $\mathsf{op}$ is known in advance by the signer, and hence, the latter can decide whether she/he wants to disclose that piece of information. The concept of MPS significantly generalizes the notion of tracing in traditional anonymity-oriented signature primitives, and can enable various new and appealing privacy-preserving applications. We formalize the definitions and security requirements for MPS. We next present a generic construction to demonstrate the feasibility of designing MPS in a modular manner and from commonly used cryptographic building blocks (ordinary signatures, public-key encryption and NIZKs). We also provide an efficient construction in the standard model based on pairings, and a lattice-based construction in the random oracle model.

We initiate research into efficiently embedding probabilistic computations in probabilistic proofs by introducing techniques for capturing Monte Carlo methods and Las Vegas algorithms in zero knowledge and exploring several potential applications of these techniques. We design and demonstrate a technique for proving the integrity of certain randomized computations, such as uncertainty quantification methods, in non-interactive zero knowledge (NIZK) by replacing conventional randomness with low-discrepancy sequences. This technique, known as the Quasi-Monte Carlo (QMC) method, functions as a form of weak algorithmic derandomization to efficiently produce adversarial-resistant worst-case uncertainty bounds for the results of Monte Carlo simulations. The adversarial resistance provided by this approach allows the integrity of results to be verifiable both in interactive and non-interactive zero knowledge without the need for additional statistical or cryptographic assumptions. To test these techniques, we design a custom domain specific language and implement an associated compiler toolchain that builds zkSNARK gadgets for expressing QMC methods. We demonstrate the power of this technique by using this framework to benchmark zkSNARKs for various examples in statistics and physics. Using $N$ samples, our framework produces zkSNARKs for numerical integration problems of dimension $d$ with $O\left(\frac{(\log N)^d}{N}\right)$ worst-case error bounds. Additionally, we prove a new result using discrepancy theory to efficiently and soundly estimate the output of computations with uncertain data with an $O\left(d\frac{\log N}{\sqrt[d]{N}}\right)$ worst-case error bound. Finally, we show how this work can be applied more generally to allow zero-knowledge proofs to capture a subset of decision problems in $\mathsf{BPP}$, $\mathsf{RP}$, and $\mathsf{ZPP}$.

Two-factor authentication(2FA)schemes that rely on a combination of knowledge factors (e.g., PIN) and device possession have gained popularity. Some of these schemes remain secure even against strong adversaries that (a) observe the traffic between a client and server, and (b) have physical access to the client’s device, or its PIN, or breach the server. However, these solutions have several shortcomings; namely, they (i) require a client to remember multiple secret values to prove its identity, (ii) involve several modular exponentiations, and (iii) are in the non-standard random oracle model. In this work, we present a 2FA protocol that resists such a strong adversary while addressing the above shortcomings. Our protocol requires a client to remember only a single secret value/PIN, does not involve any modular exponentiations, and is in a standard model. It is the first one that offers these features without using trusted chipsets. This protocol also imposes up to 40% lower communication overhead than the state-of-the-art solutions do.