All papers (21124 results)

Last updated:  2023-11-28
Key Exchange in the Post-Snowden Era: UC Secure Subversion-Resilient PAKE
Suvradip Chakraborty, Lorenzo Magliocco, Bernardo Magri, and Daniele Venturi
Password-Authenticated Key Exchange (PAKE) allows two parties to establish a common high-entropy secret from a possibly low-entropy pre-shared secret such as a password. In this work, we provide the first PAKE protocol with subversion resilience in the framework of universal composability (UC), where the latter roughly means that UC security still holds even if one of the two parties is malicious and the honest party's code has been subverted (in an undetectable manner). We achieve this result by sanitizing the PAKE protocol from oblivious transfer (OT) due to Canetti et al. (PKC'12) via cryptographic reverse firewalls in the UC framework (Chakraborty et al., EUROCRYPT'22). This requires new techniques, which help us uncover new cryptographic primitives with sanitation-friendly properties along the way (such as OT, dual-mode cryptosystems, and signature schemes). As an additional contribution, we delve deeper in the backbone of communication required in the subversion-resilient UC framework, extending it to the unauthenticated setting, in line with the work of Barak et al. (CRYPTO'05).
Last updated:  2023-11-28
Load-Balanced Server-Aided MPC in Heterogeneous Computing
Yibiao Lu, Bingsheng Zhang, and Kui Ren
Most existing MPC protocols consider the homogeneous setting, where all the MPC players are assumed to have identical communication and computation resources. In practice, the weakest player often becomes the bottleneck of the entire MPC protocol execution. In this work, we initiate the study of so-called load-balanced MPC in the heterogeneous computing. A load-balanced MPC protocol can adjust the workload of each player accordingly to maximize the overall resource utilization. In particular, we propose new notions called composite circuit and composite garbling scheme, and construct two efficient server-aided protocols with malicious security and semi-honest security, respectively. Our maliciously secure protocol is over 400$\times$ faster than the authenticated garbling protocol (CCS'17); our semi-honest protocol is up to 173$\times$ faster than the optimized BMR protocol (CCS'16).
Last updated:  2023-11-28
Unclonable Cryptography in the Plain Model
Céline Chevalier, Paul Hermouet, and Quoc-Huy Vu
By leveraging the no-cloning principle of quantum mechanics, unclonable cryptography enables us to achieve novel cryptographic protocols that are otherwise impossible classically. Two most notable examples of unclonable cryptography are quantum copy-protection and unclonable encryption. Despite receiving a lot of attention in recent years, two important open questions still remain: copy- protection for point functions in the plain model, which is usually considered as feasibility demonstration, and unclonable encryption with unclonable indistinguishability security in the plain model. In this work, by relying on previous works of Coladangelo, Liu, Liu, and Zhandry (Crypto’21) and Culf and Vidick (Quantum’22), we establish a new monogamy-of-entanglement property for subspace coset states, which allows us to obtain the following new results: • We show that copy-protection of point functions exists in the plain model, with different challenge distributions (including arguably the most natural ones). • We show, for the first time, that unclonable encryption with unclonable indistinguishability security exists in the plain model.
Last updated:  2023-11-28
Learning with Errors over Group Rings Constructed by Semi-direct Product
Jiaqi Liu and Fang-Wei Fu
The Learning with Errors (LWE) problem has been widely utilized as a foundation for numerous cryptographic tools over the years. In this study, we focus on an algebraic variant of the LWE problem called Group ring LWE (GR-LWE). We select group rings (or their direct summands) that underlie specific families of finite groups constructed by taking the semi-direct product of two cyclic groups. Unlike the Ring-LWE problem described in \cite{lyubashevsky2010ideal}, the multiplication operation in the group rings considered here is non-commutative. As an extension of Ring-LWE, it maintains computational hardness and can be potentially applied in many cryptographic scenarios. In this paper, we present two polynomial-time quantum reductions. Firstly, we provide a quantum reduction from the worst-case shortest independent vectors problem (SIVP) in ideal lattices with polynomial approximate factor to the search version of GR-LWE. This reduction requires that the underlying group ring possesses certain mild properties; Secondly, we present another quantum reduction for two types of group rings, where the worst-case SIVP problem is directly reduced to the (average-case) decision GR-LWE problem. The pseudorandomness of GR-LWE samples guaranteed by this reduction can be consequently leveraged to construct semantically secure public-key cryptosystems.
Last updated:  2023-11-27
PQC-NN: Post-Quantum Cryptography Neural Network
Abel C. H. Chen
In recent years, quantum computers and Shor’s quantum algorithm have been able to effectively solve NP (Non-deterministic Polynomial-time) problems such as prime factorization and discrete logarithm problems, posing a threat to current mainstream asymmetric cryptography, including RSA and Elliptic Curve Cryptography (ECC). As a result, the National Institute of Standards and Technology (NIST) in the United States call for Post-Quantum Cryptography (PQC) methods that include lattice-based cryptography methods, code-based cryptography methods, multivariate cryptography methods, and hash-based cryptography methods for resisting quantum computing attacks. Therefore, this study proposes a PQC neural network (PQC-NN) that maps a code-based PQC method to a neural network structure and enhances the security of ciphertexts with non-linear activation functions, random perturbation of ciphertexts, and uniform distribution of ciphertexts. The main innovations of this study include: (1) constructing a neural network structure that complies with code-based PQC, where the weight sets between the input layer and the ciphertext layer can be used as a public key for encryption, and the weight sets between the ciphertext layer and the output layer can be used as a private key for decryption; (2) adding random perturbations to the ciphertext layer, which can be removed during the decryption phase to restore the original plaintext; (3) constraining the output values of the ciphertext layer to follow a uniform distribution with a significant similarity by adding the cumulative distribution function (CDF) values of the chi-square distribution to the loss function, ensuring that the neural network produces sufficiently uniform distribution for the output values of the ciphertext layer. In practical experiments, this study uses cellular network signals as a case study to demonstrate that encryption and decryption can be performed by the proposed PQC neural network with the uniform distribution of ciphertexts. In the future, the proposed PQC neural network could be applied to various applications.
Last updated:  2023-11-27
Rectangular Attack on VOX
Gilles Macario-Rat, Jacques Patarin, Benoit Cogliati, Jean-Charles Faugère, Pierre-Alain Fouque, Louis Gouin, Robin Larrieu, and Brice Minaud
VOX has been submitted to the NIST Round 1 Additional Signature of the Post-Quantum Signature Competition in June 2023. VOX is a strengthened variant of UOV which uses the Quotient-Ring (QR) setting to reduce the public-key size. At the end of August 2023, Furue and Ikamatsu posted on the NIST mailing-list a post, indicating that the parameters of VOX can be attacked efficiently using the rectangular attack in the QR setting. In this note, we explain the attack in the specific case of VOX, we detail the complexity, and show that as Furue and Ikematsu indicated, the attack can be completely avoided by adding one more constraint on the parameter selection. Finally, we show that this constraint does not increase the sizes of the public keys or signature.
Last updated:  2023-11-26
Cryptanalysis of TS-Hash
Aleksei Udovenko
This note presents attacks on the lightweight hash function TS-Hash proposed by Tsaban, including a polynomial-time preimage attack for short messages (at most n/2 bits), high-probability differentials, a general subexponential-time preimage attack, and linearization techniques.
Last updated:  2023-11-27
Chipmunk: Better Synchronized Multi-Signatures from Lattices
Nils Fleischhacker, Gottfried Herold, Mark Simkin, and Zhenfei Zhang
Multi-signatures allow for compressing many signatures for the same message that were generated under independent keys into one small aggregated signature. This primitive is particularly useful for proof-of-stake blockchains, like Ethereum, where the same block is signed by many signers, who vouch for the block's validity. Being able to compress all signatures for the same block into a short string significantly reduces the on-chain storage costs, which is an important efficiency metric for blockchains. In this work, we consider multi-signatures in the synchronized setting, where the signing algorithm takes an additional time parameter as input and it is only required that signatures for the same time step are aggregatable. The synchronized setting is simpler than the general multi-signature setting, but is sufficient for most blockchain related applications, as signers are naturally synchronized by the length of the chain. We present Chipmunk, a concretely efficient lattice-based multi-signature scheme in the synchronized setting that allows for signing an a-priori bounded number of messages. Chipmunk allows for non-interactive aggregation of signatures and is secure against rogue-key attacks. The construction is plausibly secure against quantum adversaries as our security relies on the assumed hardness of the short integer solution problem. We significantly improve upon the previously best known construction in this setting by Fleischhacker, Simkin, and Zhang (CCS 2022). Our aggregate signature size is $5.6 \times$ smaller and for $112$ bits of security our construction allows for compressing 8192 individual signatures into a multi-signature of size around $136$ KB. We provide a full implementation of Chipmunk and provide extensive benchmarks studying our construction's efficiency.
Last updated:  2023-11-24
Beyond MPC-in-the-Head: Black-Box Constructions of Short Zero-Knowledge Proofs
Carmit Hazay, Muthuramakrishnan Venkitasubramaniam, and Mor Weiss
In their seminal work, Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC`07) presented the MPC-in-the-Head paradigm, which shows how to design Zero-Knowledge Proofs (ZKPs) from secure Multi-Party Computation (MPC) protocols. This paradigm has since then revolutionized and modularized the design of efficient ZKP systems, with far-reaching applications beyond ZKPs. However, to the best of our knowledge, all previous instantiations relied on fully-secure MPC protocols, and have not been able to leverage the fact that the paradigm only imposes relatively weak privacy and correctness requirements on the underlying MPC. In this work, we extend the MPC-in-the-Head paradigm to game-based cryptographic primitives supporting homomorphic computations (e.g., fully-homomorphic encryption, functional encryption, randomized encodings, homomorphic secret sharing, and more). Specifically, we present a simple yet generic compiler from these primitives to ZKPs which use the underlying primitive as a black box. We also generalize our paradigm to capture commit-and-prove protocols, and use it to devise tight black-box compilers from Interactive (Oracle) Proofs to ZKPs, assuming One-Way Functions (OWFs). We use our paradigm to obtain several new ZKP constructions: 1. The first ZKPs for NP relations $\mathcal{R}$ computable in (polynomial-time uniform) $NC^1$, whose round complexity is bounded by a fixed constant (independent of the depth of $\mathcal{R}$'s verification circuit), with communication approaching witness length (specifically, $n\cdot poly\left(\kappa\right)$, where $n$ is the witness length, and $\kappa$ is a security parameter), assuming DCR. Alternatively, if we allow the round complexity to scale with the depth of the verification circuit, our ZKPs can make black-box use of OWFs. 2. Constant-round ZKPs for NP relations computable in bounded polynomial space, with $O\left(n\right)+o\left(m\right)\cdot poly\left(\kappa\right)$ communication assuming OWFs, where $m$ is the instance length. This gives a black-box alternative to a recent non-black-box construction of Nassar and Rothblum (CRYPTO`22). 3. ZKPs for NP relations computable by a logspace-uniform family of depth-$d\left(m\right)$ circuits, with $n\cdot poly\left(\kappa,d\left(m\right)\right)$ communication assuming OWFs. This gives a black-box alternative to a result of Goldwasser, Kalai and Rothblum (JACM).
Last updated:  2023-11-24
On the Feasibility of Unleveled Fully-Homomorphic Signatures
Romain Gay and Bogdan Ursu
We build the first unleveled fully homomorphic signature scheme in the standard model. Our scheme is not constrained by any a-priori bound on the depth of the functions that can be homomorphically evaluated, and relies on subexponentially-secure indistinguishability obfuscation, fully-homomorphic encryption and a non-interactive zero-knowledge (NIZK) proof system with composable zero-knowledge. Our scheme is also the first to satisfy the strong security notion of context-hiding for an unbounded number of levels, ensuring that signatures computed homomorphically do not leak the original messages from which they were computed. All building blocks are instantiable from falsifiable assumptions in the standard model, avoiding the need for knowledge assumptions. The main difficulty we overcome stems from the fact that bootstrapping, which is a crucial tool for obtaining unleveled fully homomorphic encryption (FHE), has no equivalent for homomorphic signatures, requiring us to use novel techniques.
Last updated:  2023-11-24
Authenticating Medications with QR-Codes and Compact Digital Signatures
Julien Jainsky, David Naccache, Bassem Ouni, and Ofer Yifrach-Stav
This paper describes a way to protect medications against falsification, a long-standing problem in the world. We combine several existing technologies to achieve the stated goal. The building-blocks used are inherent physical randomness generated during the packaging process, artificial vision, short digital signatures and QR-codes.
Last updated:  2023-11-24
ASOZ: a decentralized payment system with privacy preserving and auditing on public blockchain
Tianjian Liu, Dawei Zhang, and Wei Wang
Show abstract
Decentralized payment system gradually get more attention in recent years. By removing the trusted third party used for accounting ledgers, it fundamentally empowers users to control their own assets. As the privacy concerns grow, some cryptocurrencies is proposed to preserve the privacy of users. However, those cryptocurrencies cause illegal transactions such as money laundering, fraudulent trading and so on. So it is necessary to design a auditing scheme. To solve this problem, many privacy-preserving and audit scheme was proposed. But there exists no scheme that effectively solve the issue of privacy-preserving and auditing on both user identity and transaction content. In this paper, we propose a design for a decentralized payment system with privacy preserving and auditing. We use cryptographic accumulators based on Merkle trees for accounting and use a combination of Twist ElGamal, NIZK (Non-Interactive Zero-Knowledge), Bulletproofs, and zk-SNARKs for privacy preserving and auditing.
Last updated:  2023-11-24
Accelerating Polynomial Multiplication for RLWE using Pipelined FFT
Neil Thanawala, Hamid Nejatollahi, and Nikil Dutt
The evolution of quantum algorithms threatens to break public key cryptography in polynomial time. The development of quantum-resistant algorithms for the post-quantum era has seen a significant growth in the field of post quantum cryptography (PQC). Polynomial multiplication is the core of Ring Learning with Error (RLWE) lattice based cryptography (LBC) which is one of the most promising PQC candidates. In this work, we present the design of fast and energy-efficient pipelined Number Theoretic Transform (NTT) based polynomial multipliers and present synthesis results on a Field Programmable Gate Array (FPGA) to evaluate their efficacy. NTT is performed using the pipelined R2SDF and R22SDF Fast Fourier Transform (FFT) architectures. In addition, we propose an energy efficient modified architecture (Modr2). The NTT-based designed polynomial multipliers employs the Modr2 architecture that achieve on average 2× better performance over the R2SDF FFT and 2.4× over the R22SDF FFT with similar levels of energy consumption. The proposed polynomial multiplier with Modr2 architecture reaches 12.5× energy efficiency over the state-ofthe-art convolution-based polynomial multiplier and 4× speedup over the systolic array NTT based polynomial multiplier for polynomial degrees of 1024, demonstrating its potential for practical deployment in future designs.
Last updated:  2023-11-24
Easy-ABE: An Easy Ciphertext-Policy Attribute-Based Encryption
Ahmad Khoureich Ka
Attribute-Based Encryption is widely recognized as a leap forward in the field of public key encryption. It allows to enforce an access control on encrypted data. Decryption time in ABE schemes can be long depending on the number of attributes and pairing operations. This drawback hinders their adoption on a broader scale. In this paper, we propose a non-monotone CP-ABE scheme that has no restrictions on the size of attribute sets and policies, allows fast decryption and is adaptively secure under the CBDH-3 assumption. To achieve this, we approached the problem from a new angle, namely using a set membership relation for access structure. We have implemented our scheme using the Java Pairing-Based Cryptography Library (JPBC) and the source code is available on GitHub.
Last updated:  2023-11-23
Early Stopping for Any Number of Corruptions
Julian Loss and Jesper Buus Nielsen
Minimizing the round complexity of byzantine broadcast is a fundamental question in distributed computing and cryptography. In this work, we present the first early stopping byzantine broadcast protocol that tolerates up to $t=n-1$ malicious corruptions and terminates in $O(\min\{f^2,t+1\})$ rounds for any execution with $f\leq t$ actual corruptions. Our protocol is deterministic, adaptively secure, and works assuming a plain public key infrastructure. Prior early-stopping protocols all either require honest majority or tolerate only up to $t=(1-\epsilon)n$ malicious corruptions while requiring either trusted setup or strong number theoretic hardness assumptions. As our key contribution, we show a novel tool called a polariser that allows us to transfer certificate-based strategies from the honest majority setting to settings with a dishonest majority.
Last updated:  2023-11-23
The NTT and residues of a polynomial modulo factors of $X^{2^d} + 1$
Sahil Sharma
The Number Theoretic Transform (NTT) plays a central role in efficient implementations of cryptographic primitives selected for Post Quantum Cryptography. Although it certainly exists, academic papers that cite the NTT omit the connection between the NTT and residues of a polynomial modulo factors of $X^{2^d} + 1$ and mention only the final expressions of what the NTT computes. This short paper establishes that connection and, in doing so, elucidates key aspects of computing the NTT. Based on this, the specific instantiations of the NTT function used in CRYSTALS-Kyber and CRYSTALS-Dilithium are derived.
Last updated:  2023-11-23
A note on Failing gracefully: Completing the picture for explicitly rejecting Fujisaki-Okamoto transforms using worst-case correctness
Kathrin Hövelmanns and Christian Majenz
The Fujisaki-Okamoto (FO) transformation is used in most proposals for post-quantum secure key encapsulation mechanisms (KEMs) like, e.g., Kyber [BDK+18]. The security analysis of FO in the presence of quantum attackers has made huge progress over the last years. Recently, [HHM22] made a particular improvement by giving a security proof that is agnostic towards how invalid ciphertexts are being treated: in contrast to previous proofs, it works regardless whether invalid ciphertexts are rejected by reporting decryption failure explicitly or implicitly (by returning pseudorandom values). The proof in [HHM22] involves a new correctness notion for the encryption scheme that is used to encapsulate the keys. This allows in principle for a smaller additive security related to decryption failures, but requires to analyze this new notion for the encryption scheme on which a concrete KEM at hand is based. This note offers a trade-off between [HHM22] and its predecessors: it offers a bound for both rejection variants, being mostly based on [HHM22], but uses a more established correctness notion.
Last updated:  2023-11-23
Pairing-Free Blind Signatures from Standard Assumptions in the ROM
Julia Kastner, Ky Nguyen, and Michael Reichle
Blind Signatures are a useful primitive for privacy preserving applications such as electronic payments, e-voting, anonymous credentials, and more. However, existing practical blind signature schemes based on standard assumptions require either pairings or lattices. We present the first construction of a round-optimal blind signature in the random oracle model based on standard assumptions without resorting to pairings or lattices. In particular, our construction is secure under the strong RSA assumption and DDH (in pairing-free groups). For our construction, we provide a NIZK-friendly signature based on strong RSA, and efficiently instantiate Fischlin's generic framework (CRYPTO'06). Our Blind Signature scheme has signatures of size 4.28 KB and communication cost 62.19 KB. On the way, we develop techniques that might be of independent interest. In particular, we provide efficient relaxed range-proofs with subversion zero-knowledge and compact commitments to elements of arbitrary groups.
Last updated:  2023-11-23
PURED: A unified framework for resource-hard functions
Alex Biryukov and Marius Lombard-Platet
Algorithm hardness can be described by 5 categories: hardness in computation, in sequential computation, in memory, in energy consumption (or bandwidth), in code size. Similarly, hardness can be a concern for solving or for verifying, depending on the context, and can depend on a secret trapdoor or be universally hard. Two main lines of research investigated such problems: cryptographic puzzles, that gained popularity thanks to blockchain consensus systems (where solving must be moderately hard, and verification either public or private), and white box cryptography (where solving must be hard without knowledge of the secret key). In this work, we improve upon the classification framework proposed by Biryukov and Perrin in Asiacypt 2017 and offer a united hardness framework, PURED, that can be used for measuring all these kinds of hardness, both in solving and verifying. We also propose three new constructions that fill gaps previously uncovered by the literature (namely, trapdoor proof of CMC, trapdoor proof of code, and a hard challenge in sequential time trapdoored in verification), and analyse their hardness in the PURED framework.
Last updated:  2023-11-26
Small Stretch Problem of the DCT Scheme and How to Fix it
Yuchao Chen, Tingting Guo, Lei Hu, Lina Shang, Shuping Mao, and Peng Wang
DCT is a beyond-birthday-bound~(BBB) deterministic authenticated encryption~(DAE) mode proposed by Forler et al. in ACISP 2016, ensuring integrity by redundancy. The instantiation scheme of DCT employs the BRW polynomial, which is more efficient than the usual polynomial function in GCM by reducing half of the multiplication operations. However, we show that DCT suffers from a small stretch problem similar to GCM. When the stretch length $\tau$ is small, choosing a special $m$-block message, we can reduce the number of queries required by a successful forgery to $\mathcal{O}(2^{\tau}/m)$. We emphasize that this attack efficiently balances space and time complexity, but does not contradict the security bounds of DCT. Finally, we propose an improved scheme named Robust DCT~(RDCT) with a minor change to DCT, which improves the security when $\tau$ is small and makes it resist the above attack.
Last updated:  2023-11-23
Entrada to Secure Graph Convolutional Networks
Nishat Koti, Varsha Bhat Kukkala, Arpita Patra, and Bhavish Raj Gopal
Graph convolutional networks (GCNs) are gaining popularity due to their powerful modelling capabilities. However, guaranteeing privacy is an issue when evaluating on inputs that contain users’ sensitive information such as financial transactions, medical records, etc. To address such privacy concerns, we design Entrada, a framework for securely evaluating GCNs that relies on the technique of secure multiparty computation (MPC). For efficiency and accuracy reasons, Entrada builds over the MPC framework of Tetrad (NDSS’22) and enhances the same by providing the necessary primitives. Moreover, Entrada leverages the GraphSC paradigm of Araki et al. (CCS’21) to further enhance efficiency. This entails designing a secure and efficient shuffle protocol specifically in the 4-party setting, which to the best of our knowledge, is done for the first time and may be of independent interest. Through extensive experiments, we showcase that the accuracy of secure GCN evaluated via Entrada is on par with its cleartext counterpart. We also benchmark efficiency of Entrada with respect to the included primitives as well as the framework as a whole. Finally, we showcase Entrada’s practicality by benchmarking GCN-based fraud detection application.
Last updated:  2023-11-23
Fast and Designated-verifier Friendly zkSNARKs in the BPK Model
Xudong Zhu, Xuyang Song, and Yi Deng
In ASIACRYPT 2016, Bellare et al. first demonstrated that it is impossible to achieve subversion soundness and standard zero knowledge simultaneously. Subsequently, there have been lots of effort to construct zero-knowledge succinct non interactive arguments of knowledge protocols (zk-SNARKs) that satisfy subversion zero knowledge (S-ZK) and standard soundness from the zk-SNARK in the common reference string (CRS) model. The various constructions could be regarded secure in the bare public key (BPK) model because of the equivalence between S-ZK in the CRS model, and uniform non-black-box zero knowledge in the BPK model has been proved by Abdolmaleki et al. in PKC 2020. In this study, We proposed the first publicly verifiable non-uniform ZK zk-SNARK scheme in the BPK model maintaining comparable efficiency with its conventional counterpart, which can also be compatible with the well-known transformation proposed by Bitansky et al. in TCC 2013 to obtain an efficient designated-verifier zk-SNARK. We achieve this goal by only adding a constant number of elements into the CRS, and using an unconventional but natural method to transform Groth’s zkSNARK in EUROCRYPT 2016. In addition, we propose a new speed-up technique that provides a trade-off. Specifically, if a logarithmic number of elements are added into the CRS, according to different circuits, the CRS verification time in our construction could be approximately 9%-23% shorter than that in the conventional counterpart.
Last updated:  2023-11-24
On the Security of Rate-limited Privacy Pass
Hien Chu, Khue Do, and Lucjan Hanzlik
The privacy pass protocol allows users to redeem anonymously issued cryptographic tokens instead of solving annoying CAPTCHAs. The issuing authority verifies the credibility of the user, who can later use the pass while browsing the web using an anonymous or virtual private network. Hendrickson et al. proposed an IETF draft (privacypass-rate-limit-tokens-00) for a rate-limiting version of the privacy pass protocol, also called rate-limited Privacy Pass (RlP). Introducing a new actor called a mediator makes both versions inherently different. The mediator applies access policies to rate-limit users’ access to the service while, at the same time, should be oblivious to the website/origin the user is trying to access. In this paper, we formally define the rate-limited Privacy Pass protocol and propose a game-based security model to capture the informal security notions introduced by Hendrickson et al.. We show a construction from simple building blocks that fulfills our security definitions and even allows for a post-quantum secure instantiation. Interestingly, the instantiation proposed in the IETF draft is a specific case of our construction. Thus, we can reuse the security arguments for the generic construction and show that the version used in practice is secure.
Last updated:  2023-11-22
Fully Malicious Authenticated PIR
Marian Dietz and Stefano Tessaro
Authenticated PIR enables a server to initially commit to a database of $N$ items, for which a client can later privately obtain individual items with complexity sublinear in $N$, with the added guarantee that the retrieved item is consistent with the committed database. A crucial requirement is privacy with abort, i.e., the server should not learn anything about a query even if it learns whether the client aborts. This problem was recently considered by Colombo et al. (USENIX '23), who proposed solutions secure under the assumption that the database is committed to honestly. Here, we close this gap, and present a solution that tolerates fully malicious servers that provide potentially malformed commitments. Our scheme has communication and client computational complexity $\mathcal{O}_{\lambda}(\sqrt{N})$, solely relies on the DDH assumption, and does not introduce heavy machinery (e.g., generic succinct proofs). Privacy with abort holds provided the server succeeds in correctly answering $\lambda$ validation queries, which, from its perspective, are computationally indistinguishable from regular PIR queries. In fact, server side, our scheme is exactly the DDH-based scheme by Colombo et al.
Last updated:  2023-11-22
Design of a Linear Layer Optimised for Bitsliced 32-bit Implementation
Gaëtan Leurent and Clara Pernot
The linear layer of block ciphers plays an important role in their security. In particular, ciphers designed following the wide-trail strategy use the branch number of the linear layer to derive bounds on the probability of linear and differential trails. At FSE 2014, the LS-design construction was introduced as a simple and regular structure to design bitsliced block ciphers. It considers the internal state as a bit matrix, and applies alternatively an identical S-Box on all the columns, and an identical L-Box on all the lines. Security bounds are derived from the branch number of the L-Box. In this paper, we focus on bitsliced linear layers inspired by the LS-design construction and the Spook AEAD algorithm. We study the construction of bitsliced linear transformations with efficient implementations using XORs and rotations (optimized for bitsliced ciphers implemented on 32-bit processors), and a high branch number. In order to increase the density of the activity patterns, the linear layer is designed on the whole state, rather than using multiple parallel copies of an L-Box. Our main result is a linear layer for 128-bit ciphers with branch number 21, improving upon the best 32-bit transformation with branch number 12, and the one of Spook with branch number 16.
Last updated:  2023-11-22
Sublinear-Communication Secure Multiparty Computation does not require FHE
Elette Boyle, Geoffroy Couteau, and Pierre Meyer
Secure computation enables mutually distrusting parties to jointly compute a function on their secret inputs, while revealing nothing beyond the function output. A long-running challenge is understanding the required communication complexity of such protocols---in particular, when communication can be sublinear in the circuit representation size of the desired function. Significant advances have been made affirmatively answering this question within the two-party setting, based on a variety of structures and hardness assumptions. In contrast, in the multi-party setting, only one general approach is known: using Fully Homomorphic Encryption (FHE). This remains the state of affairs even for just three parties, with two corruptions. We present a framework for achieving secure sublinear-communication $(N+1)$-party computation, building from a particular form of Function Secret Sharing for only $N$ parties. In turn, we demonstrate implications to sublinear secure computation for various function classes in the 3-party and 5-party settings based on an assortment of assumptions not known to imply FHE.
Last updated:  2023-11-22
ForgedAttributes: An Existential Forgery Vulnerability of CMS and PKCS#7 Signatures
Falko Strenzke
This work describes an existential signature forgery vulnerability of the current CMS and PKCS#7 signature standards. The vulnerability results from an ambiguity of how to process the signed message in the signature verification process. Specifically, the absence or presence of the so called SignedAttributes field determines whether the signature message digest receives as input the message directly or the SignedAttributes, a DER-encoded structure which contains a digest of the message. If an attacker takes a CMS or PKCS#7 signed message M which was originally signed with SignedAttributes present, then he can craft a new message M 0 that was never signed by the signer and has the DER-encoded SignedAttributes of the original message as its content and verifies correctly against the original signature of M . Due to the limited flexibility of the forged message and the limited control the attacker has over it, the fraction of vulnerable systems must be assumed to be small but due to the wide deployment of the affected protocols, such instances cannot be excluded. We propose a countermeasure based on attack-detection that prevents the attack reliably.
Last updated:  2023-11-22
Algebraic Attack on FHE-Friendly Cipher HERA Using Multiple Collisions
Fukang Liu, Abul Kalam, Santanu Sarkar, and Willi Meier
Fully homomorphic encryption (FHE) is an advanced cryptography technique to allow computations (i.e., addition and multiplication) over encrypted data. After years of effort, the performance of FHE has been significantly improved and it has moved from theory to practice. The transciphering framework is another important technique in FHE to address the issue of ciphertext expansion and reduce the client-side computational overhead. Motivated by this framework, several FHE-friendly symmetric-key primitives have been proposed since the publication of LowMC at EUROCRYPT 2015. To apply the transciphering framework to the CKKS scheme, a new transciphering framework called the Real-to-Finite-Field (RtF) framework and a corresponding FHE-friendly symmetric-key primitive called HERA were proposed at ASIACRYPT 2021. Although HERA has a very similar structure to AES, it is considerably different in the following aspects: 1) the power map $x\mapsto x^3$ is used as the S-box; 2) a randomized key schedule is used; 3) it is over a prime field $\mathbb F_p$ with $p>2^{16}$. In this work, we perform the first third-party cryptanalysis of HERA, by showing how to mount new algebraic attacks with multiple collisions in the round keys. Specifically, according to the special way to randomize the round keys in HERA, we find it possible to peel off the last nonlinear layer by using collisions in the last-round key and a simple property of the power map. In this way, we could construct an overdefined system of equations of a much lower degree in the key, and efficiently solve the system via the linearization technique. As a result, for HERA with 192 and 256 bits of security, respectively, we could break some parameters under the same assumption made by designers that the algebra constant $\omega$ for Gaussian elimination is $\omega=2$, i.e., Gaussian elimination on an $n\times n$ matrix takes $\mathcal{O}(n^{\omega})$ field operations. If using more conservative choices like $\omega\in\{2.8,3\}$, our attacks can also successfully reduce the security margins of some variants of \hera to only 1 round. However, the security of HERA with 80 and 128 bits of security is not affected by our attacks due to the high cost to find multiple collisions. In any case, our attacks reveal a weakness of HERA caused by the randomized key schedule and its small state size.
Last updated:  2023-11-22
BabySpartan: Lasso-based SNARK for non-uniform computation
Srinath Setty and Justin Thaler
Lasso (Setty, Thaler, Wahby, ePrint 2023/1216) is a recent lookup argument that ensures that the prover cryptographically commits to only "small" values. This note describes BabySpartan, a SNARK for a large class of constraint systems that achieves the same property. The SNARK is a simple combination of SuperSpartan and Lasso. The specific class of constraint systems supported is a generalization of so-called Plonkish constraint systems (and a special case of customizable constraint systems (CCS)). Whereas a recent work called Jolt (Arun, Setty, and Thaler, ePrint 2023/1217) can be viewed as an application of Lasso to uniform computation, BabySpartan can be viewed as applying Lasso to non-uniform computation.
Last updated:  2023-11-21
Somewhat Homomorphic Encryption based on Random Codes
Carlos Aguilar-Melchor, Victor Dyseryn, and Philippe Gaborit
We present a secret-key encryption scheme based on random rank metric ideal linear codes with a simple decryption circuit. It supports unlimited homomorphic additions and plaintext absorptions as well as a fixed arbitrary number of homomorphic multiplications. We study a candidate bootstrapping algorithm that requires no multiplication but additions and plaintext absorptions only. This latter operation is therefore very efficient in our scheme, whereas bootstrapping is usually the main reason which penalizes the performance of other fully homomorphic encryption schemes. However, the security reduction of our scheme restricts the number of independent ciphertexts that can be published. In particular, this prevents to securely evaluate the bootstrapping algorithm as the number of ciphertexts in the key switching material is too large. Our scheme is nonetheless the first somewhat homomorphic encryption scheme based on random ideal codes and a first step towards full homomorphism. Random ideal codes give stronger security guarantees as opposed to existing constructions based on highly structured codes. We give concrete parameters for our scheme that shows that it achieves competitive sizes and performance, with a key size of 3.7 kB and a ciphertext size of 0.9 kB when a single multiplication is allowed.
Last updated:  2023-11-21
A Modular Approach to Unclonable Cryptography
Prabhanjan Ananth and Amit Behera
We explore a new pathway to designing unclonable cryptographic primitives. We propose a new notion called unclonable puncturable obfuscation (UPO) and study its implications for unclonable cryptography. Using UPO, we present modular (and in some cases, arguably, simple) constructions of many primitives in unclonable cryptography, including, public-key quantum money, quantum copy-protection for many classes of functionalities, unclonable encryption, and single-decryption encryption. Notably, we obtain the following new results assuming the existence of UPO: - We show that any cryptographic functionality can be copy-protected as long as this functionality satisfies a notion of security, which we term as puncturable security. Prior feasibility results focused on copy-protecting specific cryptographic functionalities. - We show that copy-protection exists for any class of evasive functions as long as the associated distribution satisfies a preimage-sampleability condition. Prior works demonstrated copy-protection for point functions, which follows as a special case of our result. - We show that unclonable encryption exists in the plain model. Prior works demonstrated feasibility results in the quantum random oracle model. We put forward a candidate construction of UPO and prove two notions of security, each based on the existence of (post-quantum) sub-exponentially secure indistinguishability obfuscation and one-way functions, the quantum hardness of learning with errors, and a new conjecture called simultaneous inner product conjecture.
Last updated:  2023-11-21
Fault Attacks Sensitivity of Public Parameters in the Dilithium Verification
Andersson Calle Viera, Alexandre Berzati, and Karine Heydemann
This paper presents a comprehensive analysis of the verification algorithm of the CRYSTALS-Dilithium, focusing on a C reference implementation. Limited research has been conducted on its susceptibility to fault attacks, despite its critical role in ensuring the scheme’s security. To fill this gap, we investigate three distinct fault models - randomizing faults, zeroizing faults, and skipping faults - to identify vulnerabilities within the verification process. Based on our analysis, we propose a methodology for forging CRYSTALS-Dilithium signatures without knowledge of the secret key. Instead, we leverage specific types of faults during the verification phase and some properties about public parameters to make these signatures accepted. Additionally, we compared different attack scenarios after identifying sensitive operations within the verification algorithm. The most effective requires potentially fewer fault injections than targeting the verification check itself. Finally, we introduce a set of countermeasures designed to thwart all the identified scenarios rendering the verification algorithm intrinsically resistant to the presented attacks.
Last updated:  2023-11-21
Efficiently Testable Circuits without Conductivity
Mirza Ahad Baig, Suvradip Chakraborty, Stefan Dziembowski, Małgorzata Gałązka, Tomasz Lizurej, and Krzysztof Pietrzak
The notion of ``efficiently testable circuits'' (ETC) was recently put forward by Baig et al.~(ITCS'23). Informally, an ETC compiler takes as input any Boolean circuit $C$ and outputs a circuit/inputs tuple $(C',\mathbb{T})$ where (completeness) $C'$ is functionally equivalent to $C$ and (security) if $C'$ is tampered in some restricted way, then this can be detected as $C'$ will err on at least one input in the small test set $\mathbb{T}$. The compiler of Baig et al. detects tampering even if the adversary can tamper with \emph{all} wires in the compiled circuit. Unfortunately, the model requires a strong ``conductivity'' restriction: the compiled circuit has gates with fan-out up to 3, but wires can only be tampered in one way even if they have fan-out greater than one. In this paper, we solve the main open question from their work and construct an ETC compiler without this conductivity restriction. While Baig et al. use gadgets computing the AND and OR of particular subsets of the wires, our compiler computes inner products with random vectors. We slightly relax their security notion and only require that tampering is detected with high probability over the choice of the randomness. Our compiler increases the size of the circuit by only a small constant factor. For a parameter $\lambda$ (think $\lambda\le 5$), the number of additional input and output wires is $|C|^{1/\lambda}$, while the number of test queries to detect an error with constant probability is around $2^{2\lambda}$.
Last updated:  2023-11-30
Secret-Shared Shuffle with Malicious Security
Xiangfu Song, Dong Yin, Jianli Bai, Changyu Dong, and Ee-Chien Chang
A secret-shared shuffle (SSS) protocol permutes a secret-shared vector using a random secret permutation. It has found numerous applications, however, it is also an expensive operation and often a performance bottleneck. Chase et al. (Asiacrypt'20) recently proposed a highly efficient semi-honest two-party SSS protocol known as the CGP protocol. It utilizes purposely designed pseudorandom correlations that facilitate a communication-efficient online shuffle phase. That said, semi-honest security is insufficient in many real-world application scenarios since shuffle is usually used for highly sensitive applications. Considering this, recent works (CANS'21, NDSS'22) attempted to enhance the CGP protocol with malicious security over authenticated secret sharings. However, we find that these attempts are flawed, and malicious adversaries can still learn private information via malicious deviations. This is demonstrated with concrete attacks proposed in this paper. Then the question is how to fill the gap and design a maliciously secure CGP shuffle protocol. We answer this question by introducing a set of lightweight correlation checks and a leakage reduction mechanism. Then we apply our techniques with authenticated secret sharings to achieve malicious security. Notably, our protocol, while increasing security, is also efficient. In the two-party setting, experiment results show that our maliciously secure protocol introduces an acceptable overhead compared to its semi-honest version and is more efficient than the state-of-the-art maliciously secure SSS protocol from the MP-SPDZ library.
Last updated:  2023-11-29
Accountable Multi-Signatures with Constant Size Public Keys
Dan Boneh, Aditi Partap, and Brent Waters
A multisignature scheme is used to aggregate signatures by multiple parties on a common message $m$ into a single short signature on $m$. Multisignatures are used widely in practice, most notably, in proof-of-stake consensus protocols. In existing multisignature schemes, the verifier needs the public keys of all the signers in order to verify a multisignature issued by some subset of signers. We construct new practical multisignature schemes with three properties: (i) the verifier only needs to store a constant size public key in order to verify a multisignature by an arbitrary subset of parties, (ii) signature size is constant beyond the description of the signing set, and (iii) signers generate their secret signing keys locally, that is, without a distributed key generation protocol. Existing schemes satisfy properties (ii) and (iii). The new capability is property (i) which dramatically reduces the verifier's memory requirements from linear in the number of signers to constant. We give two pairing-based constructions: one in the random oracle model and one in the plain model. We also show that by relaxing property (iii), that is, allowing for a simple distributed key generation protocol, we can further improve efficiency while continuing to satisfy properties (i) and (ii). We give a pairing-based scheme and a lattice-based scheme in this relaxed model.
Last updated:  2023-11-29
Sloth: Key Stretching and Deniable Encryption using Secure Elements on Smartphones
Daniel Hugenroth, Alberto Sonnino, Sam Cutler, and Alastair R. Beresford
Traditional key stretching lacks a strict time guarantee due to the ease of parallelized password guessing by attackers. This paper introduces Sloth, a key stretching method leveraging the Secure Element (SE) commonly found in modern smartphones to provide a strict rate limit on password guessing. While this would be straightforward with full access to the SE, Android and iOS only provide a very limited API. Sloth utilizes the existing developer SE API and novel cryptographic constructions to build an effective rate-limit for password guessing on recent Android and iOS devices. Our approach ensures robust security even for short, randomly-generated, six-character alpha-numeric passwords against adversaries with virtually unlimited computing resources. Our solution is compatible with approximately 96% of iPhones and 45% of Android phones and Sloth seamlessly integrates without device or OS modifications, making it immediately usable by app developers today. We formally define the security of Sloth and evaluate its performance on various devices. Finally, we present HiddenSloth, a deniable encryption scheme, leveraging Sloth and the SE to withstand multi-snapshot adversaries.
Last updated:  2023-11-20
Decentralized Compromise-Tolerant Public Key Management Ecosystem with Threshold Validation
Jamal Mosakheil and Kan Yang
This paper examines the vulnerabilities inherent in prevailing Public Key Infrastructure (PKI) systems reliant on centralized Certificate Authorities (CAs), wherein a compromise of the CA introduces risks to the integrity of public key management. We present PKChain, a decentralized and compromise-tolerant public key management system built on blockchain technology, offering transparent, tamper-resistant, and verifiable services for key operations such as registration, update, query, validation, and revocation. Our innovative approach involves a novel threshold block validation scheme that combines a novel threshold cryptographic scheme with blockchain consensus. This scheme allows each validator to validate each public key record partially and proactively secures it before inclusion in a block. Additionally, to further validate and verify each block and to facilitate public verification of the public key records, we introduce an aggregate commitment signature scheme. Our contribution extends to the development of a new, efficient, and practical Byzantine Compromise-Tolerant and Verifiable (pBCTV) consensus model, integrating the proposed validation and signature schemes with practical Byzantine Fault Tolerance (pBFT). Through a comprehensive examination encompassing security analysis, performance evaluation, and a prototype implementation, we substantiate that PKChain is a secure, efficient, and robust solution for public key management.
Last updated:  2023-11-20
Compromising sensitive information through Padding Oracle and Known Plaintext attacks in Encrypt-then-TLS scenarios
Daniel Espinoza Figueroa
Let's consider a scenario where the server encrypts data using AES-CBC without authentication and then sends only the encrypted ciphertext through TLS (without IV). Then, having a padding oracle, we managed to recover the initialization vector and the sensitive data, doing a cybersecurity audit for a Chilean company.
Last updated:  2023-11-20
Fast and Secure Oblivious Stable Matching over Arithmetic Circuits
Arup Mondal, Priyam Panda, Shivam Agarwal, Abdelrahaman Aly, and Debayan Gupta
The classic stable matching algorithm of Gale and Shapley (American Mathematical Monthly '69) and subsequent variants such as those by Roth (Mathematics of Operations Research '82) and Abdulkadiroglu et al. (American Economic Review '05) have been used successfully in a number of real-world scenarios, including the assignment of medical-school graduates to residency programs, New York City teenagers to high schools, and Norwegian and Singaporean students to schools and universities. However, all of these suffer from one shortcoming: in order to avoid strategic manipulation, they require all participants to submit their preferences to a trusted third party who performs the computation. In some sensitive application scenarios, there is no appropriate (or cost-effective) trusted party. This makes stable matching a natural candidate for secure computation. Several approaches have been proposed to overcome this, based on secure multiparty computation (MPC), fully homomorphic encryption, etc.; many of these protocols are slow and impractical for real-world use. We propose a novel primitive for privacy-preserving stable matching using MPC (i.e., arithmetic circuits, for any number of parties). Specifically, we discuss two variants of oblivious stable matching and describe an improved oblivious stable matching on the random memory access model based on lookup tables. To explore and showcase the practicality of our proposed primitive, we present detailed benchmarks (at various problem sizes) of our constructions using two popular frameworks: SCALE-MAMBA and MP-SPDZ.
Last updated:  2023-11-20
Homomorphic Multiple Precision Multiplication for CKKS and Reduced Modulus Consumption
Jung Hee Cheon, Wonhee Cho, Jaehyung Kim, and Damien Stehlé
Homomorphic Encryption (HE) schemes such as BGV, BFV, and CKKS consume some ciphertext modulus for each multiplication. Bootstrapping (BTS) restores the modulus and allows homomorphic computation to continue, but it is time-consuming and requires a significant amount of modulus. For these reasons, decreasing modulus consumption is crucial topic for BGV, BFV and CKKS, on which numerous studies have been conducted. We propose a novel method, called $\mathsf{mult}^2$, to perform ciphertext multiplication in the CKKS scheme with lower modulus consumption. $\mathsf{mult}^2$ relies an a new decomposition of a ciphertext into a pair of ciphertexts that homomorphically performs a weak form of Euclidean division. It multiplies two ciphertexts in decomposed formats with homomorphic double precision multiplication, and its result approximately decrypts to the same value as does the ordinary CKKS multiplication. $\mathsf{mult}^2$ can perform homomorphic multiplication by consuming almost half of the modulus. We extend it to $\mathsf{mult}^t$ for any $t\geq 2$, which relies on the decomposition of a ciphertext into $t$ components. All other CKKS operations can be equally performed on pair/tuple formats, leading to the double-CKKS (resp. tuple-CKKS) scheme enabling homomorphic double (resp. multiple) precision arithmetic. As a result, when the ciphertext modulus and dimension are fixed, the proposed algorithms enable the evaluation of deeper circuits without bootstrapping, or allow to reduce the number of bootstrappings required for the evaluation of the same circuits. Furthermore, they can be used to increase the precision without increasing the parameters. For example, $\mathsf{mult}^2$ enables 8 sequential multiplications with 100 bit scaling factor with a ciphertext modulus of only 680 bits, which is impossible with the ordinary CKKS multiplication algorithm.
Last updated:  2023-11-19
Updatable Privacy-Preserving Blueprints
Bernardo David, Felix Engelmann, Tore Frederiksen, Markulf Kohlweiss, Elena Pagnin, and Mikhail Volkhov
Privacy-preserving blueprints enable users to create escrows using the auditor's public key. An escrow encrypts the evaluation of a function $P(t,x)$, where $t$ is a secret input used to generate the auditor's key and $x$ is the user's private input to escrow generation. Nothing but $P(t,x)$ is revealed even to a fully corrupted auditor. The original definition and construction (Kohlweiss et al., EUROCRYPT'23) only support the evaluation of functions on an input $x$ provided by a single user. We address this limitation by introducing updatable privacy-preserving blueprint schemes (UPPB), which enhance the original notion with the ability for multiple parties to non-interactively update the private value $x$ in a blueprint. Moreover, a UPPB scheme allows for verifying that a blueprint is the result of a sequence of valid updates while revealing nothing else. We present uBlu, an efficient instantiation of UPPB for computing a comparison between private user values and a private threshold $t$ set by the auditor, where the current value $x$ is the cumulative sum of private inputs, which enables applications such as privacy-preserving anti-money laundering and location tracking. Additionally, we show the feasibility of the notion generically for all value update functions and (binary) predicates from FHE and NIZKs. Our main technical contribution is a technique to keep the size of primary blueprint components independent of the number of updates and reasonable for practical applications. This is achieved by elegantly extending an algebraic NIZK by Couteau and Hartmann (CRYPTO'20) with an update function and making it compatible with our additive updates. This result is of independent interest and may find additional applications thanks to the concise size of our proofs.
Last updated:  2023-11-27
CASE: A New Frontier in Public-Key Authenticated Encryption
Shashank Agrawal, Shweta Agrawal, Manoj Prabhakaran, Rajeev Raghunath, and Jayesh Singla
We introduce a new cryptographic primitive, called Completely Anonymous Signed Encryption (CASE). CASE is a public-key authenticated encryption primitive, that offers anonymity for senders as well as receivers. A "case-packet" should appear, without a (decryption) key for opening it, to be a blackbox that reveals no information at all about its contents. To decase a case-packet fully - so that the message is retrieved and authenticated - a verifcation key is also required. Defining security for this primitive is subtle. We present a relatively simple Chosen Objects Attack (COA) security definition. Validating this definition, we show that it implies a comprehensive indistinguishability-preservation definition in the real-ideal paradigm. To obtain the latter definition, we extend the Cryptographic Agents framework of [2, 3] to allow maliciously created objects. We also provide a novel and practical construction for COA-secure CASE under standard assumptions in public-key cryptography, and in the standard model. We believe CASE can be a staple in future cryptographic libraries, thanks to its robust security guarantees and efficient instantiations based on standard assumptions.
Last updated:  2023-11-18
There Is Always a Way Out! Destruction-Resistant Key Management: Formal Definition and Practical Instantiation
Yuan Zhang, Yaqing Song, Shiyu Li, Weijia Li, Zeqi Lai, and Qiang Tang
A central advantage of deploying cryptosystems is that the security of large high-sensitive data sets can be reduced to the security of a very small key. The most popular way to manage keys is to use a $(t,n)-$threshold secret sharing scheme: a user splits her/his key into $n$ shares, distributes them among $n$ key servers, and can recover the key with the aid of any $t$ of them. However, it is vulnerable to device destruction: if all key servers and user's devices break down, the key will be permanently lost. We propose a $\mathrm{\underline{D}}$estruction-$\mathrm{\underline{R}}$esistant $\mathrm{\underline{K}}$ey $\mathrm{\underline{M}}$anagement scheme, dubbed DRKM, which ensures the key availability even if destruction occurs. In DRKM, a user utilizes her/his $n^{*}$ personal identification factors (PIFs) to derive a cryptographic key but can retrieve the key using any $t^{*}$ of the $n^{*}$ PIFs. As most PIFs can be retrieved by the user $\textit{per se}$ without requiring $\textit{stateful}$ devices, destruction resistance is achieved. With the integration of a $(t,n)-$threshold secret sharing scheme, DRKM also provides $\textit{portable}$ key access for the user (with the aid of any $t$ of $n$ key servers) before destruction occurs. DRKM can be utilized to construct a destruction-resistant cryptosystem (DRC) in tandem with any backup system. We formally prove the security of DRKM, implement a DRKM prototype, and conduct a comprehensive performance evaluation to demonstrate its high efficiency. We further utilize Cramer's Rule to reduce the required buffer to retrieve a key from 25 MB to 40 KB (for 256-bit security).
Last updated:  2023-11-17
Succinct Arguments over Towers of Binary Fields
Benjamin E. Diamond and Jim Posen
We introduce an efficient SNARK for towers of binary fields. Adapting Brakedown (CRYPTO '23), we construct a multilinear polynomial commitment scheme suitable for polynomials over tiny fields, including that with 2 elements. Our commitment scheme, unlike those of previous works, treats small-field polynomials with zero embedding overhead. We further introduce binary-field adaptations of HyperPlonk's (EUROCRYPT '23) product and permutation checks, as well as of Lasso's lookup. Our scheme's binary PLONKish variant captures standard hash functions—like Keccak-256 and Grøstl—extremely efficiently. With recourse to thorough performance benchmarks, we argue that our scheme can efficiently generate precisely those Keccak-256-proofs which critically underlie modern efforts to scale Ethereum.
Last updated:  2023-11-17
An efficient quantum parallel repetition theorem and applications
John Bostanci, Luowen Qian, Nicholas Spooner, and Henry Yuen
We prove a tight parallel repetition theorem for $3$-message computationally-secure quantum interactive protocols between an efficient challenger and an efficient adversary. We also prove under plausible assumptions that the security of $4$-message computationally secure protocols does not generally decrease under parallel repetition. These mirror the classical results of Bellare, Impagliazzo, and Naor [BIN97]. Finally, we prove that all quantum argument systems can be generically compiled to an equivalent $3$-message argument system, mirroring the transformation for quantum proof systems [KW00, KKMV07]. As immediate applications, we show how to derive hardness amplification theorems for quantum bit commitment schemes (answering a question of Yan [Yan22]), EFI pairs (answering a question of Brakerski, Canetti, and Qian [BCQ23]), public-key quantum money schemes (answering a question of Aaronson and Christiano [AC13]), and quantum zero-knowledge argument systems. We also derive an XOR lemma [Yao82] for quantum predicates as a corollary.
Last updated:  2023-11-17
A Solution to a Conjecture on the Maps $\chi_n^{(k)}$
Kamil Otal
The Boolean map $\chi_n^{(k)}:\mathbb{F}_{2^k}^n\rightarrow \mathbb{F}_{2^k}^n$, $x\mapsto u$ given by $u_i=x_i+(x_{(i+1)\ \mathrm{mod}\ n}+1)x_{(i+2)\ \mathrm{mod}\ n}$ appears in various permutations as a part of cryptographic schemes such as KECCAK-f, ASCON, Xoodoo, Rasta, and Subterranean (2.0). Schoone and Daemen investigated some important algebraic properties of $\chi_n^{(k)}$ in [IACR Cryptology ePrint Archive 2023/1708]. In particular, they showed that $\chi_n^{(k)}$ is not bijective when $n$ is even, when $n$ is odd and $k$ is even, and when $n$ is odd and $k$ is a multiple of $3$. They left the remaining cases as a conjecture. In this paper, we examine this conjecture by taking some smaller sub-cases into account by reinterpreting the problem via the Gröbner basis approach. As a result, we prove that $\chi_n^{(k)}$ is not bijective when $n$ is a multiple of 3 or 5, and $k$ is a multiple of 5 or 7. We then present an algorithmic method that solves the problem for any given arbitrary $n$ and $k$ by generalizing our approach. We also discuss the systematization of our proof and computational boundaries.
Last updated:  2023-11-25
A Lattice Attack on CRYSTALS-Kyber with Correlation Power Analysis
Yen-Ting Kuo and Atsushi Takayasu
CRYSTALS-Kyber is a key-encapsulation mechanism, whose security is based on the hardness of solving the learning-with-errors (LWE) problem over module lattices. As in its specification, Kyber prescribes the usage of the Number Theoretic Transform (NTT) for efficient polynomial multiplication. Side-channel assisted attacks against Post-Quantum Cryptography (PQC) algorithms like Kyber remain a concern in the ongoing standardization process of quantum-computer-resistant cryptosystems. Among the attacks, correlation power analysis (CPA) is emerging as a popular option because it does not require detailed knowledge about the attacked device and can reveal the secret key even if the recorded power traces are extremely noisy. In this paper, we present a two-step attack to achieve a full-key recovery on lattice-based cryptosystems that utilize NTT for efficient polynomial multiplication. First, we use CPA to recover a portion of the secret key from the power consumption of these polynomial multiplications in the decryption process. Then, using the information, we are able to fully recover the secret key by constructing an LWE problem with a smaller lattice rank and solving it with lattice reduction algorithms. Our attack can be expanded to other cryptosystems using NTT-based polynomial multiplication, including Saber. It can be further parallelized and experiments on simulated traces show that the whole process can be done within 20 minutes on a 16-core machine with 200 traces. Compared to other CPA attacks targeting NTT in the cryptosystems, our attack achieves lower runtime in practice. Furthermore, we can theoretically decrease the number of traces needed by using lattice reduction if the same measurement is used. Our lattice attack also outperforms the state-of-the-art result on integrating side-channel hints into lattices, however, the improvement heavily depends on the implementation of the NTT chosen by the users.
Last updated:  2023-11-17
Pairing-Free Blind Signatures from CDH Assumptions
Rutchathon Chairattana-Apirom, Stefano Tessaro, and Chenzhi Zhu
This paper presents new blind signatures for which concurrent security, in the random oracle model, can be proved from variants of the computational Diffie-Hellman (CDH) assumption in pairing-free groups without relying on the algebraic group model (AGM). With the exception of careful instantiations of generic non-black box techniques following Fischlin's paradigm (CRYPTO '06), prior works without the AGM in the pairing-free regime have only managed to prove security for a-priori bounded concurrency. Our most efficient constructions rely on the chosen-target CDH assumption, which has been used to prove security of Blind BLS by Boldyreva (PKC '03), and can be seen as blind versions of signatures by Goh and Jarecki (EUROCRYPT '03) and Chevallier-Mames (CRYPTO'05). We also give a less efficient scheme with security based on (plain) CDH which builds on top of a natural pairing-free variant of Rai-Choo (Hanzlik, Loss, and Wagner, EUROCRYPT '23). Our schemes have signing protocols that consist of four (in order to achieve regular unforgeability) or five moves (for strong unforgeability). The blindness of our schemes is either computational (assuming the hardness of the discrete logarithm problem), or statistical in the random oracle model.
Last updated:  2023-11-17
Privacy-Preserving Cross-Facility Early Warning for Unknown Epidemics
Shiyu Li, Yuan Zhang, Yaqing Song, Fan Wu, Feng Lyu, Kan Yang, and Qiang Tang
Syndrome-based early epidemic warning plays a vital role in preventing and controlling unknown epidemic outbreaks. It monitors the frequency of each syndrome, issues a warning if some frequency is aberrant, identifies potential epidemic outbreaks, and alerts governments as early as possible. Existing systems adopt a cloud-assisted paradigm to achieve cross-facility statistics on the syndrome frequencies. However, in these systems, all symptom data would be directly leaked to the cloud, which causes critical security and privacy issues. In this paper, we first analyze syndrome-based early epidemic warning systems and formalize two security notions, i.e., symptom confidentiality and frequency confidentiality, according to the inherent security requirements. We propose EpiOracle, a cross-facility early warning scheme for unknown epidemics. EpiOracle ensures that the contents and frequencies of syndromes will not be leaked to any unrelated parties; moreover, our construction uses only a symmetric-key encryption algorithm and cryptographic hash functions (e.g., [CBC]AES and SHA-3), making it highly efficient. We formally prove the security of EpiOracle in the random oracle model. We also implement an EpiOracle prototype and evaluate its performance using a set of real-world symptom lists. The evaluation results demonstrate its practical efficiency.
Last updated:  2023-11-16
Immunizing Backdoored PRGs
Marshall Ball, Yevgeniy Dodis, and Eli Goldin
A backdoored Pseudorandom Generator (PRG) is a PRG which looks pseudorandom to the outside world, but a saboteur can break PRG security by planting a backdoor into a seemingly honest choice of public parameters, $pk$, for the system. Backdoored PRGs became increasingly important due to revelations about NIST’s backdoored Dual EC PRG, and later results about its practical exploitability. Motivated by this, at Eurocrypt'15 Dodis et al. [21] initiated the question of immunizing backdoored PRGs. A $k$-immunization scheme repeatedly applies a post-processing function to the output of $k$ backdoored PRGs, to render any (unknown) backdoors provably useless. For $k=1$, [21] showed that no deterministic immunization is possible, but then constructed "seeded" $1$-immunizer either in the random oracle model, or under strong non-falsifiable assumptions. As our first result, we show that no seeded $1$-immunization scheme can be black-box reduced to any efficiently falsifiable assumption. This motivates studying $k$-immunizers for $k\ge 2$, which have an additional advantage of being deterministic (i.e., "seedless"). Indeed, prior work at CCS'17 [37] and CRYPTO'18 [7] gave supporting evidence that simple $k$-immunizers might exist, albeit in slightly different settings. Unfortunately, we show that simple standard model proposals of [37, 7] (including the XOR function [7]) provably do not work in our setting. On a positive, we confirm the intuition of [37] that a (seedless) random oracle is a provably secure $2$-immunizer. On a negative, no (seedless) $2$-immunization scheme can be black-box reduced to any efficiently falsifiable assumption, at least for a large class of natural $2$-immunizers which includes all "cryptographic hash functions." In summary, our results show that $k$-immunizers occupy a peculiar place in the cryptographic world. While they likely exist, and can be made practical and efficient, it is unlikely one can reduce their security to a "clean" standard-model assumption.
Last updated:  2023-11-16
SoK: Collusion-resistant Multi-party Private Set Intersections in the Semi-honest Model
Jelle Vos, Mauro Conti, and Zekeriya Erkin
Private set intersection protocols allow two parties with private sets of data to compute the intersection between them without leaking other information about their sets. These protocols have been studied for almost 20 years, and have been significantly improved over time, reducing both their computation and communication costs. However, when more than two parties want to compute a private set intersection, these protocols are no longer applicable. While extensions exist to the multi-party case, these protocols are significantly less efficient than the two-party case. It remains an open question to design collusion-resistant multi-party private set intersection (MPSI) protocols that come close to the efficiency of two-party protocols. This work is made more difficult by the immense variety in the proposed schemes and the lack of systematization. Moreover, each new work only considers a small subset of previously proposed protocols, leaving out important developments from older works. Finally, MPSI protocols rely on many possible constructions and building blocks that have not been summarized. This work aims to point protocol designers to gaps in research and promising directions, pointing out common security flaws and sketching a frame of reference. To this end, we focus on the semi-honest model. We conclude that current MPSI protocols are not a one-size-fits-all solution, and instead there exist many protocols that each prevail in their own application setting.
Last updated:  2023-11-16
Watermarks in the Sand: Impossibility of Strong Watermarking for Generative Models
Hanlin Zhang, Benjamin L. Edelman, Danilo Francati, Daniele Venturi, Giuseppe Ateniese, and Boaz Barak
Watermarking generative models consists of planting a statistical signal (watermark) in a model’s output so that it can be later verified that the output was generated by the given model. A strong watermarking scheme satisfies the property that a computationally bounded attacker cannot erase the watermark without causing significant quality degradation. In this paper, we study the (im)possibility of strong watermarking schemes. We prove that, under well-specified and natural assumptions, strong watermarking is impossible to achieve. This holds even in the private detection algorithm setting, where the watermark insertion and detection algorithms share a secret key, unknown to the attacker. To prove this result, we introduce a generic efficient watermark attack; the attacker is not required to know the private key of the scheme or even which scheme is used. Our attack is based on two assumptions: (1) The attacker has access to a “quality oracle” that can evaluate whether a candidate output is a high-quality response to a prompt, and (2) The attacker has access to a “perturbation oracle” which can modify an output with a nontrivial probability of maintaining quality, and which induces an efficiently mixing random walk on high-quality outputs. We argue that both assumptions can be satisfied in practice by an attacker with weaker computational capabilities than the watermarked model itself, to which the attacker has only black-box access. Furthermore, our assumptions will likely only be easier to satisfy over time as models grow in capabilities and modalities. We demonstrate the feasibility of our attack by instantiating it to attack three existing watermarking schemes for large language models: Kirchenbauer et al. (2023), Kuditipudi et al. (2023), and Zhao et al. (2023). The same attack successfully removes the watermarks planted by all three schemes, with only minor quality degradation.
Last updated:  2023-11-16
Beyond Security: Achieving Fairness in Mailmen-Assisted Timed Data Delivery
Shiyu Li, Yuan Zhang, Yaqing Song, Hongbo Liu, Nan Cheng, Hongwei Li, Dahai Tao, and Kan Yang
Timed data delivery is a critical service for time-sensitive applications that allows a sender to deliver data to a recipient, but only be accessible at a specific future time. This service is typically accomplished by employing a set of mailmen to complete the delivery mission. While this approach is commonly used, it is vulnerable to attacks from realistic adversaries, such as a greedy sender (who accesses the delivery service without paying the service charge) and malicious mailmen (who release the data prematurely without being detected). Although some research works have been done to address these adversaries, most of them fail to achieve fairness. In this paper, we formally define the fairness requirement for mailmen-assisted timed data delivery and propose a practical scheme, dubbed DataUber, to achieve fairness. DataUber ensures that honest mailmen receive the service charge, lazy mailmen do not receive the service charge, and malicious mailmen are punished. Specifically, DataUber consists of two key techniques: 1) a new cryptographic primitive, i.e., Oblivious and Verifiable Threshold Secret Sharing (OVTSS), enabling a dealer to distribute a secret among multiple participants in a threshold and verifiable way without knowing any one of the shares, and 2) a smart-contract-based complaint mechanism, allowing anyone to become a reporter to complain about a mailman's misbehavior to a smart contract and receive a reward. Furthermore, we formally prove the security of DataUber and demonstrate its practicality through a prototype implementation.
Last updated:  2023-11-16
Decentralized Private Steam Aggregation from Lattices
Uddipana Dowerah and Aikaterini Mitrokotsa
As various industries and government agencies increasingly seek to build quantum computers, the development of post-quantum constructions for different primitives becomes crucial. Lattice-based cryptography is one of the top candidates for constructing quantum-resistant primitives. In this paper, we propose a decentralized Private Stream Aggregation (PSA) protocol based on the Learning with Errors (LWE) problem. PSA allows secure aggregation of time-series data over multiple users without compromising the privacy of the individual data. In almost all previous constructions, a trusted entity is used for the generation of keys. We consider a scenario where the users do not want to rely on a trusted authority. We, therefore, propose a decentralized PSA (DPSA) scheme where each user generates their own keys without the need for a trusted setup. We give a concrete construction based on the hardness of the LWE problem both in the random oracle model and in the standard model.
Last updated:  2023-11-17
Scalable and Adaptively Secure Any-Trust Distributed Key Generation and All-hands Checkpointing
Hanwen Feng, Tiancheng Mai, and Qiang Tang
The classical distributed key generation protocols (DKG) are resurging due to their widespread applications in blockchain. While efforts have been made to improve DKG communication, practical large scale deployments are still yet to come, due to various challenges including broadcast channel scalability and worst-case complaint phase. In this paper, we propose a practical DKG for DL-based cryptosystems, with only (quasi-)linear computation/communication cost per participant, with the help of a public ledger, and beacon; Notably, our DKG only incurs constant-size blockchain storage cost for broadcast, even in the face of worst-case complaints. Moreover, our protocol satisfies adaptive security. The key to our improvements lies in delegating the most costly operations to an Any-Trust group. This group is randomly sampled and consists of a small number of individuals. The population only trusts that at least one member in the group is honest, without knowing which one. Additionally, we introduce an extended broadcast channel based on a blockchain and data dispersal network (such as IPFS), enabling reliable broadcasting of arbitrary-size messages at the cost of constant-size blockchain storage, which may be of independent interest. Our DKG leads to a fully practical instantiation of Filecoin's checkpointing mechanism, in which all validators of a Proof-of-Stake (PoS) blockcahin periodically run DKG and threshold signing to create checkpoints on Bitcoin, thereby enhancing the security of the PoS chain. In comparison with another checkpointing approach of Babylon (Oakland, 2023), ours enjoys a significally smaller monetary cost of Bitcoin transaction fees. For a PoS chain with $2^{12}$ validators, our cost is merely 0.6% of that incurred by Babylon's approach.
Last updated:  2023-11-16
Robust Combiners and Universal Constructions for Quantum Cryptography
Taiga Hiroka, Fuyuki Kitagawa, Ryo Nishimaki, and Takashi Yamakawa
A robust combiner combines many candidates for a cryptographic primitive and generates a new candidate for the same primitive. Its correctness and security hold as long as one of the original candidates satisfies correctness and security. A universal construction is a closely related notion to a robust combiner. A universal construction for a primitive is an explicit construction of the primitive that is correct and secure as long as the primitive exists. It is known that a universal construction for a primitive can be constructed from a robust combiner for the primitive in many cases. Although robust combiners and universal constructions for classical cryptography are widely studied, robust combiners and universal constructions for quantum cryptography have not been explored so far. In this work, we define robust combiners and universal constructions for several quantum cryptographic primitives including one-way state generators, public-key quantum money, quantum bit commitments, and unclonable encryption, and provide constructions of them. On a different note, it was an open problem how to expand the plaintext length of unclonable encryption. In one of our universal constructions for unclonable encryption, we can expand the plaintext length, which resolves the open problem.
Last updated:  2023-11-16
A note on ``HAKECC: highly efficient authentication and key agreement scheme based on ECDH for RFID in IOT environment''
Zhengjun Cao
We show that the Nikooghadam-Shahriari-Saeidi authentication and key agreement scheme [J. Inf. Secur. Appl., 76, 103523 (2023)] cannot resist impersonation attack, not as claimed. An adversary can impersonate the RFID reader to cheat the RFID tag. The drawback results from its simple secret key invoking mechanism. We also find it seems difficult to revise the scheme due to the inherent flaw.
Last updated:  2023-11-15
On the Feasibility of E2E Verifiable Online Voting – A Case Study From Durga Puja Trial
Horia Druliac, Matthew Bardsley, Chris Riches, Christian Dunn, Luke Harrison, Bimal Roy, and Feng Hao
India is the largest democracy by population and has one of the largest deployments of e-voting in the world for national elections. However, the e-voting machines used in India are not end-to-end (E2E) verifiable. The inability to verify the tallying integrity of an election by the public leaves the outcome open to disputes. E2E verifiable e-voting systems are commonly regarded as the most promising solution to address this problem, but they had not been implemented or trialed in India. It was unclear whether such systems would be usable and practical to the Indian people. Previous works such as Helios require a set of tallying authorities (TAs) to perform the decryption and tallying operations, but finding and managing TAs can prove difficult. This paper presents a TA-free E2E verifiable online voting system based on the DRE-ip protocol. In collaboration with the local authority of New Town, Kolkata, India, we conducted an online voting trial as part of the 2022 Durga Puja festival celebration, during which residents of New Town were invited to use mobile phones to vote for their favourite pujas (festival decorations) in an E2E verifiable manner. 543 participants attended the Durga Puja trial and 95 of them provided feedback by filling in an anonymous survey after voting. Based on the voter feedback, participants generally found the system easy to use. This was the first time that an E2E online voting system had been built and tested in India, suggesting its feasibility for non-statutory voting scenarios.
Last updated:  2023-11-15
A Comprehensive Survey on Non-Invasive Fault Injection Attacks
Amit Mazumder Shuvo, Tao Zhang, Farimah Farahmandi, and Mark Tehranipoor
Non-invasive fault injection attacks have emerged as significant threats to a spectrum of microelectronic systems ranging from commodity devices to high-end customized processors. Unlike their invasive counterparts, these attacks are more affordable and can exploit system vulnerabilities without altering the hardware physically. Furthermore, certain non-invasive fault injection strategies allow for remote vulnerability exploitation without the requirement of physical proximity. However, existing studies lack extensive investigation into these attacks across diverse target platforms, threat models, emerging attack strategies, assessment frameworks, and mitigation approaches. In this paper, we provide a comprehensive overview of contemporary research on non-invasive fault injection attacks. Our objective is to consolidate and scrutinize the various techniques, methodologies, target systems susceptible to the attacks, and existing mitigation mechanisms advanced by the research community. Besides, we categorize attack strategies based on several aspects, present a detailed comparison among the categories, and highlight research challenges with future direction. By underlining and discussing the landscape of cutting-edge, non-invasive fault injection, we hope more researchers, designers, and security professionals examine the attacks further and take such threats into consideration while developing effective countermeasures.
Last updated:  2023-11-17
Homomorphic Polynomial Public Key Cryptography for Quantum-secure Digital Signature
Randy Kuang, Maria Perepechaenko, Mahmoud Sayed, and Dafu Lou
In their 2022 study, Kuang et al. introduced the Multivariable Polynomial Public Key (MPPK) cryptography, a quantum-safe public key cryptosystem leveraging the mutual inversion relationship between multiplication and division. MPPK employs multiplication for key pair construction and division for decryption, generating public multivariate polynomials. Kuang and Perepechaenko expanded the cryptosystem into the Homomorphic Polynomial Public Key (HPPK), transforming product polynomials over large hidden rings using homomorphic encryption through modular multiplications. Initially designed for key encapsulation mechanism (KEM), HPPK ensures security through homomorphic encryption of public polynomials over concealed rings. This paper extends its application to a digital signature scheme. The framework of HPPK KEM can not be directly applied to the digital signatures dues to the different nature of verification procedure compared to decryption procedure. Thus, in order to use the core ideas of the HPPK KEM scheme in the framework of digital signatures, the authors introduce an extension of the Barrett reduction algorithm. This extension transforms modular multiplications over hidden rings into divisions in the verification equation, conducted over a prime field. The extended algorithm non-linearly embeds the signature into public polynomial coefficients, employing the floor function of big integer divisions. This innovative approach overcomes vulnerabilities associated with linear relationships of earlier MPPK DS schemes. The security analysis reveals exponential complexity for both private key recovery and forged signature attacks, taking into account that the bit length of the rings is twice that of the prime field size. The effectiveness of the proposed Homomorphic Polynomial Public Key Digital Signature (HPPK DS) scheme is illustrated through a practical toy example, showcasing its intricate functionality and enhanced security features.
Last updated:  2023-11-15
The Impact of Hash Primitives and Communication Overhead for Hardware-Accelerated SPHINCS+
Patrick Karl, Jonas Schupp, and Georg Sigl
SPHINCS+ is a signature scheme included in the first NIST post-quantum standard, that bases its security on the underlying hash primitive. As most of the runtime of SPHINCS+ is caused by the evaluation of several hash- and pseudo-random functions, instantiated via the hash primitive, offloading this computation to dedicated hardware accelerators is a natural step. In this work, we evaluate different architectures for hardware acceleration of such a hash primitive with respect to its use-case and evaluate them in the context of SPHINCS+. We attach hardware accelerators for different hash primitives (SHAKE256 and Asconxof for both full and round-reduced versions) to CPU interfaces having different transfer speeds. We show, that for most use-cases, data transfer determines the overall performance if accelerators are equipped with FIFOs.
Last updated:  2023-11-15
Introducing Clapoti(s): Evaluating the isogeny class group action in polynomial time
Aurel Page and Damien Robert
In this short note, we present a simplified (but slower) version Clapoti of Clapotis, whose full description will appear later. Let 𝐸/𝔽_𝑞 be an elliptic curve with an effective primitive orientation by a quadratic imaginary order 𝑅 ⊂ End(𝐸). Let 𝔞 be an invertible ideal in 𝑅. Clapoti is a randomized polynomial time algorithm in 𝑂 ((log Δ_𝑅 + log 𝑞)^𝑂(1) ) operations to compute the class group action 𝐸 ↦ 𝐸_𝔞 ≃ 𝐸/𝐸[𝔞].
Last updated:  2023-11-15
The Non-Uniform Perebor Conjecture for Time-Bounded Kolmogorov Complexity is False
Noam Mazor and Rafael Pass
The Perebor (Russian for “brute-force search”) conjectures, which date back to the 1950s and 1960s are some of the oldest conjectures in complexity theory. The conjectures are a stronger form of the NP ̸ = P conjecture (which they predate) and state that for “meta-complexity” problems, such as the Time-bounded Kolmogorov complexity Problem, and the Minimum Circuit Size Problem, there are no better algorithms than brute force search. In this paper, we disprove the non-uniform version of the Perebor conjecture for the Time-Bounded Kolmogorov complexity problem. We demonstrate that for every polynomial t(·), there exists of a circuit of size $2^{4n/5+o(n)}$ that solves the t(·)-bounded Kolmogorov complexity problem on every instance. Our algorithm is black-box in the description of the Universal Turing Machine employed in the definition of Kolmogorov Complexity, and leverages the characterization of one-way functions through the hardness of the time-bounded Kolmogorov complexity problem of Liu and Pass (FOCS’20), and the time-space trade-off for one-way functions of Fiat and Naor (STOC’91). We additionally demonstrate that no such black-box algorithm can have sub-exponential circuit size. Along the way (and of independent interest), we extend the result of Fiat and Naor and demonstrate that any efficiently computable function can be inverted (with probability 1) by a circuit of size 2^{4n/5+o(n)}; as far as we know, this yields the first formal proof that a non-trivial circuit can invert any efficient function.
Last updated:  2023-11-15
Distributed Differential Privacy via Shuffling vs Aggregation: a Curious Study
Yu Wei, Jingyu Jia, Yuduo Wu, Changhui Hu, Changyu Dong, Zheli Liu, Xiaofeng Chen, Yun Peng, and Shaowei Wang
How to achieve distributed differential privacy (DP) without a trusted central party is of great interest in both theory and practice. Recently, the shuffle model has attracted much attention. Unlike the local DP model in which the users send randomized data directly to the data collector/analyzer, in the shuffle model an intermediate untrusted shuffler is introduced to randomly permute the data, which have already been randomized by the users, before they reach the analyzer. The most appealing aspect is that while shuffling does not explicitly add more noise to the data, it can make privacy better. The privacy amplification effect in consequence means the users need to add less noise to the data than in the local DP model, but can achieve the same level of differential privacy. Thus, protocols in the shuffle model can provide better accuracy than those in the local DP model. What looks interesting to us is that the architecture of the shuffle model is similar to private aggregation, which has been studied for more than a decade. In private aggregation, locally randomized user data are aggregated by an intermediate untrusted aggregator. Thus, our question is whether aggregation also exhibits some sort of privacy amplification effect? And if so, how good is this ``aggregation model'' in comparison with the shuffle model. We conducted the first comparative study between the two, covering privacy amplification, functionalities, protocol accuracy, and practicality. The results as yet suggest that the new shuffle model does not have obvious advantages over the old aggregation model. On the contrary, protocols in the aggregation model outperform those in the shuffle model, sometimes significantly, in many aspects.
Last updated:  2023-11-15
Secure Transformer Inference
Mu Yuan, Lan Zhang, and Xiang-Yang Li
We present a three-party protocol that can protect both Transformer parameters and user data during the inference phase. For each feedforward inference process, our protocol only introduces permutation computation of input and output data on the user side. Our protocol, Secure Transformer Inference Protocol (STIP), can be applied to real-world services like ChatGPT.
Last updated:  2023-11-28
ZKSMT: A VM for Proving SMT Theorems in Zero Knowledge
Daniel Luick, John Kolesar, Timos Antonopoulos, William R. Harris, James Parker, Ruzica Piskac, Eran Tromer, Xiao Wang, and Ning Luo
Verification of program safety is often reducible to proving the unsatisfiability (i.e., validity) of a formula in Satisfiability Modulo Theories (SMT): Boolean logic combined with theories that formalize arbitrary first-order fragments. Zero-knowledge (ZK) proofs allow SMT formulas to be validated without revealing the underlying formulas or their proofs to other parties, which is a crucial building block for proving the safety of proprietary programs. Recently, Luo et al. (CCS 2022) studied the simpler problem of proving the unsatisfiability of pure Boolean formulas, but it does not support safety proofs generated by SMT solvers. This work presents ZKSMT, a novel framework for proving the validity of SMT formulas in ZK. We design a virtual machine (VM) tailored to efficiently represent the verification process of SMT validity proofs in ZK. Our VM can support the vast majority of popular theories when proving program safety while being complete and sound. To demonstrate this, we instantiate the commonly used theories of equality and linear integer arithmetic in our VM with theory-specific optimizations for proving them in ZK. ZKSMT achieves high practicality even when running on realistic SMT formulas generated by Boogie, a common tool for software verification. It achieves a three-order-of-magnitude improvement compared to a baseline that executes the proof verification code in a general ZK system.
Last updated:  2023-11-20
Guardianship in Group Key Exchange for Limited Environments
Elsie Mestl Fondevik, Britta Hale, and Xisen Tian
Post-compromise security (PCS) has been a core goal of end-to-end encrypted messaging applications for many years, both in one-to-one continuous key agreement (CKA) and for groups (CGKA). At its essence, PCS relies on a compromised party to perform a key update in order to `self-heal'. However, due to bandwidth constraints, receive-only mode, and various other environmental demands of the growing number of use cases for such CGKA protocols, a group member may not be able to issue such updates. In this work, we address the issue of devices functioning in limited mode through the introduction of guardianship, where a designated guardian can perform key updates on the behalf of its paired edge device. We introduce a Guardianship PCS (GPCS) security, and provide an associated security experiment. We investigate various architectural designs in the pursuit of GPCS, provide constructions and security analyses, and describe trade-offs.
Last updated:  2023-11-14
Biscuit: New MPCitH Signature Scheme from Structured Multivariate Polynomials
Luk Bettale, Delaram Kahrobaei, Ludovic Perret, and Javier Verbel
This paper describes Biscuit, a new multivariate-based signature scheme derived using the MPCitH approach. The security of Biscuit is related to the problem of solving a set of quadratic structured systems of algebraic equations. These equations are highly compact and can be evaluated using very few multiplications. The core of Biscuit is a rather simple MPC protocol which consists of the parallel execution of a few secure multiplications using standard optimized multiplicative triples. This paper also includes several improvements with respect to Biscuit submission to the last NIST PQC standardization process for additional signature schemes. Notably, we introduce a new hypercube variant of Biscuit, refine the security analysis with recent third-party attacks, and present a new avx2 implementation of Biscuit.
Last updated:  2023-11-14
Non-Interactive Zero-Knowledge Functional Proofs
Gongxian Zeng, Junzuo Lai, Zhengan Huang, Linru Zhang, Xiangning Wang, Kwok-Yan Lam, Huaxiong Wang, and Jian Weng
In this paper, we consider to generalize NIZK by empowering a prover to share a witness in a fine-grained manner with verifiers. Roughly, the prover is able to authorize a verifier to obtain extra information of witness, i.e., besides verifying the truth of the statement, the verifier can additionally obtain certain function of the witness from the accepting proof using a secret functional key provided by the prover. To fulfill these requirements, we introduce a new primitive called \emph{non-interactive zero-knowledge functional proofs (fNIZKs)}, and formalize its security notions. We provide a generic construction of fNIZK for any $\textsf{NP}$ relation $\mathcal{R}$, which enables the prover to share any function of the witness with a verifier. For a widely-used relation about set membership proof (implying range proof), we construct a concrete and efficient fNIZK, through new building blocks (set membership encryption and dual inner-product encryption), which might be of independent interest.
Last updated:  2023-11-14
Pulsar: Secure Steganography through Diffusion Models
Tushar M. Jois, Gabrielle Beck, and Gabriel Kaptchuk
Widespread efforts to subvert acccess to strong cryptography has renewed interest in steganography, the practice of embedding sensitive messages in mundane cover messages. Recent efforts at provably secure steganography have only focused on text-based generative models and cannot support other types of models, such as diffusion models, which are used for high-quality image synthesis. In this work, we initiate the study of securely embedding steganographic messages into the output of image diffusion models. We identify that the use of variance noise during image generation provides a suitable steganographic channel. We develop our construction, Pulsar, by building optimizations to make this channel practical for communication. Our implementation of Pulsar is capable of embedding $\approx 275$-$542$ bytes (on average) into a single image without altering the distribution of the generated image, all in the span of $\approx 3$ seconds of online time on a laptop. In addition, we discuss how the results of Pulsar can inform future research into diffusion models. Pulsar shows that diffusion models are a promising medium for steganography and censorship resistance.
Last updated:  2023-11-19
Adaptively Secure Consensus with Linear Complexity and Constant Round under Honest Majority in the Bare PKI Model, and Separation Bounds from the Idealized Message-Authentication Model
Matthieu Rambaud
We consider the mainstream model in secure computation known as the bare PKI setup, also as the {bulletin-board PKI}. It allows players to broadcast once and non-interactively before they receive their inputs and start the execution. A bulletin-board PKI is essentially the minimum setup known so far to implement the model known as {messages-authentication}, i.e., when $P$ is forwarded a signed message, it considers it to be issued by $R$ if and only if $R$ signed it. It is known since [Lamport et al, 82] that BA under honest majority (let alone secure computation) would not be possible without messages-authentication. But as further highlighted by [Borcherding, 96], messages-authentication cannot not simply be implemented with digital signatures, without a bulletin-board of public keys. So the bulletin-board PKI setup and the messages-authentication model seem very close: this raizes the question whether there is a separation between them. In the bulletin-board PKI setup, the most communication-efficient synchronous BA is the one of [Boyle-Cohen-Goel, Podc'21 \& J. Cryptol.'24], which has $O(n.\text{polylog}(n))$ bit complexity, $f<n(1/3-\epsilon)$ resilience and tolerates an adversary which cannot adaptively corrupt after the setup. Our main upper-bound is a BA (and also a VBA) in this same model with strictly better parameters: {quasi-optimal} resilience $f<n(1/2-\epsilon)$, with an expected bit complexity of communications which is {linear} in $n$, and tolerance to an {adaptive} rushing adversary (but which unavoidably cannot remove messages sent). As [BCG'21], they have constant expected latency. All previous BAs or VBAs achieving the same metrics as our upper bound, are either in the static adversary model: Sleepy [Pass-Shi, Asiacrypt'17], Snow White [Daian-Pass-Shi, FC'19], or assume more than a bare PKI setup: (i) The model of Thunderella [Pass-Shi, EC'17], Algorand [Gilad et al, SOSP'17], Praos [David et al, EC'18], [Goyal et al, FC'21] and [Momose et al, CCS'22 and CCS'23] assumes a public random seed which is unpredictable until strictly after all players published on the bulletin board; (ii) [Abraham et al, Podc'19] assume a trusted entity which honestly samples the keys of all players; (iii) All known implementations of the setups (i) and (ii), as well as the setup of [Blum et al, TCC'20], require interactions, furthermore in the form of BAs. (iv) [Garay-Kiayas-Shen '23] assume that honest players work more than the adversary, or, [Eckey-Faust-Loss et al '17 '22] at least as fast. Of independent interest, our tool is a very simple non-interactive mechanism which {sets-up a self-sortition function from non-interactive publications on the bulletin board}, and still, guarantees an honest majority in every committee up to probability exponentially small in both $\epsilon$ and in the multicast complexity. We provide the following further results: {- Optimality.} We show that resilience up to a tight honest majority $f<n/2$ is impossible for any multicast-based adaptively secure BA with subquadratic communication, whatever the setup. {- Separation.} We show impossibility of subquadratic multicast-based BA in the messages-authentication model. Our model for this lower bound is even stronger, since it onboards other assumptions at least as strong as all popular implications of a bulletin-board PKI setup: {secure channels}, {a (possibly structured) random string}, {NIZK}. {- Partial synchrony.} Given that the multicast lower-bound holds a fortiori, and that the upper-bound adapts seamlessly (for $f<n(1/3-\epsilon)$), the separation also holds. We show a second separation, which holds for general BAs, non-necessarily multicast-based: any partially-synchronous BA in the messages-authentication model, if it has linear message complexity, then it has latency at least {logarithmic in $f$}. {- Extension to VBA.} We extend to VBA the logarithmic latency lower bound. This is the first communication lower bound for randomized VBA to our knowledge. It shows that the separation under partial synchrony also holds for VBA. Along the way, we close the characterization of [Civit et al, Podc'23] of validity conditions in authenticated consensus, by apparently new results on VBA: both BA and VBA are infeasible under partial synchrony beyond $f<n/3$, whatever the setup; whereas synchronous VBA is feasible up to $f=n-1$ (contrary to BA).
Last updated:  2023-11-13
How to Use Quantum Indistinguishability Obfuscation
Andrea Coladangelo and Sam Gunn
Quantum copy protection, introduced by Aaronson, enables giving out a quantum program-description that cannot be meaningfully duplicated. Despite over a decade of study, copy protection is only known to be possible for a very limited class of programs. As our first contribution, we show how to achieve "best-possible" copy protection for all programs. We do this by introducing quantum state indistinguishability obfuscation (qsiO), a notion of obfuscation for quantum descriptions of classical programs. We show that applying qsiO to a program immediately achieves best-possible copy protection. Our second contribution is to show that, assuming injective one-way functions exist, qsiO is concrete copy protection for a large family of puncturable programs --- significantly expanding the class of copy-protectable programs. A key tool in our proof is a new variant of unclonable encryption (UE) that we call coupled unclonable encryption (cUE). While constructing UE in the standard model remains an important open problem, we are able to build cUE from one-way functions. If we additionally assume the existence of UE, then we can further expand the class of puncturable programs for which qsiO is copy protection. Finally, we construct qsiO relative to an efficient quantum oracle.
Last updated:  2023-11-13
HashRand: Efficient Asynchronous Random Beacon without Threshold Cryptographic Setup
Akhil Bandarupalli, Adithya Bhat, Saurabh Bagchi, Aniket Kate, and Michael Reiter
Regular access to unpredictable and bias-resistant randomness is important for applications such as blockchains, voting, and secure distributed computing. Distributed random beacon protocols address this need by distributing trust across multiple nodes, with the majority of them assumed to be honest. These protocols have found applications in blockchain technology, leading to the proposal of several distributed random beacon protocols, with some already implemented. However, many current random beacon systems rely on threshold cryptographic setups or exhibit high computational costs, while others assume partial or bounded synchronous networks. To overcome these limitations, we propose HashRand, a computation and communication-efficient asynchronous random beacon protocol that uses a secure Hash function to generate beacons and pairwise secure channels. HashRand has a per-node communication complexity of $\mathcal{O}(\lambda n \log(n))$ bits per beacon. The computational efficiency of HashRand is attributed to the two orders of magnitude lower time of a one-way Hash computation compared to discrete log exponentiation. Interestingly, besides reduced overhead, HashRand achieves Post-Quantum security by leveraging the secure Hash function against quantum adversaries, setting it apart from other random beacon protocols that use discrete log cryptography. In a geo-distributed testbed of $n=160$ nodes, HashRand produces 1 beacon every second, which is at least 4x higher than Spurt. We also demonstrate the practical utility of HashRand by implementing a Post-Quantum secure Asynchronous SMR protocol, which has a response rate of over 122k txns per second over a WAN at $n=40$ nodes.
Last updated:  2023-11-13
That’s not my signature! Fail-stop signatures for a post-quantum world
Cecilia Boschini, Hila Dahari, Moni Naor, and Eyal Ronen
The Snowden's revelations kick-started a community-wide effort to develop cryptographic tools against mass surveillance. In this work, we propose to add another primitive to that toolbox: Fail-Stop Signatures (FSS) [EC'89]. FSS are digital signatures enhanced with a forgery-detection mechanism that can protect a PPT signer from more powerful attackers. Despite the fascinating concept, research in this area stalled after the '90s. However, the ongoing transition to post-quantum cryptography, with its hiccups due to the novelty of underlying assumptions, has become the perfect use case for FSS. This paper aims to reboot research on FSS with practical use in mind: Our framework for FSS includes ``fine-grained'' security definitions (that assume a powerful, but bounded adversary e.g: can break $128$-bit of security, but not $256$-bit). As an application, we show new FSS constructions for the post-quantum setting. We show that FSS are equivalent to standard, provably secure digital signatures that do not require rewinding or programming random oracles, and that this implies lattice-based FSS. Our main construction is an FSS version of SPHINCS, which required building FSS versions of all its building blocks: WOTS, XMSS, and FORS. In the process, we identify and provide generic solutions for two fundamental issues arising when deriving a large number of private keys from a single seed, and when building FSS for Hash-and-Sign-based signatures.
Last updated:  2023-11-13
Formal verification of the post-quantum security properties of IKEv2 PPK (RFC 8784) using the Tamarin Prover
Sophie Stevens
The Internet Key Exchange version 2 (IKEv2) (RFC 7296) is a component of IPsec used to authenticate two parties (the initiator and responder) to each other and to establish a set of security parameters for the communications. The security parameters include secret keys to encrypt and authenticate data as well as the negotiation of a set of cryptographic algorithms. The core documentation uses exclusively Diffie-Hellman exchanges to agree the security information. However, this is not a quantum-secure option due to the ability of Shor's algorithm to break the security assumption underlying the Diffie-Hellman. A post-quantum solution is to include a preshared key in the exchange, as proposed by the extension RFC 8784; assuming that this preshared key has sufficient entropy, the keys created in the IKEv2 exchange will be resistant to a quantum computer. In this paper, we investigate the security claims of RFC 8784 using formal verification methods. We find that keys created using the preshared key are secret from an adversary. However, certain authentication properties of the protocol that are weakened under the assumption that Diffie-Hellman is insecure are not recovered using the preshared key.
Last updated:  2023-11-13
Secure Encryption and Key Exchange using Arbiter PUF
Raja Adhithan Radhakrishnan
Show abstract
This paper introduces a novel approach to enhancing cryp- tographic security. It proposes the use of one-time message sharing com- bined with Physically Unclonable Functions (PUF) to securely exchange keys and generate an S-subbyte-box for encryption. This innovative tech- nique aims to elevate the security standards of cryptographic applica- tions.
Last updated:  2023-11-13
A Statistical Verification Method of Random Permutations for Hiding Countermeasure Against Side-Channel Attacks
Jong-Yeon Park, Jang-Won Ju, Wonil Lee, Bo-Gyeong Kang, Yasuyuki Kachi, and Kouichi Sakurai
As NIST is putting the final touches on the standardization of PQC (Post Quantum Cryptography) public key algorithms, it is a racing certainty that peskier cryptographic attacks undeterred by those new PQC algorithms will surface. Such a trend in turn will prompt more follow-up studies of attacks and countermeasures. As things stand, from the attackers’ perspective, one viable form of attack that can be implemented thereupon is the so-called “side-channel attack”. Two best-known countermeasures heralded to be durable against side-channel attacks are: “masking” and “hiding”. In that dichotomous picture, of particular note are successful single-trace attacks on some of the NIST’s PQC then-candidates, which worked to the detriment of the former: “masking”. In this paper, we cast an eye over the latter: “hiding”. Hiding proves to be durable against both side-channel attacks and another equally robust type of attacks called “fault injection attacks”, and hence is deemed an auspicious countermeasure to be implemented. Mathematically, the hiding method is fundamentally based on random permutations. There has been a cornucopia of studies on generating random permutations. However, those are not tied to implementation of the hiding method. In this paper, we propose a reliable and efficient verification of permutation implementation, through employing Fisher–Yates’ shuffling method. We introduce the concept of an 𝑛-th order permutation and explain how it can be used to verify that our implementation is more efficient than its previous-gen counterparts for hiding countermeasures.
Last updated:  2023-11-12
Dora: Processor Expressiveness is (Nearly) Free in Zero-Knowledge for RAM Programs
Aarushi Goel, Mathias Hall-Andersen, and Gabriel Kaptchuk
Existing protocols for proving the correct execution of a RAM program in zero-knowledge are plagued by a processor expressiveness trade-off : supporting fewer instructions results in smaller processor circuits (which improves performance), but may result in more program execution steps because non-supported instruction must be emulated over multiple processor steps (which diminishes performance). We present Dora, a concretely efficient zero-knowledge protocol for RAM programs that sidesteps this tension by making it (nearly) free to add additional instructions to the processor. The computational and communication complexity of proving each step of a computation in Dora, is constant in the number of supported instructions. Dora is also highly generic and only assumes the existence of linearly homomorphic commitments. We implement Dora and demonstrate that on commodity hardware it can prove the correct execution of a processor with thousands of instruction, each of which has thousands of gates, in just a few milliseconds per step.
Last updated:  2023-11-11
Forging tropical signatures
Lorenz Panny
A recent preprint [ePrint 2023/1475] suggests the use of polynomials over a tropical algebra to construct a digital signature scheme "based on" the problem of factoring such polynomials, which is known to be NP‑hard. This short note presents two very efficient forgery attacks on the scheme, bypassing the need to factorize tropical polynomials and thus demonstrating that security in fact rests on a different, empirically easier problem.
Last updated:  2023-11-14
An Algorithmic Approach to $(2,2)$-isogenies in the Theta Model and Applications to Isogeny-based Cryptography
Pierrick Dartois, Luciano Maino, Giacomo Pope, and Damien Robert
In this paper, we describe an algorithm to compute chains of $(2,2)$-isogenies between products of elliptic curves in the theta model. The description of the algorithm is split into various subroutines to allow for a precise field operation counting. We present a constant time implementation of our algorithm in Rust and an alternative implementation in SageMath. Our work in SageMath runs ten times faster than a comparable implementation of an isogeny chain using the Richelot correspondence. The Rust implementation runs up to forty times faster than the equivalent isogeny in SageMath and has been designed to be portable for future research in higher-dimensional isogeny-based cryptography.
Last updated:  2023-11-11
A masking method based on orthonormal spaces, protecting several bytes against both SCA and FIA with a reduced cost
Claude Carlet, Abderrahman Daif, Sylvain Guilley, and Cédric Tavernier
In the attacker models of Side-Channel Attacks (SCA) and Fault Injection Attacks (FIA), the opponent has access to a noisy version of the internal behavior of the hardware. Since the end of the nineties, many works have shown that this type of attacks constitutes a serious threat to cryptosystems implemented in embedded devices. In the state-of-the-art, there exist several countermeasures to protect symmetric encryption (especially AES-128). Most of them protect only against one of these two attacks (either SCA or FIA). The main known counter-measure against SCA is masking; it makes the complexity of SCA growing exponentially with its order d. The most general version of masking is based on error correcting codes. It has the advantage of offering in principle a protection against both types of attacks (SCA and FIA), but all the functions implemented in the algorithm need to be masked accordingly, and this is not a simple task in general. We propose a particular version of such construction that has several advantages: it has a very low computation complexity, it offers a concrete protection against both SCA and FIA, and finally it allows flexibility: being not specifically dedicated to AES, it can be applied to any block cipher with any S-boxes. In the state-of-art, masking schemes all come with pros and cons concerning the different types of complexity (time, memory, amount of randomness). Our masking scheme concretely achieves the complexity of the best known scheme, for each complexity type
Last updated:  2023-11-24
New Public-Key Cryptosystem Blueprints Using Matrix Products in $\mathbb F_p$
Remi Geraud-Stewart and David Naccache
Given a set of matrices $\mathbf{A} := \{A_0, \dotsc, A_{k-1}\}$, and a matrix $M$ guaranteed to be the product of some ordered subset of $\mathbf{L}\subset\mathbf{A}$, can $\mathbf{L}$ be efficiently recovered? We begin by observing that the answer is positive under some assumptions on $\mathbf{A}$. Noting that appropriate transformations seem to make $\mathbf{L}$'s recovery difficult we provide the blueprint of two new public-key cryptosystems based upon this problem. We term those constructions "blueprints because, given their novelty, we are still uncertain of their exact security. Yet, we daringly conjecture that even if attacks are found on the proposed constructions, these attacks could be thwarted by adjustments in the key generation, key size or the encryption mechanism, thereby resulting on the long run in fully-fledged public-key cryptosystems that do not seem to belong to any of the mainstream public-key encryption paradigms known to date.
Last updated:  2023-11-11
Don't Eject the Impostor: Fast Three-Party Computation With a Known Cheater (Full Version)
Andreas Brüggemann, Oliver Schick, Thomas Schneider, Ajith Suresh, and Hossein Yalame
Secure multi-party computation (MPC) enables (joint) computations on sensitive data while maintaining privacy. In real-world scenarios, asymmetric trust assumptions are often most realistic, where one somewhat trustworthy entity interacts with smaller clients. We generalize previous two-party computation (2PC) protocols like MUSE (USENIX Security'21) and SIMC (USENIX Security'22) to the three-party setting (3PC) with one malicious party, avoiding the performance limitations of dishonest-majority inherent to 2PC. We introduce two protocols, Auxiliator and Socium, in a machine learning (ML) friendly design with a fast online phase and novel verification techniques in the setup phase. These protocols bridge the gap between prior 3PC approaches that considered either fully semi-honest or malicious settings. Auxiliator enhances the semi-honest two-party setting with a malicious helper, significantly improving communication by at least two orders of magnitude. Socium extends the client-malicious setting with one malicious client and a semi-honest server, achieving substantial communication improvement by at least one order of magnitude compared to SIMC. Besides an implementation of our new protocols, we provide the first open-source implementation of the semi-honest 3PC protocol ASTRA (CCSW'19) and a variant of the malicious 3PC protocol SWIFT (USENIX Security'21).
Last updated:  2023-11-11
Explicit Lower Bounds for Communication Complexity of PSM for Concrete Functions
Kazumasa Shinagawa and Koji Nuida
Private Simultaneous Messages (PSM) is a minimal model of secure computation, where the input players with shared randomness send messages to the output player simultaneously and only once. In this field, finding upper and lower bounds on communication complexity of PSM protocols is important, and in particular, identifying the optimal one where the upper and lower bounds coincide is the ultimate goal. However, up until now, functions for which the optimal communication complexity has been determined are few: An example of such a function is the two-input AND function where $(2\log_2 3)$-bit communication is optimal. In this paper, we provide new upper and lower bounds for several concrete functions. For lower bounds, we introduce a novel approach using combinatorial objects called abstract simplicial complexes to represent PSM protocols. Our method is suitable for obtaining non-asymptotic explicit lower bounds for concrete functions. By deriving lower bounds and constructing concrete protocols, we show that the optimal communication complexity for the equality and majority functions with three input bits are $3\log_2 3$ bits and $6$ bits, respectively. We also derive new lower bounds for the $n$-input AND function, three-valued comparison function, and multiplication over finite rings.
Last updated:  2023-11-11
Round-Optimal Black-Box Multiparty Computation from Polynomial-Time Assumptions
Michele Ciampi, Rafail Ostrovsky, Luisa Siniscalchi, and Hendrik Waldner
A central direction of research in secure multiparty computation with dishonest majority has been to achieve three main goals: 1. reduce the total number of rounds of communication (to four, which is optimal); 2. use only polynomial-time hardness assumptions, and 3. rely solely on cryptographic assumptions in a black-box manner. This is especially challenging when we do not allow a trusted setup assumption of any kind. While protocols achieving two out of three goals in this setting have been designed in recent literature, achieving all three simultaneously remained an elusive open question. Specifically, it was answered positively only for a restricted class of functionalities. In this paper, we completely resolve this long-standing open question. Specifically, we present a protocol for all polynomial-time computable functions that does not require any trusted setup assumptions and achieves all three of the above goals simultaneously.
Last updated:  2023-11-11
Pseudorandom Isometries
Prabhanjan Ananth, Aditya Gulati, Fatih Kaleoglu, and Yao-Ting Lin
We introduce a new notion called ${\cal Q}$-secure pseudorandom isometries (PRI). A pseudorandom isometry is an efficient quantum circuit that maps an $n$-qubit state to an $(n+m)$-qubit state in an isometric manner. In terms of security, we require that the output of a $q$-fold PRI on $\rho$, for $ \rho \in {\cal Q}$, for any polynomial $q$, should be computationally indistinguishable from the output of a $q$-fold Haar isometry on $\rho$. By fine-tuning ${\cal Q}$, we recover many existing notions of pseudorandomness. We present a construction of PRIs and assuming post-quantum one-way functions, we prove the security of ${\cal Q}$-secure pseudorandom isometries (PRI) for different interesting settings of ${\cal Q}$. We also demonstrate many cryptographic applications of PRIs, including, length extension theorems for quantum pseudorandomness notions, message authentication schemes for quantum states, multi-copy secure public and private encryption schemes, and succinct quantum commitments.
Last updated:  2023-11-10
Evaluation of Arithmetic Sum-of-Products Expressions in Linear Secret Sharing Schemes with a Non-Interactive Computation Phase
Miguel de Vega, Andrei Lapets, Stanislaw Jarecki, Wicher Malten, Mehmet Ugurbil, and Wyatt Howe
Among secure multi-party computation protocols, linear secret sharing schemes often do not rely on cryptographic assumptions and are among the most straightforward to explain and to implement correctly in software. However, basic versions of such schemes either limit participants to evaluating linear operations involving private values or require those participants to communicate synchronously during a computation phase. A straightforward, information-theoretically secure extension to such schemes is presented that can evaluate arithmetic sum-of-products expressions that contain multiplication operations involving non-zero private values. Notably, this extension does not require that participants communicate during the computation phase. Instead, a preprocessing phase is required that is independent of the private input values (but is dependent on the number of factors and terms in the sum-of-products expression).
Last updated:  2023-11-10
Broadcast-Optimal Four-Round MPC in the Plain Model
Michele Ciampi, Ivan Damgård, Divya Ravi, Luisa Siniscalchi, Yu Xia, and Sophia Yakoubov
Motivated by the fact that broadcast is an expensive, but useful, resource for the realization of multi-party computation protocols (MPC), Cohen, Garay, and Zikas (Eurocrypt 2020), and subsequently Damgård, Magri, Ravi, Siniscalchi and Yakoubov (Crypto 2021), and, Damgård, Ravi, Siniscalchi and Yakoubov (Eurocrypt 2023), focused on 𝘴𝘰-𝘤𝘢𝘭𝘭𝘦𝘥 𝘣𝘳𝘰𝘢𝘥𝘤𝘢𝘴𝘵 𝘰𝘱𝘵𝘪𝘮𝘢𝘭 𝘔𝘗𝘊. In particular, the authors focus on two-round MPC protocols (in the CRS model), and give tight characterizations of which security guarantees are achievable if broadcast is available in the first round, the second round, both rounds, or not at all. This work considers the natural question of characterizing broadcast optimal MPC in the plain model where no set-up is assumed. We focus on four-round protocols, since four is known to be the minimal number of rounds required to securely realize any functionality with black-box simulation. We give a complete characterization of which security guarantees, (namely selective abort, selective identifiable abort, unanimous abort and identifiable abort) are feasible or not, depending on the exact selection of rounds in which broadcast is available.
Last updated:  2023-11-09
Byzantine Agreement Decomposed: Honest Majority Asynchronous Total-Order Broadcast from Reliable Broadcast
Simon Holmgaard Kamp and Jesper Buus Nielsen
It is well-known that Asynchronous Total Order Broadcast (ATOB) requires randomisation and that at most $t < n/3$ out of $n$ players are corrupted. This is opposed to synchronous total-order broadcast (STOB) which can tolerate $t < n/2$ corruptions and can be deterministic. We show that these requirements can be conceptually separated, by constructing an ATOB protocol which tolerates $t < n/2$ corruptions from blackbox use of Common Coin and Reliable Broadcast. We show the power of this conceptually simple contribution by reproving, using simpler protocols, existing results on STOB with optimistic responsiveness and asynchronous fallback. We also use the framework to prove the first ATOB with sub-quadratic communication and optimal corruption threshold $t < n/3$, new ATOBs with covert security and mixed adversary structures, and a new STOB with asymmetric synchrony assumptions.
Last updated:  2023-11-09
Concrete Security for Succinct Arguments from Vector Commitments
Alessandro Chiesa, Marcel Dall'Agnol, Ziyi Guan, and Nicholas Spooner
We study the concrete security of a fundamental family of succinct interactive arguments, stemming from the works of Kilian (1992) and Ben-Sasson, Chiesa, and Spooner ("BCS", 2016). These constructions achieve succinctness by combining probabilistic proofs and vector commitments. Our first result concerns the succinct interactive argument of Kilian, realized with any probabilistically-checkable proof (PCP) and any vector commitment. We establish the tightest known bounds on the security of this protocol. Prior analyses incur large overheads unsuitable for concrete security, or assume special (and restrictive) properties of the underlying PCP. Our second result concerns an interactive variant of the BCS succinct non-interactive argument, which here we call IBCS, realized with any public-coin interactive oracle proof (IOP) and any vector commitment. We establish tight bounds on the security of this protocol. While this variant has been informally discussed in the literature, no prior security analysis, even asymptotic, existed before this work. Finally, we study the capabilities and limitations of succinct arguments based on vector commitments. We show that a generalization of the IBCS protocol, which we call the Finale protocol, is secure when realized with any public-query IOP (a notion that we introduce) that satisfies a natural "random continuation sampling" (RCS) property. We also show a partial converse: if the Finale protocol satisfies the RCS property (which in particular implies its security), then so does the underlying public-query IOP.
Last updated:  2023-11-09
Aloha-HE: A Low-Area Hardware Accelerator for Client-Side Operations in Homomorphic Encryption
Florian Krieger, Florian Hirner, Ahmet Can Mert, and Sujoy Sinha Roy
Homomorphic encryption (HE) has gained broad attention in recent years as it allows computations on encrypted data enabling secure cloud computing. Deploying HE presents a notable challenge since it introduces a performance overhead by orders of magnitude. Hence, most works target accelerating server-side operations on hardware platforms, while little attention has been given to client-side operations. In this paper, we present a novel design methodology to implement and accelerate the client-side HE operations on area-constrained hardware. We show how to design an optimized floating-point unit tailored for the encoding of complex values. In addition, we introduce a novel hardware-friendly algorithm for modulo-reduction of floating-point numbers and propose various concepts for achieving efficient resource sharing between modular ring and floating-point arithmetic. Finally, we use this methodology to implement an end-to-end hardware accelerator, Aloha-HE, for the client-side operations of the CKKS scheme. In contrast to existing work, Aloha-HE supports both encoding and encryption and their counterparts within a unified architecture. Aloha-HE achieves a speedup of up to 59x compared to prior hardware solutions.
Last updated:  2023-11-09
Exploiting the Symmetry of $\mathbb{Z}^n$: Randomization and the Automorphism Problem
Kaijie Jiang, Anyu Wang, Hengyi Luo, Guoxiao Liu, Yang Yu, and Xiaoyun Wang
$\mathbb{Z}^n$ is one of the simplest types of lattices, but the computational problems on its rotations, such as $\mathbb{Z}$SVP and $\mathbb{Z}$LIP, have been of great interest in cryptography. Recent advances have been made in building cryptographic primitives based on these problems, as well as in developing new algorithms for solving them. However, the theoretical complexity of $\mathbb{Z}$SVP and $\mathbb{Z}$LIP are still not well understood. In this work, we study the problems on rotations of $\mathbb{Z}^n$ by exploiting the symmetry property. We introduce a randomization framework that can be roughly viewed as `applying random automorphisms’ to the output of an oracle, without accessing the automorphism group. Using this framework, we obtain new reduction results for rotations of $\mathbb{Z}^n$. First, we present a reduction from $\mathbb{Z}$LIP to $\mathbb{Z}$SCVP. Here $\mathbb{Z}$SCVP is the problem of finding the shortest characteristic vectors, which is a special case of CVP where the target vector is a deep hole of the lattice. Moreover, we prove a reduction from $\mathbb{Z}$SVP to $\gamma$-$\mathbb{Z}$SVP for any constant $\gamma = O(1)$ in the same dimension, which implies that $\mathbb{Z}$SVP is as hard as its approximate version for any constant approximation factor. Second, we investigate the problem of finding a nontrivial automorphism for a given lattice, which is called LAP. Specifically, we use the randomization framework to show that $\mathbb{Z}$LAP is as hard as $\mathbb{Z}$LIP. We note that our result can be viewed as a $\mathbb{Z}^n$-analogue of Lenstra and Silverberg's result in [JoC2017], but with a different assumption: they assume the $G$-lattice structure, while we assume the access to an oracle that outputs a nontrivial automorphism.
Last updated:  2023-11-20
Signatures with Memory-Tight Security in the Quantum Random Oracle Model
Keita Xagawa
Memory tightness of reductions in cryptography, in addition to the standard tightness related to advantage and running time, is important when the underlying problem can be solved efficiently with large memory as discussed in Auerbach, Cash, Fersch, and Kiltz (CRYPTO 2017). Diemert, Geller, Jager, and Lyu (ASIACRYPT 2021) and Ghoshal, Ghosal, Jaeger, and Tessaro (EUROCRYPT 2022) gave memory-tight proofs for the multi-challenge security of digital signatures in the random oracle model. This paper studies the memory-tight reductions for _post-quantum_ signature schemes in the _quantum_ random oracle model. Concretely, we show that signature schemes from lossy identification are multi-challenge secure in the quantum random oracle model via memory-tight reductions. Moreover, we show that the signature schemes from lossy identification achieve more enhanced securities considering _quantum_ signing oracles proposed by Boneh and Zhandry (CRYPTO 2013) and Alagic, Majenz, Russel, and Song (EUROCRYPT 2020). We additionally show that signature schemes from preimage-sampleable functions achieve those securities via memory-tight reductions.
Last updated:  2023-11-09
Hintless Single-Server Private Information Retrieval
Baiyu Li, Daniele Micciancio, Mariana Raykova, and Mark Schultz-Wu
We present two new constructions for private information retrieval (PIR) in the classical setting where the clients do not need to do any preprocessing or store any database dependent information, and the server does not need to store any client-dependent information. Our first construction HintlessPIR eliminates the client preprocessing step from the recent LWE-based SimplePIR (Henzinger et. al., USENIX Security 2023) by outsourcing the "hint" related computation to the server, leveraging a new concept of homomorphic encryption with composable preprocessing. We realize this concept on RLWE encryption schemes, and thanks to the composibility of this technique we are able to preprocess almost all the expensive parts of the homomorphic computation and reuse across multiple executions. As a concrete application, we achieve very efficient matrix vector multiplication that allows us to build HintlessPIR. For a database of size 8GB, HintlessPIR achieves throughput about 3.7GB/s without requiring any client or server state. We additionally formalize the matrix vector multiplication protocol as LinPIR primitive, which may be of independent interests. In our second construction TensorPIR we reduce the communications of HintlessPIR from square root to cubic root in the database size. For this purpose we extend our HE with preprocessing techniques to composition of key-switching keys and the query expansion algorithm. We show how to use RLWE encryption with preprocessing to outsource LWE decryption for ciphertexts generated by homomorphic multiplications. This allows the server to do more complex processing using a more compact query under LWE. We implement and benchmark HintlessPIR which achieves better concrete costs than TensorPIR for a large set of databases of interest. We show that it improves the communication of recent preprocessing constructions when clients do not have large numbers of queries or database updates frequently. The computation cost for removing the hint is small and decreases as the database becomes larger, and it is always more efficient than other constructions with client hints such as Spiral PIR (Menon and Wu, S&P 2022). In the setting of anonymous queries we also improve on Spiral's communication.
Last updated:  2023-11-08
On the Masking-Friendly Designs for Post-Quantum Cryptography
Suparna Kundu, Angshuman Karmakar, and Ingrid Verbauwhede
Masking is a well-known and provably secure countermeasure against side-channel attacks. However, due to additional redundant computations, integrating masking schemes is expensive in terms of performance. The performance overhead of integrating masking countermeasures is heavily influenced by the design choices of a cryptographic algorithm and is often not considered during the design phase. In this work, we deliberate on the effect of design choices on integrating masking techniques into lattice-based cryptography. We select Scabbard, a suite of three lattice-based post-quantum key-encapsulation mechanisms (KEM), namely Florete, Espada, and Sable. We provide arbitrary-order masked implementations of all the constituent KEMs of the Scabbard suite by exploiting their specific design elements. We show that the masked implementations of Florete, Espada, and Sable outperform the masked implementations of Kyber in terms of speed for any order masking. Masked Florete exhibits a $73\%$, $71\%$, and $70\%$ performance improvement over masked Kyber corresponding to the first-, second-, and third-order. Similarly, Espada exhibits $56\%$, $59\%$, and $60\%$ and Sable exhibits $75\%$, $74\%$, and $73\%$ enhanced performance for first-, second-, and third-order masking compared to Kyber respectively. Our results show that the design decisions have a significant impact on the efficiency of integrating masking countermeasures into lattice-based cryptography.
Last updated:  2023-11-08
A practical key-recovery attack on LWE-based key- encapsulation mechanism schemes using Rowhammer
Puja Mondal, Suparna Kundu, Sarani Bhattacharya, Angshuman Karmakar, and Ingrid Verbauwhede
Physical attacks are serious threats to cryptosystems deployed in the real world. In this work, we propose a microarchitectural end-to-end attack methodology on generic lattice-based post-quantum key encapsulation mechanisms to recover the long-term secret key. Our attack targets a critical component of a Fujisaki-Okamoto transform that is used in the construction of almost all lattice-based key encapsulation mechanisms. We demonstrate our attack model on practical schemes such as Kyber and Saber by using Rowhammer. We show that our attack is highly practical and imposes little preconditions on the attacker to succeed. As an additional contribution, we propose an improved version of the plaintext checking oracle, which is used by almost all physical attack strategies on lattice-based key-encapsulation mechanisms. Our improvement reduces the number of queries to the plaintext checking oracle by as much as 39% for Saber and approximately 23% for Kyber768. This can be of independent interest and can also be used to reduce the complexity of other attacks.
Last updated:  2023-11-08
Construction-D lattice from Garcia-Stichtenoth tower code
Elena Kirshanova and Ekaterina Malygina
We show an explicit construction of an efficiently decodable family of $n$-dimensional lattices whose minimum distances achieve $\Omega(\sqrt{n} / (\log n)^{\varepsilon+o(1)})$ for $\varepsilon>0$. It improves upon the state-of-the-art construction due to Mook-Peikert (IEEE Trans.\ Inf.\ Theory, no. 68(2), 2022) that provides lattices with minimum distances $\Omega(\sqrt{n/ \log n})$. These lattices are construction-D lattices built from a sequence of BCH codes. We show that replacing BCH codes with subfield subcodes of Garcia-Stichtenoth tower codes leads to a better minimum distance. To argue on decodability of the construction, we adapt soft-decision decoding techniques of Koetter-Vardy (IEEE Trans.\ Inf.\ Theory, no.\ 49(11), 2003) to algebraic-geometric codes.
Last updated:  2023-11-08
CompactTag: Minimizing Computation Overheads in Actively-Secure MPC for Deep Neural Networks
Yongqin Wang, Pratik Sarkar, Nishat Koti, Arpita Patra, and Murali Annavaram
Secure Multiparty Computation (MPC) protocols enable secure evaluation of a circuit by several parties, even in the presence of an adversary who maliciously corrupts all but one of the parties. These MPC protocols are constructed using the well-known secret-sharing-based paradigm (SPDZ and SPD$\mathbb{Z}_{2^k}$), where the protocols ensure security against a malicious adversary by computing Message Authentication Code (MAC) tags on the input shares and then evaluating the circuit with these input shares and tags. However, this tag computation adds a significant runtime overhead, particularly for machine learning (ML) applications with computationally intensive linear layers, such as convolutions and fully connected layers. To alleviate the tag computation overhead, we introduce CompactTag, a lightweight algorithm for generating MAC tags specifically tailored for linear layers in ML. Linear layer operations in ML, including convolutions, can be transformed into Toeplitz matrix multiplications. For the multiplication of two matrices with dimensions T1 × T2 and T2 × T3 respectively, SPD$\mathbb{Z}_{2^k}$ required O(T1 · T2 · T3) local multiplications for the tag computation. In contrast, CompactTag only requires O(T1 · T2 + T1 · T3 + T2 · T3) local multiplications, resulting in a substantial performance boost for various ML models. We empirically compared our protocol to the SPD$\mathbb{Z}_{2^k}$ protocol for various ML circuits, including ResNet Training-Inference, Transformer Training-Inference, and VGG16 Training-Inference. SPD$\mathbb{Z}_{2^k}$ dedicated around 30% of its online runtime for tag computation. CompactTag speeds up this tag computation bottleneck by up to 23×, resulting in up to 1.47× total online phase runtime speedups for various ML workloads.
Last updated:  2023-11-08
Simulation-Secure Threshold PKE from LWE with Polynomial Modulus
Daniele Micciancio and Adam Suhl
In LWE based cryptosystems, using small (polynomially large) ciphertext modulus improves both efficiency and security. In threshold encryption, one often needs "simulation security": the ability to simulate decryption shares without the secret key. Existing lattice-based threshold encryption schemes provide one or the other but not both. Simulation security has seemed to require superpolynomial flooding noise, and the schemes with polynomial modulus use Rényi divergence based analyses that are sufficient for game-based but not simulation security. In this work, we give the first construction of simulation-secure lattice-based threshold PKE with polynomially large modulus. The construction itself is relatively standard, but we use an improved analysis, proving that when the ciphertext noise and flooding noise are both Gaussian, simulation is possible even with very small flooding noise. Our modulus is small not just asymptotically but also concretely: this technique gives parameters roughly comparable to those of highly optimized non-threshold schemes like FrodoKEM. As part of our proof, we show that LWE remains hard in the presence of some types of leakage; these results and techniques may also be useful in other contexts where noise flooding is used.
Last updated:  2023-11-08
A Formal Treatment of Envelope Encryption
Shoichi Hirose and Kazuhiko Minematsu
Envelope encryption is a method to encrypt data with two distinct keys in its basic form. Data is first encrypted with a data-encryption key, and then the data-encryption key is encrypted with a key-encryption key. Despite its deployment in major cloud services, as far as we know, envelope encryption has not received any formal treatment. To address this issue, we first formalize the syntax and security requirements of envelope encryption in the symmetric-key setting. Then, we show that it can be constructed by combining encryptment and authenticated encryption with associated data (AEAD). Encryptment is one-time AEAD satisfying that a small part of a ciphertext works as a commitment to the corresponding secret key, message, and associated data. Finally, we show that the security of the generic construction is reduced to the security of the underlying encryptment and AEAD.
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