All papers (22073 results)

Last updated:  2024-05-24
Can We Beat Three Halves Lower Bound?: (Im)Possibility of Reducing Communication Cost for Garbled Circuits
Chunghun Baek and Taechan Kim
Recent improvements to garbled circuits are mainly focused on reducing their size. The state-of-the-art construction of Rosulek and Roy (Crypto 2021) requires $1.5\kappa$ bits for garbling AND gates in the free-XOR setting. This is below the previously proven lower bound $2\kappa$ in the linear garbling model of Zahur, Rosulek, and Evans (Eurocrypt 2015). Whether their construction is optimal in a more inclusive model than the linear garbling model still remains open. This paper begins by providing a comprehensive model for a large class of practical garbling schemes and proves the lower bound for the size of the garbled AND gates in our model. We show that garbled AND gates require at least $1.5\kappa$ bits in our new model with the free-XOR setting. It is remarkable to see that the construction by Rosulek and Roy is already optimal despite the fact that our model possibly captures any potential extension of their construction.
Last updated:  2024-05-23
On Maximum Size Simultaneous Linear Approximations in Ascon and Keccak and Related Translation and Differential Properties
Nicolas T. Courtois, Frédéric Amiel, and Alexandre Bonnard de Fonvillars
In this paper we study the S-box known as Xi initially proposed by Daemen in 1995 and very widely used ever since in Keccak, Ascon, and many other. This type of ciphers is typically analyzed [in recent research] in terms of subspace trail attacks [TeDi19] and vector space invariants. An interesting question is then, when different spaces are mapped to each other by translations with a constant. In this paper we relax this fundamental question and we consider arbitrary sets of points and their translations. We generalize previous S-box partial linearization results on Keccak and Ascon from Eurocrypt 2017. We basically introduce new ways to linearize the Ascon S-box to the maximum possible extent. On this basis we show further remarkable properties and some surprising connections between [simultaneous] linear and [prominent] differential properties. We exhibit a new family of maximum size and optimal approximation properties with 11 points, beyond the maximum size of any set in the DDT table. We prove a theorem which guarantees that this type of properties are stable by arbitrary input-side translations which holds for all quadratic permutations. All this will be placed in the context of previous work on classification of 5-bit quadratic permutations.
Last updated:  2024-05-23
Algebraic Structure of the Iterates of $\chi$
Björn Kriepke and Gohar Kyureghyan
We consider the map $\chi:\mathbb{F}_2^n\to\mathbb{F}_2^n$ for $n$ odd given by $y=\chi(x)$ with $y_i=x_i+x_{i+2}(1+x_{i+1})$, where the indices are computed modulo $n$. We suggest a generalization of the map $\chi$ which we call generalized $\chi$-maps. We show that these maps form an Abelian group which is isomorphic to the group of units in $\mathbb{F}_2[X]/(X^{(n+1)/2})$. Using this isomorphism we easily obtain closed-form expressions for iterates of $\chi$ and explain their properties.
Last updated:  2024-05-23
A Note on Zero-Knowledge for NP and One-Way Functions
Yanyi Liu, Noam Mazor, and Rafael Pass
We present a simple alternative exposition of the the recent result of Hirahara and Nanashima (STOC’24) showing that one-way functions exist if (1) every language in NP has a zero-knowledge proof/argument and (2) ZKA contains non-trivial languages. Our presentation does not rely on meta-complexity and we hope it may be useful for didactic purposes.
Last updated:  2024-05-23
Symmetric Signcryption and E2EE Group Messaging in Keybase
Joseph Jaeger, Akshaya Kumar, and Igors Stepanovs
We introduce a new cryptographic primitive called symmetric signcryption, which differs from traditional signcryption because the sender and recipient share a secret key. We prove that a natural composition of symmetric encryption and signatures achieves strong notions of security against attackers that can learn and control many keys. We then identify that the core encryption algorithm of the Keybase encrypted messaging protocol can be modeled as a symmetric signcryption scheme. We prove the security of this algorithm, though our proof requires assuming non-standard, brittle security properties of the underlying primitives.
Last updated:  2024-05-23
Incompressible Functional Encryption
Rishab Goyal, Venkata Koppula, Mahesh Sreekumar Rajasree, and Aman Verma
Incompressible encryption (Dziembowski, Crypto'06; Guan, Wichs, Zhandry, Eurocrypt'22) protects from attackers that learn the entire decryption key, but cannot store the full ciphertext. In incompressible encryption, the attacker must try to compress a ciphertext within pre-specified memory bound $S$ before receiving the secret key. In this work, we generalize the notion of incompressibility to functional encryption. In incompressible functional encryption, the adversary can corrupt non-distinguishing keys at any point, but receives the distinguishing keys only after compressing the ciphertext to within $S$ bits. An important efficiency measure for incompressible encryption is the ciphertext-rate ( i.e., $\mathsf{rate} = \frac{|m|}{|\mathsf{ct}|}\;$). We give many new results for incompressible functional encryption: 1. Incompressible attribute-based encryption for circuits from standard assumptions, with $\mathsf{ct}$-rate-$\frac{1}{2}$ and short secret keys, 2. Incompressible functional encryption for circuits from (non-incompressible) functional encryption, with (a) $\mathsf{ct}$-rate-$\frac{1}{2}$ and short secret keys, (b) $\mathsf{ct}$-rate-$1$ and large secret keys. Our results achieve optimal efficiency, as incompressible attribute-based/functional encryption with $\mathsf{ct}$-rate-$1$ as well as short secret keys has strong implausibility barriers. Moreover, our assumptions are minimal as incompressible attribute-based/functional encryption are strictly stronger than their non-incompressible counterparts.
Last updated:  2024-05-25
Nonadaptive One-Way to Hiding Implies Adaptive Quantum Reprogramming
Joseph Jaeger
An important proof technique in the random oracle model involves reprogramming it on hard to predict inputs and arguing that an attacker cannot detect that this occurred. In the quantum setting, a particularly challenging version of this considers adaptive reprogramming wherein the points to be reprogrammed (or output values they should be programmed to) are dependent on choices made by the adversary. Frameworks for analyzing adaptive reprogramming were given by, e.g., by Unruh (CRYPTO 2014), Grilo-Hövelmanns-Hülsing-Majenz (ASIACRYPT 2021), and Pan-Zeng (PKC 2024). We show, counterintuitively, that these adaptive results follow directly from the non-adaptive one-way to hiding theorem of Ambainis-Hamburg-Unruh (CRYPTO 2019). These implications contradict beliefs (whether stated explicitly or implicitly) that some properties of the adaptive frameworks cannot be provided by the Ambainis-Hamburg-Unruh result.
Last updated:  2024-05-23
Weak Consistency mode in Key Transparency: OPTIKS
Esha Ghosh and Melissa Chase
The need for third-party auditors in privacy-preserving Key Transparency (KT) systems presents a deployment challenge. In this short note, we take a simple privacy-preserving KT system that provides strong security guarantees in the presence of an honest auditor (OPTIKS) and show how to add a auditor-free mode to it. The auditor-free mode offers slightly weaker security. We formalize this security property and prove that our proposed protocol satisfies our security definition.
Last updated:  2024-05-22
New Limits of Provable Security and Applications to ElGamal Encryption
Sven Schäge
We provide new results showing that ElGamal encryption cannot be proven CCA1-secure – a long-standing open problem in cryptography. Our result follows from a very broad, meta-reduction-based impossibility result on random self-reducible relations with efficiently re-randomizable witnesses. The techniques that we develop allow, for the first time, to provide impossibility results for very weak security notions where the challenger outputs fresh challenge statements at the end of the security game. This can be used to finally tackle encryption-type definitions that have remained elusive in the past. We show that our results have broad applicability by casting several known cryptographic setups as instances of random self-reducible and re-randomizable relations. These setups include general semi-homomorphic PKE and the large class of certified homomorphic one-way bijections. As a result, we also obtain new impossibility results for the IND-CCA1 security of the PKEs of Paillier and Damg ̊ard–Jurik, and many one-more inversion assumptions like the one-more DLOG or the one-more RSA assumption.
Last updated:  2024-05-24
Detecting Rogue Decryption in (Threshold) Encryption via Self-Incriminating Proofs
James Hsin-yu Chiang, Bernardo David, Tore Kasper Frederiksen, Arup Mondal, and Esra Yeniaras
Keeping decrypting parties accountable in public key encryption is notoriously hard since the secret key owner can decrypt any arbitrary ciphertext. Threshold encryption aims to solve this issue by distributing the power to decrypt among a set of parties, who must interact via a decryption protocol. However, such parties can employ cryptographic tools such as Multiparty Computation (MPC) to decrypt arbitrary ciphertexts without being detected. We introduce the notion of (threshold) encryption with Self-Incriminating Proofs, where parties must produce a self-incriminating proof of decryption when decrypting every ciphertext. In the standard public key encryption case, the adversary could destroy these proofs, so we strengthen our notion to guarantee that the proofs are published when decryption succeeds. This creates a decryption audit trail, which is useful in scenarios where decryption power is held by a single trusted party (e.g., a Trusted Execution Environment) who must be kept accountable. In the threshold case, we ensure that at least one of the parties who execute the decryption protocol will learn a self-incriminating proof, even if they employ advanced tools such as MPC. The fact that a party learns the proof and may leak it at any moment functions as a deterrent for parties who do not wish to be identified as malicious decryptors (e.g., a commercial operator of a service based on threshold encryption). We investigate the (im)possibility and applications of our notions while providing matching constructions under appropriate assumptions. In the threshold case, we build on recent results on Individual Cryptography (CRYPTO 2023).
Last updated:  2024-05-22
Hide-and-Seek and the Non-Resignability of the BUFF Transform
Jelle Don, Serge Fehr, Yu-Hsuan Huang, Jyun-Jie Liao, and Patrick Struck
The BUFF transform, due to Cremers et al. (S&P'21), is a generic transformation for digital signature scheme, with the purpose of obtaining additional security guarantees beyond unforgeability: exclusive ownership, message-bound signatures, and non-resignability. Non-resignability (which essentially challenges an adversary to re-sign an unknown message for which it only obtains the signature) turned out to be a delicate matter, as recently Don et al. (CRYPTO'24) showed that the initial definition is essentially unachievable; in particular, it is not achieved by the BUFF transform. This led to the introduction of new, weakened versions of non-resignability, which are (potentially) achievable. In particular, it was shown that a salted variant of the BUFF transform does achieves some weakened version of non-resignability. However, the salting requires additional randomness and leads to slightly larger signatures. Whether the original BUFF transform also achieves some meaningful notion of non-resignability remained a natural open question. In this work, we answer this question in the affirmative. We show that the BUFF transform satisfies the (almost) strongest notions of non-resignability one can hope for, facing the known impossibility results. Our results cover both the statistical and the computational case, and both the classical and the quantum setting. At the core of our analysis lies a new security game for random oracles that we call Hide-and-Seek. While seemingly innocent at first glance, it turns out to be surprisingly challenging to rigorously analyze.
Last updated:  2024-05-22
Stickel's Key Agreement Algebraic Variation
Daniel Nager
In this document we present a further development of non-commutative algebra based key agreement due to E. Stickel and a way to deal with the algebraic break due to V. Sphilrain.
Last updated:  2024-05-25
Minimize the Randomness in Rasta-Like Designs: How Far Can We Go?
Lorenzo Grassi, Fukang Liu, Christian Rechberger, Fabian Schmid, Roman Walch, and Qingju Wang
The Rasta design strategy allows building low-round ciphers due to its efficient prevention of statistical attacks and algebraic attacks by randomizing the cipher, which makes it especially suitable for hybrid homomorphic encryption (HHE), also known as transciphering. Such randomization is obtained by pseudorandomly sampling new invertible matrices for each round of each new cipher evaluation. However, naively sampling a random invertible matrix for each round significantly impacts the plain evaluation runtime, though it does not impact the homomorphic evaluation cost. To address this issue, Dasta was proposed at ToSC 2020 to reduce the cost of generating the random matrices. In this work, we address this problem from a different perspective: How far can the randomness in Rasta-like designs be reduced in order to minimize the plain evaluation runtime without sacrificing the security? To answer this question, we carefully studied the main threats to Rasta-like ciphers and the role of random matrices in ensuring security. We apply our results to the recently proposed cipher $\text{PASTA}$, proposing a modified version called $\text{PASTA}_\text{v2}$ instantiated with one initial random matrix and fixed linear layers - obtained by combining two MDS matrices with the Kronecker product - for the other rounds. Compared with $\text{PASTA}$, the state-of-the-art cipher for BGV- and BFV-style HHE, our evaluation shows that $\text{PASTA}_\text{v2}$ is up to 100% faster in plain while having the same homomorphic runtime in the SEAL homomorphic encryption library and up to 30% faster evaluation time in HElib, respectively.
Last updated:  2024-05-22
Physical Ring Signature
Xavier Bultel
Ring signatures allow members of a group (called "ring") to sign a message anonymously within the group, which is chosen ad hoc at the time of signing (the members do not need to have interacted before). In this paper, we propose a physical version of ring signatures. Our signature is based on one-out-of-many signatures, a method used in many real cryptographic ring signatures. It consists of boxes containing coins locked with padlocks that can only be opened by a particular group member. To sign a message, a group member shakes the boxes of the other members of the group so that the coins are in a random state ("heads" or "tails", corresponding to bits $0$ and $1$), and opens their box to arrange the coins so that the exclusive "or" of the coins corresponds to the bits of the message they wish to sign. We present a prototype that can be used with coins, or with dice for messages encoded in larger (non-binary) alphabets. We suggest that this system can be used to explain ring signatures to the general public in a fun way. Finally, we propose a semi-formal analysis of the security of our signature based on real cryptographic security proofs.
Last updated:  2024-05-22
FairSec: Fair and Maliciously Secure Circuit-PSI via SPDZ-Compatible Oblivious PRF
Yaxi Yang, Xiaojian Liang, Xiangfu Song, Linting Huang, Hongyu Ren, Changyu Dong, and Jianying Zhou
Private Set Intersection (PSI) allows two parties to compute the intersection of their input sets without revealing more information than the computation results. PSI and its variants have numerous applications in practice. Circuit-PSI is a famous variant and aims to compute any functionality $f$ on items in the intersection set. However, the existing circuit-PSI protocols only provide security against \emph{semi-honest} adversaries. One straightforward solution is to extend a pure garbled-circuit-based PSI (NDSS'12) to a maliciously secure circuit-PSI, but it will result in non-concrete complexity. Another is converting state-of-the-art semi-honest circuit-PSI protocols (EUROCRYPT'21; PoPETS'22) to be secure in the malicious setting. However, it will come across \emph{the consistency issue} since parties can not guarantee the inputs of functionality $f$ stay unchanged as obtained from the last step. This paper addresses the aforementioned issue by introducing FairSec, the first malicious circuit-PSI protocol. The central building block of FairSec, called Distributed Dual-key Oblivious PRF (DDOPRF), provides an oblivious evaluation of secret-shared inputs with dual keys. Additionally, we ensure the compatibility of DDOPRF with SPDZ, enhancing the versatility of our circuit-PSI protocol. Notably, our construction allows us to guarantee fairness within circuit-PSI effortlessly. Importantly, FairSec also achieves linear computation and communication complexities.
Last updated:  2024-05-22
A Fault-Resistant NTT by Polynomial Evaluation and Interpolation
Sven Bauer, Fabrizio De Santis, Kristjane Koleci, and Anita Aghaie
Show abstract
In computer arithmetic operations, the Number Theoretic Transform (NTT) plays a significant role in the efficient implementation of cyclic and nega-cyclic convolutions with the application of multiplying large integers and large degree polynomials. Multiplying polynomials is a common operation in lattice-based cryptography. Hence, the NTT is a core component of several lattice-based cryptographic algorithms. Two well-known examples are the key encapsulation mechanism Kyber and the digital signature algorithm Dilithium. In this work, we introduce a novel and efficient method for safeguarding the NTT against fault attacks. This new countermeasure is based on polynomial evaluation and interpolation. We prove its error detection capability, calculate the required additional computational effort, and show how to concretely use it to secure the NTT in Kyber and Dilithium against fault injection attacks. Finally, we provide concrete implementation results of the proposed novel technique on a resource-constrained ARM Cortex-M4 microcontroller, e.g., the technique exhibits a 72% relative overhead, when applied to Dilithium.
Last updated:  2024-05-22
A new attack against search-LWE using Diophantine approximations
Robin Frot and Daniel Zentai
In this paper, we present a new attack against search-LWE instances with a small secret key. The method consists of lifting the public key to $\mathbb Z$ and finding a good Diophantine approximation of the public key divided by the modulus $a$. This is done using lattice reduction algorithms. The lattice considered, and the approximation quality needed is similar to known decision-LWE attacks for small keys. However, we do not require an in-depth analysis of the reduction algorithm (any reduction algorithm giving small enough vectors is enough for us), and our method solves the search problem directly, which is harder than the decision problem.
Last updated:  2024-05-22
Modelling Ciphers with Overdefined Systems of Quadratic Equations: Application to Friday, Vision, RAIN and Biscuit
Fukang Liu, Mohammad Mahzoun, and Willi Meier
It is well-known that a system of equations becomes easier to solve when it is overdefined. In this work, we study how to overdefine the system of equations to describe the arithmetic oriented (AO) ciphers Friday, Vision, and RAIN, as well as a special system of quadratic equations over $\mathbb F_{2^{\ell}}$ used in the post-quantum signature scheme Biscuit. Our method is inspired by Courtois-Pieprzyk's and Murphy-Robshaw's methods to model AES with overdefined systems of quadratic equations over $\mathbb F_2$ and $\mathbb F_{2^8}$, respectively. However, our method is more refined and much simplified compared with Murphy-Robshaw's method, since it can take full advantage of the low-degree $\mathbb F_2$-linearized affine polynomials used in Friday and Vision, and the overdefined system of equations over $\mathbb F_{2^{\ell}}$ can be described in a clean way with our method. For RAIN, we instead consider quadratic Boolean equations rather than equations over large finite fields $\mathbb F_{2^{\ell}}$. Specifically, we demonstrate that the special structure of RAIN allows us to set up much more linearly independent quadratic Boolean equations than those obtained only with Courtois-Pieprzyk's method. Moreover, we further demonstrate that the underlying key-recovery problem in Biscuit (NIST PQC Round 1 Additional Signatures) can also be described by solving a much overdefined system of quadratic equations over $\mathbb F_{2^{\ell}}$. On the downside, the constructed systems of quadratic equations for these ciphers cannot be viewed as semi-regular, which makes it challenging to upper bound the complexity of the Gröbner basis attack. However, such a new modelling method can significantly improve the lower bound of the complexity of the Gröbner basis attacks on these ciphers, i.e., we view the complexity of solving a random system of quadratic equations of the same scale as the lower bound. How to better estimate the upper and lower bounds of the Gröbner basis attacks on these ciphers based on our modelling method is left as an open problem.
Last updated:  2024-05-22
SmartBean: Transparent, Concretely Efficient, Polynomial Commitment Scheme with Logarithmic Verification and Communication Costs that Runs on Any Group
Frank Y.C. Lu
We introduce a new, concretely efficient, transparent polynomial commitment scheme with logarithmic verification time and communication cost that can run on any group. Existing group-based polynomial commitment schemes must use less efficient groups, such as class groups of unknown order or pairing-based groups to achieve transparency (no trusted setup), making them expensive to adopt in practice.  We offer the first group-based polynomial commitment scheme that can run on any group s.t. it does not rely on expensive pairing operations or require class groups of unknown order to achieve transparency while still providing logarithmic verifier time and communication cost.  The prover work of our work is dominated by $4n \,\mathbb{G}$ multi-exponentiations, the verifier work is dominated by 4 log $n \, \mathbb{G}$ exponentiations, and the communication cost is 4 log $n \, \mathbb{G}$. Since our protocol can run on fast groups such as Curve25519, we can easily accelerate the multi-exponentiations with Pippenger's algorithm. The concrete performance of our work shows a significant improvement over the current state of the art in almost every aspect.
Last updated:  2024-05-22
Universal Blockchain Assets
Owen Vaughan
We present a novel protocol for issuing and transferring tokens across blockchains without the need of a trusted third party or cross-chain bridge. In our scheme, the blockchain is used for double-spend protection only, while the authorisation of token transfers is performed off-chain. Due to the universality of our approach, it works in almost all blockchain settings. It can be implemented immediately on UTXO blockchains such as Bitcoin without modification, and on account-based blockchains such as Ethereum by introducing a smart contract that mimics the properties of a UTXO. We provide a proof-of-concept implementation of an NFT that is issued on Bitcoin, transferred to Ethereum, and then transferred back to Bitcoin. Our new approach means that users no longer need to be locked into one blockchain when issuing and transferring tokens.
Last updated:  2024-05-24
Differential Cryptanalysis on Quantum Computers
Kyungbae Jang, Yujin Oh, and Hwajeong Seo
As quantum computing progresses, extensive research has been conducted to find quantum advantages in the field of cryptography. Combining quantum algorithms with classical cryptographic analysis methods, such as differential cryptanalysis and linear cryptanalysis, has the potential to reduce complexity. In this paper, we present a quantum differential finding circuit for differential cryptanalysis. In our quantum circuit, both plaintext and input difference are in a superposition state. Actually, while our method cannot achieve a direct speedup with quantum computing, it offers a different perspective by relying on quantum probability in a superposition state. For the quantum simulation, given the limited number of qubits, we simulate our quantum circuit by implementing the Toy-ASCON quantum circuit.
Last updated:  2024-05-21
Relating Code Equivalence to Other Isomorphism Problems
Huck Bennett and Kaung Myat Htay Win
We study the complexity of the Code Equivalence Problem on linear error-correcting codes by relating its variants to isomorphism problems on other discrete structures---graphs, lattices, and matroids. Our main results are a fine-grained reduction from the Graph Isomorphism Problem to the Linear Code Equivalence Problem over any field $\mathbb{F}$, and a reduction from the Linear Code Equivalence Problem over any field $\mathbb{F}_p$ of prime, polynomially bounded order $p$ to the Lattice Isomorphism Problem. Both of these reductions are simple and natural. We also give reductions between variants of the Code Equivalence Problem, and study the relationship between isomorphism problems on codes and linear matroids.
Last updated:  2024-05-21
Doubly-Efficient Batch Verification in Statistical Zero-Knowledge
Or Keret, Ron D. Rothblum, and Prashant Nalini Vasudevan
A sequence of recent works, concluding with Mu et al. (Eurocrypt, 2024) has shown that every problem $\Pi$ admitting a non-interactive statistical zero-knowledge proof (NISZK) has an efficient zero-knowledge batch verification protocol. Namely, an NISZK protocol for proving that $x_1,\dots,x_k \in \Pi$ with communication that only scales poly-logarithmically with $k$. A caveat of this line of work is that the prover runs in exponential-time, whereas for NP problems it is natural to hope to obtain a doubly-efficient proof - that is, a prover that runs in polynomial-time given the $k$ NP witnesses. In this work we show that every problem in $NISZK \cap UP$ has a doubly-efficient interactive statistical zero-knowledge proof with communication $poly(n,\log(k))$ and $poly(\log(k),\log(n))$ rounds. The prover runs in time $poly(n,k)$ given access to the $k$ UP witnesses. Here $n$ denotes the length of each individual input, and UP is the subclass of NP relations in which YES instances have unique witnesses. This result yields doubly-efficient statistical zero-knowledge batch verification protocols for a variety of concrete and central cryptographic problems from the literature.
Last updated:  2024-05-21
Information-theoretic Multi-server Private Information Retrieval with Client Preprocessing
Jaspal Singh, Yu Wei, and Vassilis Zikas
A private information retrieval (PIR) protocol allows a client to fetch any entry from single or multiple servers who hold a public database (of size $n$) while ensuring no server learns any information about the client's query. Initial works on PIR were focused on reducing the communication complexity of PIR schemes. However, standard PIR protocols are often impractical to use in applications involving large databases, due to its inherent large server-side computation complexity, that's at least linear in the database size. Hence, a line of research has focused on considering alternative PIR models that can achieve improved server complexity. The model of private information retrieval with client prepossessing has received a lot of interest beginning with the work due to Corrigan-Gibbs and Kogan (Eurocrypt 2020). In this model, the client interacts with two servers in an offline phase and it stores a local state, which it uses in the online phase to perform PIR queries. Constructions in this model achieve online client/server computation and bandwidth that's sublinear in the database size, at the cost of a one-time expensive offline phase. Till date all known constructions in this model are based on symmetric key primitives or on stronger public key assumptions like Decisional Diffie-Hellman (DDH) and Learning with Error (LWE). This work initiates the study of unconditional PIR with client prepossessing - where we avoid using any cryptographic assumptions. We present a new PIR protocol for $2t$ servers (where $t \in [2,\log_2n/2]$) with threshold 1, where client and server online computation is $\widetilde{O}(\sqrt{n})$ (the $\widetilde{O}(.)$ notation hides $\textsf{poly}\log$ factors) - matching the computation costs of other works based on cryptographic assumptions. The client storage and online communication complexity are $\widetilde{O}(n^{0.5+1/2t})$ and $\widetilde{O}(n^{1/2})$ respectively. Compared to previous works our PIR with client preprocessing protocol also has a very concretely efficient client/server online computation phase - which is dominated by xor operations, compared to cryptographic operations that are orders of magnitude slower. As a building block for our construction, we introduce a new information-theoretic primitive called \textit{privately multi-puncturable random set }(\pprs), which might be of independent interest. This new primitive can be viewed as as a generalization of privately puncturable pseudo-random set, which is the key cryptographic building block used in previous works on PIR with client preprocessing.
Last updated:  2024-05-21
Elliptic Curve Cryptography for the masses: Simple and fast finite field arithmetic
Michael Scott
Shaped prime moduli are often considered for use in elliptic curve and isogeny-based cryptography to allow for faster modular reduction. Here we focus on the most common choices for shaped primes that have been suggested, that is pseudo-Mersenne, generalized Mersenne and Montgomery-friendly primes. We consider how best to to exploit these shapes for maximum efficiency, and provide an open source tool to automatically generate, test and time working high-level language finite-field code. Next we consider the advantage to be gained from implementations that are written in assembly language and which exploit special instructions, SIMD hardware if present, and the particularities of the algorithm being implemented.
Last updated:  2024-05-21
Ideal-to-isogeny algorithm using 2-dimensional isogenies and its application to SQIsign
Hiroshi Onuki and Kohei Nakagawa
The Deuring correspondence is a correspondence between supersingular elliptic curves and quaternion orders. Under this correspondence, an isogeny between elliptic curves corresponds to a quaternion ideal. This correspondence plays an important role in isogeny-based cryptography and several algorithms to compute an isogeny corresponding to a quaternion ideal (ideal-to-isogeny algorithms) have been proposed. In particular, SQIsign is a signature scheme based on the Deuring correspondence and uses an ideal-to-isogeny algorithm. In this paper, we propose a novel ideal-to-isogeny algorithm using isogenies of dimension $2$. Our algorithm is based on Kani's reducibility theorem, which gives a connection between isogenies of dimension $1$ and $2$. By using the characteristic $p$ of the base field of the form $2^fg - 1$ for a small odd integer $g$, our algorithm works by only $2$-isogenies and $(2, 2)$-isogenies in the operations in $\mathbb{F}_{p^2}$. We apply our algorithm to SQIsign and compare the efficiency of the new algorithm with the existing one. Our analysis shows that the key generation and the signing in our algorithm are at least twice as fast as those in the existing algorithm at the NIST security level 1. This advantage becomes more significant at higher security levels. In addition, our algorithm also improves the efficiency of the verification in SQIsign.
Last updated:  2024-05-25
Measure-Rewind-Extract: Tighter Proofs of One-Way to Hiding and CCA Security in the Quantum Random Oracle Model
Jiangxia Ge, Heming Liao, and Rui Xue
The One-Way to Hiding (O2H) theorem, first given by Unruh (J ACM 2015) and then restated by Ambainis et al. (CRYPTO 2019), is a crucial technique for solving the reprogramming problem in the quantum random oracle model (QROM). It provides an upper bound $d\cdot\sqrt{\epsilon}$ for the distinguisher's advantage, where $d$ is the query depth and $\epsilon$ denotes the advantage of a one-wayness attacker. Later, in order to obtain a tighter upper bound, Kuchta et al. (EUROCRYPT 2020) proposed the Measure-Rewind-Measure (MRM) technique and then proved the Measure-Rewind-Measure O2H (MRM-O2H) theorem, which provides the upper bound $d\cdot\epsilon$. They also proposed an open question: Can we combine their MRM technique with Ambainis et al.'s semi-classical oracle technique (CRYPTO 2019) or Zhandry's compressed oracle technique (CRYPTO 2019) to prove a new O2H theorem with an upper bound even tighter than $d\cdot\epsilon$? In this paper, we give an affirmative answer for the above question. We propose a new technique named Measure-Rewind-Extract (MRE) by combining the MRM technique with the semi-classical oracle technique. By using MRE technique, we prove the Measure-Rewind-Extract O2H (MRE-O2H) theorem, which provides the upper bound $\sqrt{d}\cdot\epsilon$. As an important application of our MRE-O2H theorem, for the $FO^{\cancel{\bot}}$, $FO_m^{\cancel{\bot}}$, $FO^{\bot}$ and $FO_m^\bot$ proposed by Hofheinz et al. (TCC 2017), i.e., the key encapsulation mechanism (KEM) variants of the Fujisaki-Okamoto transformation, we prove the following results in the QROM: Their IND-CCA security can be reduced to the IND-CPA security of the underlying public key encryption (PKE) scheme without the square-root advantage loss. In particular, compared with the IND-CCA proof of $FO^{\cancel{\bot}}$ given by Kuchta et al. (EUROCRYPT 2020), ours removes the injectivity assumption and has a tighter security bound. Under the assumption that the underlying PKE scheme is unique randomness recoverable, we for the first time prove that their IND-CCA security can be reduced to the OW-CPA security of the underlying PKE scheme without the square-root advantage loss.
Last updated:  2024-05-21
Instance-Hiding Interactive Proofs
Changrui Mu and Prashant Nalini Vasudevan
In an Instance-Hiding Interactive Proof (IHIP) [Beaver et al. CRYPTO 90], an efficient verifier with a _private_ input x interacts with an unbounded prover to determine whether x is contained in a language L. In addition to completeness and soundness, the instance-hiding property requires that the prover should not learn anything about x in the course of the interaction. Such proof systems capture natural privacy properties, and may be seen as a generalization of the influential concept of Randomized Encodings [Ishai et al. FOCS 00, Applebaum et al. FOCS 04, Agrawal et al. ICALP 15], and as a counterpart to Zero-Knowledge proofs [Goldwasser et al. STOC 89]. We investigate the properties and power of such instance-hiding proofs, and show the following: 1. Any language with an IHIP is contained in AM/poly and coAM/poly. 2. If an average-case hard language has an IHIP, then One-Way Functions exist. 3. There is an oracle with respect to which there is a language that has an IHIP but not an SZK proof. 4. IHIP's are closed under composition with any efficiently computable function. We further study a stronger version of IHIP (that we call Strong IHIP) where the view of the honest prover can be efficiently simulated. For these, we obtain stronger versions of some of the above: 5. Any language with a Strong IHIP is contained in AM and coAM. 6. If a _worst-case_ hard language has a Strong IHIP, then One-Way Functions exist.
Last updated:  2024-05-20
Spec-o-Scope: Cache Probing at Cache Speed
Gal Horowitz, Eyal Ronen, and Yuval Yarom
Show abstract
Over the last two decades, microarchitectural side channels have been the focus of a large body of research on the development of new attack techniques, exploiting them to attack various classes of targets and designing mitigations. One line of work focuses on increasing the speed of the attacks, achieving higher levels of temporal resolution that can allow attackers to learn finer-grained information. The most recent addition to this line of work is Prime+Scope [CCS '21], which only requires a single access to the L1 cache to confirm the absence of victim activity in a cache set. While significantly faster than prior attacks, Prime+Scope is still an order of magnitude slower than cache access. In this work, we set out to close this gap. We draw on techniques from research into microarchitectural weird gates, software constructs that exploit transient execution to perform arbitrary computation on cache state. We design the Spec-o-Scope gate, a new weird gate that performs 10 cache probes in quick succession, which forms the basis for our eponymous attack. Our Spec-o-Scope attack achieves an order of magnitude improvement in temporal resolution compared to the previous state-of-the-art of Prime+Scope, reducing the measurement time from ~70 cycles to only 5 --- only one cycle more than an L1 cache access. We experimentally verify that our attack can detect timing differences in a 5 cycle resolution. Finally, using our Spec-o-Scope attack, we are able to show the first microarchitectural side-channel attack on an unmodified AES S-box-based implementation, which uses generic CPU features and does not require manipulation of the operating system's scheduler.
Last updated:  2024-05-20
Byzantine Reliable Broadcast with One Trusted Monotonic Counter
Yackolley Amoussou-Guenou, Lionel Beltrando, Maurice Herlihy, and Maria Potop-Butucaru
Byzantine Reliable Broadcast is one of the most popular communication primitives in distributed systems. Byzantine reliable broadcast ensures that processes agree to deliver a message from an initiator even if some processes (perhaps including the initiator) are Byzantine. In asynchronous settings it is known since the prominent work of Bracha [Bracha87] that Byzantine reliable broadcast can be implemented deterministically if $n \geq 3t+1$ where $t$ is an upper bound on the number of Byzantine processes. Here, we study Byzantine Reliable Broadcast when processes are equipped with trusted execution environments (TEEs), special software or hardware designed to prevent equivocation. Our contribution is twofold. First, we show that, despite common belief, when each process is equipped with a TEE, Bracha's algorithm still needs $n \geq 3t+1$. Second, we present a novel algorithm that uses a single TEE (at the initiator) that implements Byzantine Reliable Asynchronous Broadcast with $n \geq 2t+1$.
Last updated:  2024-05-20
SQIPrime: A dimension 2 variant of SQISignHD with non-smooth challenge isogenies
Max Duparc and Tako Boris Fouotsa
We introduce SQIPrime, a post-quantum digital signature scheme based on the Deuring correspondence and Kani's Lemma. Compared to its predecessors that are SQISign and especially SQISignHD, SQIPrime further expands the use of high dimensional isogenies, already in use in the verification in SQISignHD, to both key generation and commitment. In doing so, it no longer relies on smooth degree isogenies (of dimension 1). SQIPrime operates with a prime number of the form $p = 2^\alpha f-1$, as opposed to SQISignHD that uses SIDH primes. The most intriguing novelty in SQIPrime is the use of non-smooth degree isogenies as challenge isogeny. In fact, in the SQISign family identification scheme, the challenge isogeny is computed by the verifier, who is not well-equipped to compute an isogeny of large non-smooth degree. To overcome this obstacle, the verifier samples the kernel of the challenge isogeny and the task of computing this isogeny is accomplished by the prover. The response is modified in such a way that the verifier can check that his challenge isogeny was correctly computed by the prover, on top of verifying the usual response in the SQISign family. We describe two variants of SQIPrime: SQIPrime4D which uses dimension 4 isogenies to represent the response isogeny, and SQIPrime2D which solely uses dimension 2 isogenies to represent the response isogeny and hence is more efficient compared to SQIPrime4D and to SQISignHD.
Last updated:  2024-05-20
Reducing the Share Size of Weighted Threshold Secret Sharing Schemes via Chow Parameters Approximation
Oriol Farràs and Miquel Guiot
A secret sharing scheme is a cryptographic primitive that allows a dealer to share a secret among a set of parties, so that only authorized subsets of them can recover it. The access structure of the scheme is the family of authorized subsets. In a weighted threshold access structure, each party is assigned a weight according to its importance, and the authorized subsets are those in which the sum of their weights is at least the threshold value. For these access structures, the share size of the best known secret sharing schemes is either linear on the weights or quasipolynomial on the number of parties, which leads to long shares, in general. In certain settings, a way to circumvent this efficiency problem is to approximate the access structure by another one that admits more efficient schemes. This work is dedicated to the open problem posed by this strategy: Finding secret sharing schemes with a good tradeoff between the efficiency and the accuracy of the approximation. We present a method to approximate weighted threshold access structures by others that admit schemes with small shares. This method is based on the techniques for the approximation of the Chow parameters developed by De et al. [Journal of the ACM, 2014]. Our method provides secret sharing schemes with share size $n^{1+o(1)}$, where $n$ is the number of parties, and whose access structure is close to the original one. Namely, in this approximation the condition of being authorized or not is preserved for almost all subsets of parties. In addition, applying the recent results on computational secret sharing schemes by Applebaum et al. [STOC, 2023] we show that there exist computational secret sharing schemes whose security is based on the RSA assumption and whose share size is polylogarithmic in the number of parties.
Last updated:  2024-05-20
SQIsign2D-East: A New Signature Scheme Using 2-dimensional Isogenies
Kohei Nakagawa and Hiroshi Onuki
Isogeny-based cryptography is cryptographic schemes whose security is based on the hardness of a mathematical problem called the isogeny problem, and is attracting attention as one of the candidates for post-quantum cryptography. A representative isogeny-based cryptography is the signature scheme called SQIsign, which was submitted to the NIST PQC standardization competition. SQIsign has attracted much attention because of its very short signature and key size among the candidates for the NIST PQC standardization. Recently, a lot of new schemes have been proposed that use high-dimensional isogenies. Among them, the signature scheme called SQIsignHD has an even shorter signature size than SQIsign. However, it requires 4-dimensional isogeny computations for the signature verification. In this paper, we propose a new signature scheme, SQIsign2D-East, which requires only two-dimensional isogeny computations for verification, thus reducing the computational cost of verification. First, we generalized an algorithm called RandIsogImg, which computes a random isogeny of non-smooth degree. Then, by using this generalized RandIsogImg, we construct a new signature scheme SQIsign2D-East.
Last updated:  2024-05-20
Sublinear-Round Broadcast without Trusted Setup
Andreea B. Alexandru, Julian Loss, Charalampos Papamanthou, Giorgos Tsimos, and Benedikt Wagner
Byzantine broadcast is one of the fundamental problems in distributed computing. Many of its practical applications, from multiparty computation to consensus mechanisms for blockchains, require increasingly weaker trust assumptions, as well as scalability for an ever-growing number of users $n$. This rules out existing solutions which run in a linear number of rounds in $n$ or rely on trusted setup requirements. In this paper, we propose the first sublinear-round and trustless Byzantine broadcast protocol for the dishonest majority setting. Unlike previous sublinear-round protocols, our protocol assumes neither the existence of a trusted dealer who honestly issues keys and correlated random strings to the parties nor random oracles. Instead, we present a solution whose setup is limited to an unstructured uniform reference string and a plain public key infrastructure (a.k.a. bulletin-board PKI). Our broadcast protocol builds on top of a moderated gradecast protocol which parties can use to reach weak agreement on shared random strings. Using these strings, we can then run in an unbiased fashion a committee-based Byzantine protocol, similar to that of Chan et al. (PKC 2020), which terminates in a sublinear number of rounds. To this end, we propose a novel construction for committee election, which does not rely either on random oracles or on a trusted setup, and uses NIZKs and time-lock puzzles. Our protocol is resilient against an adaptive adversary who corrupts any constant fraction of parties.
Last updated:  2024-05-23
Time-Based Cryptography From Weaker Assumptions: Randomness Beacons, Delay Functions and More
Damiano Abram, Lawrence Roy, and Mark Simkin
The assumption that certain computations inherently require some sequential time has established itself as a powerful tool for cryptography. It allows for security and liveness guarantees in distributed protocols that are impossible to achieve with classical hardness assumptions. Unfortunately, many constructions from the realm of time-based cryptography are based on new and poorly understood hardness assumptions, which tend not to stand the test of time (cf. Leurent et al. 2023, Peikert & Tang 2023). In this work, we make progress on several fronts. We formally define the concept of a delay function and present a construction thereof from minimal assumptions. We show that these functions, in combination with classical cryptographic objects that satisfy certain efficiency criteria, would allow for constructing delay encryption, which is otherwise only known to exist based on a new hardness assumption about isogenies. We formally define randomness beacons as they are used in the context of blockchains, and we show that (linearly homomorphic) time-lock puzzles allow for efficiently constructing them. Our work puts time-based cryptography on a firmer theoretical footing, provides new constructions from simpler assumptions, and opens new avenues for constructing delay encryption.
Last updated:  2024-05-20
The Ouroboros of ZK: Why Verifying the Verifier Unlocks Longer-Term ZK Innovation
Denis Firsov and Benjamin Livshits
Verifying the verifier in the context of zero-knowledge proof is an essential part of ensuring the long-term integrity of the zero-knowledge ecosystem. This is vital for both zero-knowledge rollups and also other industrial applications of ZK. In addition to further minimizing the required trust and reducing the trusted computing base (TCB), having a verified verifier opens the door to decentralized proof generation by potentially untrusted parties. We outline a research program and justify the need for more work at the intersection of ZK and formal verification research.
Last updated:  2024-05-20
Bootstrapping Bits with CKKS
Youngjin Bae, Jung Hee Cheon, Jaehyung Kim, and Damien Stehlé
The Cheon-Kim-Kim-Song (CKKS) fully homomorphic encryption scheme is designed to efficiently perform computations on real numbers in an encrypted state. Recently, Drucker et al. [J. Cryptol.] proposed an efficient strategy to use CKKS in a black-box manner to perform computations on binary data. In this work, we introduce several CKKS bootstrapping algorithms designed specifically for ciphertexts encoding binary data. Crucially, the new CKKS bootstrapping algorithms enable to bootstrap ciphertexts containing the binary data in the most significant bits. First, this allows to decrease the moduli used in bootstrapping, saving a larger share of the modulus budget for non-bootstrapping operations. In particular, we obtain full-slot bootstrapping in ring degree $2^{14}$ for the first time. Second, the ciphertext format is compatible with the one used in the DM/CGGI fully homomorphic encryption schemes. Interestingly, we may combine our CKKS bootstrapping algorithms for bits with the fast ring packing technique from Bae et al. [CRYPTO'23]. This leads to a new bootstrapping algorithm for DM/CGGI that outperforms the state-of-the-art approaches when the number of bootstraps to be performed simultaneously is in the low hundreds.
Last updated:  2024-05-20
Breaking Verifiable Delay Functions in the Random Oracle Model
Ziyi Guan, Artur Riazanov, and Weiqiang Yuan
A verifiable delay function (VDF) is a cryptographic primitive that takes a long time to compute, but produces a unique output that is efficiently and publicly verifiable. Mahmoody, Smith and Wu (ICALP 2020) prove that VDFs satisfying both perfect completeness and adaptive perfect uniqueness do not exist in the random oracle model. Moreover, Ephraim, Freitag, Komargodski, and Pass (EUROCRYPT 2020) construct a VDF with perfect completeness and computational uniqueness, a much weaker guarantee compare to perfect uniqueness, in the random oracle model under the repeated squaring assumption. In this work, we close the gap between existing constructions and known lower bounds by showing that VDFs with imperfect completeness and non-adaptive computational uniqueness cannot be constructed in the pure random oracle model (without additional computational assumptions).
Last updated:  2024-05-19
Information-Theoretic Multi-Server PIR with Global Preprocessing
Ashrujit Ghoshal, Baitian Li, Yaohua Ma, Chenxin Dai, and Elaine Shi
We propose a new unified framework to construct multi-server, information-theoretic Private Information Retrieval (PIR) schemes that leverage global preprocesing to achieve sublinear computation per query. Despite a couple earlier attempts, our understanding of PIR schemes in the global preprocessing model remains limited, and so far, we only know a few sparse points in the broad design space. With our new unified framework, we can generalize the results of Beimel, Ishai, and Malkin to broader parameter regimes, thus enabling a tradeoff between bandwidth and computation. Specifically, for any constant $S > 1$, we can get an $S$-server scheme whose bandwidth consumption is as small as $n^{1/(S+1) + \epsilon}$ while achieving computation in the $n^\delta$ regime for some constant $\delta \in (0, 1)$. Moreover, we can get a scheme with polylogarithmic bandwidth and computation, requiring only polylogarithmic number of servers.
Last updated:  2024-05-19
Decentralized Multi-Client Functional Encryption with Strong Security
Ky Nguyen, David Pointcheval, and Robert Schädlich
Decentralized Multi-Client Functional Encryption (DMCFE) extends the basic functional encryption to multiple clients that do not trust each other. They can independently encrypt the multiple plaintext-inputs to be given for evaluation to the function embedded in the functional decryption key, defined by multiple parameter-inputs. And they keep control on these functions as they all have to contribute to the generation of the functional decryption keys. Tags can be used in the ciphertexts and the keys to specify which inputs can be combined together. As any encryption scheme, DMCFE provides privacy of the plaintexts. But the functions associated to the functional decryption keys might be sensitive too (e.g. a model in machine learning). The function-hiding property has thus been introduced to additionally protect the function evaluated during the decryption process. In this paper, we provide new proof techniques to analyze a new concrete construction of function-hiding DMCFE for inner products, with strong security guarantees in the random oracle model: the adversary can adaptively query multiple challenge ciphertexts and multiple challenge keys, with unbounded repetitions of the same message tags in the ciphertext-queries and a fixed polynomially-large number of repetitions of the same key tags in the key-queries, allowing static corruption of the secret encryption keys. Previous constructions were proven secure in the selective setting only.
Last updated:  2024-05-19
On SIS-problem-based random Feistel ciphers and its statistical evaluation of resistance against differential cryptanalysis
Yu Morishima and Masahiro Kaminaga
Provable security based on a robust mathematical framework is the gold standard for security evaluation in cryptography. Several provable secure cryptosystems have been studied for public key cryptography. However, provably secure symmetric-key cryptography has received little attention. Although there are known provably secure symmetric-key cryptosystems based on the hardness of factorization and discrete logarithm problems, they are not only slower than conventional block ciphers but can also be broken by quantum computers. Our study aims to tackle this latter problem by proposing a new provably secure Feistel cipher using collision resistant hash functions based on a Short Integer Solution problem (SIS). Even if cipher primitives are resistant to quantum algorithms, it is crucial to determine whether the cipher is resilient to differential cryptanalysis, a fundamental and powerful attack against symmetric-key cryptosystems. In this paper, we demonstrate that the proposed cipher family is secure against differential cryptanalysis by deriving an upper bound on the maximum differential probability. In addition, we demonstrate the potential success of differential cryptanalysis for short block sizes and statistically evaluate the average resistance of cipher instances based on differential characteristic probabilities. This method approximates the S-box output using a folded two-dimensional normal distribution and employs a generalized extreme value distribution. This evaluation method is first introduced in this paper and serves as the basis for studying the differential characteristics of lattice matrices and the number of secure rounds. This study is foundational research on differential cryptanalysis against block ciphers using a lattice matrix based on SIS.
Last updated:  2024-05-18
Extractable Witness Encryption for Signed Vector Digests from Pairings and Trust-Scalable One-Time Programs
Sora Suegami
Witness encryption (WE) allows a ciphertext to be encrypted under an NP problem such that anyone holding a valid witness for that problem can decrypt it (flexible decryptors), without interaction with others (non-interaction). However, existing schemes are either impractical or achieve only a part of these WE features. We propose a novel WE scheme that 1) is based on bilinear maps such as pairings, 2) achieves the property of flexible decryptors, and 3) still requires the decryptor's communication with a trusted signer, who only performs a fixed amount of computation and communication at regular intervals, regardless of the number of ciphertexts. It provides extractable security and can be extended to a threshold multiple signers setting, avoiding reliance on a single signer. As a significant application of our WE scheme, we build a novel one-time program (OTP) scheme in which the signers' computational and communication costs remain constant, independent of the number of OTPs to be evaluated simultaneously. This feature ensures scalable OTP evaluations without risking decreased signer participation or compromised decentralization due to increased operational costs for the signers.
Last updated:  2024-05-18
Lattice-based Broadcast Authenticated Searchable Encryption for Cloud Storage
Yibo Cao, Shiyuan Xu, Xiu-Bo Chen, Gang Xu, and Siu-Ming Yiu
The extensive use of cloud storage has created an urgent need to search and share data. Public key authenticated encryption with keyword search (PAEKS) allows for the retrieval from encrypted data, while resisting the insider keyword guessing attacks (IKGAs). Most PAEKS schemes only work with single-receiver model, exhibiting very limited applicability. To address this concern, there have been researches on broadcast authenticated encryption with keyword search (BAEKS) to achieve multi-receiver ciphertext search. But to our best knowledge, existing BAEKS schemes are susceptible to quantum computing attacks. In this paper, we propose lattice-based BAEKS, the first post-quantum broadcast authenticated encryption with keyword search, providing robust quantum-safety in multi-receiver model. Specifically, we leverage several lattice sampling algorithms and rejection sampling technique to construct our BAEKS scheme. Furthermore, we incorporate minimal cover set technique and lattice basis extension algorithm to construct an enhanced version, namely FS-BAEKS. Moreover, we give a rigorous security analysis of our scheme. Ultimately, the best computational overhead of BAEKS and Test algorithms in our BAEKS scheme delivers up to approximately 12-x and 402-x faster over prior arts when the number of receivers is six, respectively, which is practical for cloud storage systems.
Last updated:  2024-05-17
SQIsign2D-West: The Fast, the Small, and the Safer
Andrea Basso, Luca De Feo, Pierrick Dartois, Antonin Leroux, Luciano Maino, Giacomo Pope, Damien Robert, and Benjamin Wesolowski
We introduce SQIsign2D-West, a variant of SQIsign using two-dimensional isogeny representations. SQIsignHD was the first variant of SQIsign to use higher dimensional isogeny representations. Its eight-dimensional variant is geared towards provable security but is deemed unpractical. Its four-dimensional variant is geared towards efficiency and has significantly faster signing times than SQIsign, but slower verification owing to the complexity of the four-dimensional representation. Its authors commented on the apparent difficulty of getting any improvement over SQIsign by using two-dimensional representations. In this work, we introduce new algorithmic tools that make two-dimensional representations a viable alternative. These lead to a signature scheme with sizes comparable to SQIsignHD, slightly slower signing than SQIsignHD but still much faster than SQIsign, and the fastest verification of any known variant of SQIsign. We achieve this without compromising on the security proof: the assumptions behind SQIsign2D-West are similar to those of the eight-dimensional variant of SQIsignHD. Additionally, like SQIsignHD, SQIsign2D-West favourably scales to high levels of security Concretely, for NIST level I we achieve signing times of 80 ms and verifying times of 4.5 ms, using optimised arithmetic based on intrinsics available to the Ice Lake architecture. For NIST level V, we achieve 470 ms for signing and 31 ms for verifying.
Last updated:  2024-05-17
Enhancing Watermarked Language Models to Identify Users
Aloni Cohen, Alexander Hoover, and Gabe Schoenbach
A zero-bit watermarked language model produces text that is indistinguishable from that of the underlying model, but which can be detected as machine-generated using a secret key. Unfortunately, merely detecting AI-generated spam, say, as watermarked may not prevent future abuses. If we could additionally trace the text to a spammer's API token or account, we could then cut off their access or pursue legal action. We introduce multi-user watermarks, which allow tracing model-generated text to individual users or to groups of colluding users. We construct multi-user watermarking schemes from undetectable zero-bit watermarking schemes. Importantly, our schemes provide both zero-bit and multi-user assurances at the same time: detecting shorter snippets just as well as the original scheme, and tracing longer excerpts to individuals. Along the way, we give a generic construction of a watermarking scheme that embeds long messages into generated text. Ours are the first black-box reductions between watermarking schemes for language models. A major challenge for black-box reductions is the lack of a unified abstraction for robustness — that marked text is detectable even after edits. Existing works give incomparable robustness guarantees, based on bespoke requirements on the language model's outputs and the users' edits. We introduce a new abstraction to overcome this challenge, called AEB-robustness. AEB-robustness provides that the watermark is detectable whenever the edited text "approximates enough blocks" of model-generated output. Specifying the robustness condition amounts to defining approximates, enough, and blocks. Using our new abstraction, we relate the robustness properties of our message-embedding and multi-user schemes to that of the underlying zero-bit scheme, in a black-box way. Whereas prior works only guarantee robustness for a single text generated in response to a single prompt, our schemes are robust against adaptive prompting, a stronger and more natural adversarial model.
Last updated:  2024-05-17
Admissible Parameters for the Crossbred Algorithm and Semi-regular Sequences over Finite Fields
John Baena, Daniel Cabarcas, Sharwan K. Tiwari, Javier Verbel, and Luis Villota
Multivariate public key cryptography (MPKC) is one of the most promising alternatives to build quantum-resistant signature schemes, as evidenced in NIST's call for additional post-quantum signature schemes. The main assumption in MPKC is the hardness of the Multivariate Quadratic (MQ) problem, which seeks for a common root to a system of quadratic polynomials over a finite field. Although the Crossbred algorithm is among the most efficient algorithm to solve MQ over small fields, its complexity analysis stands on shaky ground. In particular, it is not clear for what parameters it works and under what assumptions. In this work, we provide a rigorous analysis of the Crossbred algorithm over any finite field. We provide a complete explanation of the series of admissible parameters proposed in previous literature and explicitly state the regularity assumptions required for its validity. Moreover, we show that the series does not tell the whole story, hence we propose an additional condition for Crossbred to work. Additionally, we define and characterize a notion of regularity for systems over a small field, which is one of the main building blocks in the series of admissible parameters.
Last updated:  2024-05-17
Formal Definition and Verification for Combined Random Fault and Random Probing Security
Sonia Belaid, Jakob Feldtkeller, Tim Güneysu, Anna Guinet, Jan Richter-Brockmann, Matthieu Rivain, Pascal Sasdrich, and Abdul Rahman Taleb
In our highly digitalized world, an adversary is not constrained to purely digital attacks but can monitor or influence the physical execution environment of a target computing device. Such side-channel or fault-injection analysis poses a significant threat to otherwise secure cryptographic implementations. Hence, it is important to consider additional adversarial capabilities when analyzing the security of cryptographic implementations besides the default black-box model. For side-channel analysis, this is done by providing the adversary with knowledge of some internal values, while for fault-injection analysis the capabilities of the adversaries include manipulation of some internal values. In this work, we extend probabilistic security models for physical attacks, by introducing a general random probing model and a general random fault model to capture arbitrary leakage and fault distributions, as well as the combination of these models. Our aim is to enable a more accurate modeling of low-level physical effects. We then analyze important properties, such as the impact of adversarial knowledge on faults and compositions, and provide tool-based formal verification methods that allow the security assessment of design components. These methods are introduced as extension of previous tools VERICA and IronMask which are implemented, evaluated and compared.
Last updated:  2024-05-17
(Strong) aPAKE Revisited: Capturing Multi-User Security and Salting
Dennis Dayanikli and Anja Lehmann
Asymmetric Password-Authenticated Key Exchange (aPAKE) protocols, particularly Strong aPAKE (saPAKE) have enjoyed significant attention, both from academia and industry, with the well-known OPAQUE protocol currently undergoing standardization. In (s)aPAKE, a client and a server collaboratively establish a high-entropy key, relying on a previously exchanged password for authentication. A main feature is its resilience against offline and precomputation (for saPAKE) attacks. OPAQUE, as well as most other aPAKE protocols, have been designed and analyzed in a single-user setting, i.e., modelling that only a single user interacts with the server. By the composition framework of UC, security for the actual multi-user setting is then conjectured. As any real-world (s)aPAKE instantiation will need to cater multiple users, this introduces a dangerous gap in which developers are tasked to extend the single-user protocol securely and in a UC-compliant manner. In this work, we extend the (s)aPAKE definition to directly model the multi-user setting, and explicitly capture the impact that a server compromise has across user accounts. We show that the currently standardized multi-user version of OPAQUE might not provide the expected security, as it is insecure against offline attacks as soon as the file for one user in the system is compromised. This is due to using shared state among different users, which violates the UC composition framework. However, we show that another change introduced in the standardization draft which also involves a shared state does not compromise security. When extending the aPAKE security in the multi-client setting, we notice that the widely used security definition captures significantly weaker security guarantees than what is offered by many protocols. Essentially, the aPAKE definition assumes that the server stores unsalted password-hashes, whereas several protocols explicitly use a salt to protect against precomputation attacks. We therefore propose a definitional framework that captures different salting approaches -- thus showing that the security gap between aPAKE and saPAKE can be smaller than expected.
Last updated:  2024-05-17
Efficient Second-Order Masked Software Implementations of Ascon in Theory and Practice
Barbara Gigerl, Florian Mendel, Martin Schläffer, and Robert Primas
In this paper, we present efficient protected software implementations of the authenticated cipher Ascon, the recently announced winner of the NIST standardization process for lightweight cryptography. Our implementations target theoretical and practical security against second-order power analysis attacks. First, we propose an efficient second-order extension of a previously presented first-order masking of the Keccak S-box that does not require online randomness. The extension itself is inspired by a previously presented second-order masking of an AND-XOR construction. We then discuss implementation tricks that further improve performance and reduce the chance of unintended combination of shares during the execution of masked software on microprocessors. This allows us to retain the theoretic protection orders of masking in practice with low performance overhead, which we also confirm via TVLA on ARM microprocessors. The formal correctness of our designs is additionally verified using Coco on the netlist of a RISC-V IBEX core. We benchmark our masked software designs on 32-bit ARM and RISC-V microprocessor platforms. On both platforms, we can perform Ascon-128 authenticated encryption with a throughput of about 300 or 550 cycles/byte when operating on 2 or 3 shares. When utilizing a leveled implementation technique, the throughput of our masked implementations generally increases to about 90 cycles/byte. We publish our masked software implementations together with a generic software framework for evaluating performance and side-channel resistance of various masked cryptographic implementations.
Last updated:  2024-05-16
Adversary Resilient Learned Bloom Filters
Allison Bishop and Hayder Tirmazi
Creating an adversary resilient Learned Bloom filter with provable guarantees is an open problem. We define a strong adversarial model for the Learned Bloom Filter. We also construct two adversary resilient variants of the Learned Bloom Filter called the Uptown Bodega Filter and the Downtown Bodega Filter. Our adversarial model extends an existing adversarial model designed for the classical (i.e not ``learned'') Bloom Filter by Naor and Yogev and considers computationally bounded adversaries that run in probabilistic polynomial time (PPT). We show that if pseudo-random permutations exist, then a secure Learned Bloom Filter may be constructed with $\lambda$ extra bits of memory and at most one extra pseudo-random permutation in the critical path. We further show that, if pseudo-random permutations exist, then a high utility Learned Bloom Filter may be constructed with $2\lambda$ extra bits of memory and at most one extra pseudo-random permutation in the critical path. Finally, we construct a hybrid adversarial model for the case where a fraction of the workload is chosen by an adversary. We show realistic scenarios where using the Downtown Bodega Filter gives better performance guarantees compared to alternative approaches in this model.
Last updated:  2024-05-16
Summation-based Private Segmented Membership Test from Threshold-Fully Homomorphic Encryption
Nirajan Koirala, Jonathan Takeshita, Jeremy Stevens, and Taeho Jung
In many real-world scenarios, there are cases where a client wishes to check if a data element they hold is included in a set segmented across a large number of data holders. To protect user privacy, the client’s query and the data holders’ sets should remain encrypted throughout the whole process. Prior work on Private Set Intersection (PSI), Multi-Party PSI (MPSI), Private Membership Test (PMT), and Oblivious RAM (ORAM) falls short in this scenario in many ways. They either require data holders to possess the sets in plain- text, incur prohibitively high latency for aggregating results from a large number of data holders, leak the information about the party holding the intersection element, or induce a high false positive. This paper introduces the primitive of a Private Segmented Mem- bership Test (PSMT). We give a basic construction of a protocol to solve PSMT using a threshold variant of approximate-arithmetic homomorphic encryption and show how to overcome existing challenges to construct a PSMT protocol without leaking information about the party holding the intersection element or false positives for a large number of data holders ensuring IND-CPA^𝐷 security. Our novel approach is superior to existing state-of-the-art approaches in scalability with regard to the number of supported data holders. This is enabled by a novel summation-based homo- morphic membership check rather than a product-based one, as well as various novel ideas addressing technical challenges. Our PSMT protocol supports many more parties (up to 4096 in experiments) compared to prior related work that supports only around 100 parties efficiently. Our experimental evaluation shows that our method’s aggregation of results from data holders can run in 92.5s for 1024 data holders and a set size of 2^25, and our method’s over- head increases very slowly with the increasing number of senders. We also compare our PSMT protocol to other state-of-the-art PSI and MPSI protocols and discuss our improvements in usability with a better privacy model and a larger number of parties
Last updated:  2024-05-16
More Embedded Curves for SNARK-Pairing-Friendly Curves
Aurore Guillevic
Embedded curves are elliptic curves defined over a prime field whose order (characteristic) is the prime subgroup order (the scalar field) of a pairing-friendly curve. Embedded curves have a large prime-order subgroup of cryptographic size but are not pairing-friendly themselves. Sanso and El Housni published families of embedded curves for BLS pairing-friendly curves. Their families are parameterized by polynomials, like families of pairing-friendly curves are. However their work did not found embedded families for KSS pairing-friendly curves. In this note we show how the problem of finding families of embedded curves is related to the problem of finding optimal formulas for $\mathbb{G}_1$ subgroup membership testing on the pairing-friendly curve side. Then we apply Smith's technique and Dai, Lin, Zhao, and Zhou criteria to obtain the formulas of embedded curves with KSS, and outline a generic algorithm for solving this problem in all cases. We provide two families of embedded curves for KSS18 and give examples of cryptographic size. We also suggest alternative embedded curves for BLS that have a seed of much lower Hamming weight than Sanso et al.~and much higher 2-valuation for fast FFT. In particular we highlight BLS12 curves which have a prime-order embedded curve that form a plain cycle (no pairing), and a second (plain) embedded curve in Montgomery form. A Brezing-Weng outer curve to have a pairing-friendly 2-chain is also possible like in the BLS12-377-BW6-761 construction. All curves have $j$-invariant 0 and an endomorphism for a faster arithmetic on the curve side.
Last updated:  2024-05-16
Simultaneous Haar Indistinguishability with Applications to Unclonable Cryptography
Prabhanjan Ananth, Fatih Kaleoglu, and Henry Yuen
Unclonable cryptography is concerned with leveraging the no-cloning principle to build cryptographic primitives that are otherwise impossible to achieve classically. Understanding the feasibility of unclonable encryption, one of the key unclonable primitives, satisfying indistinguishability security in the plain model has been a major open question in the area. So far, the existing constructions of unclonable encryption are either in the quantum random oracle model or are based on new conjectures. We present a new approach to unclonable encryption via a reduction to a novel question about nonlocal quantum state discrimination: how well can non-communicating -- but entangled -- players distinguish between different distributions over quantum states? We call this task simultaneous state indistinguishability. Our main technical result is showing that the players cannot distinguish between each player receiving independently-chosen Haar random states versus all players receiving the same Haar random state. We leverage this result to present the first construction of unclonable encryption satisfying indistinguishability security, with quantum decryption keys, in the plain model. We also show other implications to single-decryptor encryption and leakage-resilient secret sharing.
Last updated:  2024-05-16
Speeding Up Multi-Scalar Multiplications for Pairing-Based zkSNARKs
Xinxin Fan, Veronika Kuchta, Francesco Sica, and Lei Xu
Multi-scalar multiplication (MSM) is one of the core components of many zero-knowledge proof systems, and a primary performance bottleneck for proof generation in these schemes. One major strategy to accelerate MSM is utilizing precomputation. Several algorithms (e.g., Pippenger and BGMW) and their variants have been proposed in this direction. In this paper, we revisit the recent precomputation-based MSM calculation method proposed by Luo, Fu and Gong at CHES 2023 and generalize their approach. In particular, we presented a general construction of optimal buckets. This improvement leads to significant performance improvements, which are verified by both theoretical analysis and experiments.
Last updated:  2024-05-16
Reducing the CRS Size in Registered ABE Systems
Rachit Garg, George Lu, Brent Waters, and David J. Wu
Attribute-based encryption (ABE) is a generalization of public-key encryption that enables fine-grained access control to encrypted data. In (ciphertext-policy) ABE, a central trusted authority issues decryption keys for attributes $x$ to users. In turn, ciphertexts are associated with a decryption policy $\mathcal{P}$. Decryption succeeds and recovers the encrypted message whenever $\mathcal{P}(x) = 1$. Recently, Hohenberger, Lu, Waters, and Wu (Eurocrypt 2023) introduced the notion of registered ABE, which is an ABE scheme without a trusted central authority. Instead, users generate their own public/secret keys (just like in public-key encryption) and then register their keys (and attributes) with a key curator. The key curator is a transparent and untrusted entity. Currently, the best pairing-based registered ABE schemes support monotone Boolean formulas and an a priori bounded number of users $L$. A major limitation of existing schemes is that they require a (structured) common reference string (CRS) of size $L^2 \cdot |\mathcal{U}|$ where $|\mathcal{U}|$ is the size of the attribute universe. In other words, the size of the CRS scales quadratically with the number of users and multiplicatively with the size of the attribute universe. The large CRS makes these schemes expensive in practice and limited to a small number of users and a small universe of attributes. In this work, we give two ways to reduce the CRS size in pairing-based registered ABE schemes. First, we introduce a combinatoric technique based on progression-free sets that enables registered ABE for the same class of policies but with a CRS whose size is sub-quadratic in the number of users. Asymptotically, we obtain a scheme where the CRS size is nearly linear in the number of users $L$ (i.e., $L^{1 + o(1)}$). If we take a more concrete-efficiency-oriented focus, we can instantiate our framework to obtain a construction with a CRS of size $L^{\log_2 3} \approx L^{1.6}$. For instance, in a scheme for 100,000 users, our approach reduces the CRS by a factor of over $115\times$ compared to previous approaches (and without incurring any overhead in encryption/decryption time). Our second approach for reducing the CRS size is to rely on a partitioning-based argument when arguing security of the registered ABE scheme. Previous approaches took a dual-system approach. Using a partitioning-based argument yields a registered ABE scheme where the size of the CRS is independent of the size of the attribute universe. The cost is the resulting scheme satisfies a weaker notion of static security. Our techniques for reducing the CRS size can be combined, and taken together, we obtain a pairing-based registered ABE scheme that supports monotone Boolean formulas with a CRS size of $L^{1 + o(1)}$. Notably, this is the first pairing-based registered ABE scheme that does not require imposing a bound on the size of the attribute universe during setup time. As an additional application, we also show how to apply our techniques based on progression-free sets to the batch argument (BARG) for $\mathsf{NP}$ scheme of Waters and Wu (Crypto 2022) to obtain a scheme with a nearly-linear CRS without needing to rely on non-black-box bootstrapping techniques.
Last updated:  2024-05-16
PERK: Compact Signature Scheme Based on a New Variant of the Permuted Kernel Problem
Slim Bettaieb, Loïc Bidoux, Victor Dyseryn, Andre Esser, Philippe Gaborit, Mukul Kulkarni, and Marco Palumbi
In this work we introduce PERK a compact digital signature scheme based on the hardness of a new variant of the Permuted Kernel Problem (PKP). PERK achieves the smallest signature sizes for any PKP-based scheme for NIST category I security with 6 kB, while obtaining competitive signing and verification timings. PERK also compares well with the general state-of-the-art. To substantiate those claims we provide an optimized constant-time AVX2 implementation, a detailed performance analysis and different size-performance trade-offs. Technically our scheme is based on a Zero-Knowledge Proof of Knowledge following the MPC-in-the-Head paradigm and employing the Fiat-Shamir transform. We provide comprehensive security proofs, ensuring EUF-CMA security for PERK in the random oracle model. The efficiency of PERK greatly stems from our particular choice of PKP variant which allows for an application of the challenge-space amplification technique due to Bidoux-Gaborit (C2SI 2023). Our second main contribution is an in-depth study of the hardness of the introduced problem variant. First, we establish a link between the hardness of our problem variant and the hardness of standard PKP. Then, we initiate an in-depth study of the concrete complexity to solve our variant. We present a novel algorithm which outperforms previous approaches for certain parameter regimes. However, the proximity of our problem variant to the standard variant can be controlled via a specific parameter. This enables us to effectively safeguard against our new attack and potential future extensions by a choice of parameters that ensures only a slight variation from standard PKP.
Last updated:  2024-05-16
Scaling Lattice Sieves across Multiple Machines
Martin R. Albrecht and Joe Rowell
Lattice sieves are algorithms for finding short vectors in lattices. We present an implementation of two such sieves – known as “BGJ1” and “BDGL” in the literature – that scales across multiple servers (with varying success). This class of algorithms requires exponential memory which had put into question their ability to scale across sieving nodes. We discuss our architecture and optimisations and report experimental evidence of the efficiency of our approach.
Last updated:  2024-05-16
The Art of Bonsai: How Well-Shaped Trees Improve the Communication Cost of MLS
Céline Chevalier, Guirec Lebrun, Ange Martinelli, and Jérôme Plût
Messaging Layer Security (MLS) is a Secure Group Messaging protocol that uses for its handshake a binary tree – called a Ratchet Tree – in order to reach a logarithmic communication cost w.r.t. the number of group members. This Ratchet Tree represents users as its leaves; therefore any change in the group membership results in adding or removing a leaf associated with that user. MLS consequently implements what we call a tree evolution mechanism, consisting in a user add algorithm – determining where to insert a new leaf – and a tree expansion process – stating how to increase the size of the tree when no space is available for a new user. The tree evolution mechanism currently used by MLS is de- signed so that it naturally left-balances the Ratchet Tree. However, such a Ratchet Tree structure is often quite inefficient in terms of communication cost. Furthermore, one may wonder whether the binary tree used in that Ratchet Tree has a degree optimized for the features of a handshake in MLS – called a commit. Therefore, we study in this paper how to improve the communication cost of a commit in MLS by considering both the tree evolution mechanism and the tree degree used for the Ratchet Tree. To do so, we determine the tree structure that optimizes its communication cost, and we propose optimized algorithms for both the user add and tree expansion processes, that allow to remain close to that optimal structure and thus to have a communication cost as close to optimal as possible. We also determine the Ratchet Tree degree that is best suited to a given set of parameters induced by the encryption scheme used by MLS. This study shows that when using classical (i.e. pre-quantum) ciphersuites, a binary tree is indeed the most appropriate Ratchet Tree; nevertheless, when it comes to post-quantum algorithms, it generally becomes more interesting to use instead a ternary tree. Our improvements do not change TreeKEM protocol and are easy to implement. With parameter sets corresponding to practical ciphersuites, they reduce TreeKEM’s communication cost by 5 to 10%. In particular, the 10% gain appears in the Post-Quantum setting – when both an optimized tree evolution mechanism and a ternary tree are necessary –, which is precisely the context where any optimization of the protocol’s communication cost is welcome, due to the important bandwidth of PQ encrypted communication.
Last updated:  2024-05-16
$\mathsf{FRAST}$: TFHE-friendly Cipher Based on Random S-boxes
Mingyu Cho, Woohyuk Chung, Jincheol Ha, Jooyoung Lee, Eun-Gyeol Oh, and Mincheol Son
A transciphering framework, also known as hybrid homomorphic encryption, is a practical method of combining a homomorphic encryption~(HE) scheme with a symmetric cipher in the client-server model to reduce computational and communication overload on the client side. As a server homomorphically evaluates a symmetric cipher in this framework, new design rationales are required for ``HE-friendly'' ciphers that take into account the specific properties of the HE schemes. In this paper, we propose a new TFHE-friendly cipher, dubbed $\mathsf{FRAST}$, with a TFHE-friendly round function based on a random S-box to minimize the number of rounds. The round function of $\mathsf{FRAST}$ can be efficiently evaluated in TFHE by a new optimization technique, dubbed double blind rotation. Combined with our new WoP-PBS method, the double blind rotation allows computing multiple S-box calls in the round function of $\mathsf{FRAST}$ at the cost of a single S-box call. In this way, $\mathsf{FRAST}$ enjoys $2.768$ (resp. $10.57$) times higher throughput compared to $\mathsf{Kreyvium}$ (resp. $\mathsf{Elisabeth}$) for TFHE keystream evaluation in the offline phase of the transciphering framework at the cost of slightly larger communication overload.
Last updated:  2024-05-16
An NVMe-based Secure Computing Platform with FPGA-based TFHE Accelerator
Yoshihiro Ohba, Tomoya Sanuki, Claude Gravel, and Kentaro Mihara
In this paper, we introduce a new approach to secure computing by implementing a platform that utilizes an NVMe-based system with an FPGA-based Torus FHE accelerator, SSD, and middleware on the host-side. Our platform is the first of its kind to offer complete secure computing capabilities for TFHE using an FPGA-based accelerator. We have defined secure computing instructions to evaluate 14-bit to 14-bit functions using TFHE, and our middleware allows for communication of ciphertexts, keys, and secure computing programs while invoking secure computing programs through NVMe commands with metadata. Our CMux gate implementation features an optimized NTT/INTT circuit that eliminates pre-NTT and post-INTT operations by pre-scaling and pre-transforming constant polynomials such as the bootstrapping and private-functional key-switching keys. Our performance evaluation demonstrates that our secure computing platform outperforms CPU-based and GPU-based platforms by 15 to 120 times and by 2.5 to 3 times, respectively, in gate bootstrapping execution time. Additionally, our platform uses 7 to 12 times less electric energy consumption during the gate bootstrapping execution time compared to CPU-based platforms and 1.15 to 1.2 times less compared to GPU-based platforms.
Last updated:  2024-05-15
Improved Conditional Cube Attacks on Ascon AEADs in Nonce-Respecting Settings -- with a Break-Fix Strategy
Kai Hu
The best-known distinguisher on 7-round Ascon-128 and Ascon-128a AEAD uses a 60-dimensional cube where the nonce bits are set to be equal in the third and fourth rows of the Ascon state during initialization (Rohit et al. ToSC 2021/1). It was not known how to use this distinguisher to mount key-recovery attacks. In this paper, we investigate this problem using a new strategy called \textit{break-fix} for the conditional cube attack. The idea is to introduce slightly-modified cubes which increase the degrees of 7-round output bits to be more than 59 (break phase) and then find key conditions which can bring the degree back to 59 (fix phase). Using this idea, key-recovery attacks on 7-round Ascon-128, Ascon-128a and Ascon-80pq are proposed. The attacks have better time/memory complexities than the existing attacks, and in some cases improve the weak-key attacks as well.
Last updated:  2024-05-15
Efficient Universally-Verifiable Electronic Voting with Everlasting Privacy
David Pointcheval
Universal verifiability is a must-to-have for electronic voting schemes. It is essential to ensure honest behavior of all the players during the whole process, together with the eligibility. However, it should not endanger the privacy of the individual votes, which is another major requirement. Whereas the first property prevents attacks during the voting process, privacy of the votes should hold forever, which has been called everlasting privacy. A classical approach for universal verifiability is to add some proofs together with the encrypted votes, which requires publication of the latter, while eligibility needs a link between the votes and the voters: it definitely excludes long-term privacy. An alternative is the use of perfectly-hiding commitments, on which proofs are published, while ciphertexts are kept private for computing the tally. In this paper, we show how recent linearly-homomorphic signatures can be exploited for all the proofs, leading to very efficient procedures towards universal verifiability with both strong receipt-freeness and everlasting privacy. Privacy will indeed be unconditional, after the publication of the results and the proofs, whereas the soundness of the proofs holds in the algebraic group model and the random oracle model.
Last updated:  2024-05-15
A Deniability Analysis of Signal's Initial Handshake PQXDH
Rune Fiedler and Christian Janson
Many use messaging apps such as Signal to exercise their right to private communication. To cope with the advent of quantum computing, Signal employs a new initial handshake protocol called PQXDH for post-quantum confidentiality, yet keeps guarantees of authenticity and deniability classical. Compared to its predecessor X3DH, PQXDH includes a KEM encapsulation and a signature on the ephemeral key. In this work we show that PQXDH does not meet the same deniability guarantees as X3DH due to the signature on the ephemeral key. Our analysis relies on plaintext awareness of the KEM, which Signal's implementation of PQXDH does not provide. As for X3DH, both parties (initiator and responder) obtain different deniability guarantees due to the asymmetry of the protocol. For our analysis of PQXDH, we introduce a new model for deniability of key exchange that allows a more fine-grained analysis. Our deniability model picks up on the ideas of prior work and facilitates new combinations of deniability notions, such as deniability against malicious adversaries in the big brother model, i.e. where the distinguisher knows all secret keys. Our model may be of independent interest.
Last updated:  2024-05-15
Multi-Client Functional Encryption with Public Inputs and Strong Security
Ky Nguyen, Duong Hieu Phan, and David Pointcheval
Recent years have witnessed a significant development for functional encryption (FE) in the multi-user setting, particularly with multi-client functional encryption (MCFE). The challenge becomes more important when combined with access control, such as attribute-based encryption (ABE), which was actually not covered by the FE and MCFE frameworks. On the other hand, as for complex primitives, many works have studied the admissibility of adversaries to ensure that the security model encompasses all real threats of attacks. In this paper, adding a public input to FE/MCFE, we cover many previous primitives, notably attribute-based function classes. Furthermore, with the strongest admissibility for inner-product functionality, our framework is quite versatile, as it encrypts multiple sub-vectors, allows repetitions and corruptions, and eventually also encompasses public-key FE and classical ABE, bridging the private setting of MCFE with the public setting of FE and ABE. Finally, we propose an MCFE with public inputs with the class of functions that combines inner-products (on private inputs) and attribute-based access-control (on public inputs) for LSSS policies. We achieve the first AB-MCFE for inner-products with strong admissibility and with adaptive security. This also leads to MIFE for inner products, public-key single-input inner-product FE with LSSS key-policy and KPABE for LSSS, with adaptive security while the previous AB-MCFE construction of Agrawal et al. from CRYPTO '23 considers a slightly larger functionality of average weighted sum but with selective security only.
Last updated:  2024-05-15
BGJ15 Revisited: Sieving with Streamed Memory Access
Ziyu Zhao, Jintai Ding, and Bo-Yin Yang
The focus of this paper is to tackle the issue of memory access within sieving algorithms for lattice problems. We have conducted an in-depth analysis of an optimized BGJ sieve (Becker-Gama-Joux 2015), and our findings suggest that its inherent structure is significantly more memory-efficient compared to the asymptotically fastest BDGL sieve (Becker-Ducas-Gama-Laarhoven 2016). Specifically, it necessitates merely $2^{0.2075n + o(n)}$ streamed (non-random) main memory accesses for the execution of an $n$-dimensional sieving. We also provide evidence that the time complexity of this refined BGJ sieve could potentially be $2^{0.292n + o(n)}$, or at least something remarkably close to it. Actually, it outperforms the BDGL sieve in all dimensions that are practically achievable. We hope that this study will contribute to the resolution of the ongoing debate regarding the measurement of RAM access overhead in large-scale, sieving-based lattice attacks. The concept above is also supported by our implementation. Actually, we provide a highly efficient, both in terms of time and memory, CPU-based implementation of the refined BGJ sieve within an optimized sieving framework. This implementation results in approximately 40% savings in RAM usage and is at least $2^{4.5}$ times more efficient in terms of gate count compared to the previous 4-GPU implementation (Ducas-Stevens-Woerden 2021). Notably, we have successfully solved the 183-dimensional SVP Darmstadt Challenge in 30 days using a 112-core server and approximately 0.87TB of RAM. The majority of previous sieving-based SVP computations relied on the HK3-sieve (Herold-Kirshanova 2017), hence this implementation could offer further insights into the behavior of these asymptotically faster sieving algorithms when applied to large-scale problems. Moreover, our refined cost estimation of SVP based on this implementation suggests that some of the NIST PQC candidates, such as Falcon-512, are unlikely to achieve NIST's security requirements.
Last updated:  2024-05-14
Quantum Key-Revocable Dual-Regev Encryption, Revisited
Prabhanjan Ananth, Zihan Hu, and Zikuan Huang
Quantum information can be used to achieve novel cryptographic primitives that are impossible to achieve classically. A recent work by Ananth, Poremba, Vaikuntanathan (TCC 2023) focuses on equipping the dual-Regev encryption scheme, introduced by Gentry, Peikert, Vaikuntanathan (STOC 2008), with key revocation capabilities using quantum information. They further showed that the key-revocable dual-Regev scheme implies the existence of fully homomorphic encryption and pseudorandom functions, with both of them also equipped with key revocation capabilities. Unfortunately, they were only able to prove the security of their schemes based on new conjectures and left open the problem of basing the security of key revocable dual-Regev encryption on well-studied assumptions. In this work, we resolve this open problem. Assuming polynomial hardness of learning with errors (over sub-exponential modulus), we show that key-revocable dual-Regev encryption is secure. As a consequence, for the first time, we achieve the following results: 1. Key-revocable public-key encryption and key-revocable fully-homomorphic encryption satisfying classical revocation security and based on polynomial hardness of learning with errors. Prior works either did not achieve classical revocation or were based on sub-exponential hardness of learning with errors. 2. Key-revocable pseudorandom functions satisfying classical revocation from the polynomial hardness of learning with errors. Prior works relied upon unproven conjectures.
Last updated:  2024-05-13
Mutable Batch Arguments and Applications
Rishab Goyal
Non-interactive batch arguments (BARGs) let a prover compute a single proof $\pi$ proving validity of a `batch' of $k$ $\mathbf{NP}$ statements $x_1, \ldots, x_{k}$. The two central features of BARGs are succinctness and soundness. Succinctness states that proof size, $|\pi|$ does not grow with $k$; while soundness states a polytime cheating prover cannot create an accepting proof for any invalid batch of statements. In this work, we put forth a new concept of mutability for batch arguments, called mutable batch arguments. Our goal is to re-envision how we think about and use BARGs. Traditionally, a BARG proof string $\pi$ is an immutable encoding of $k$ $\mathbf{NP}$ witness $\omega_1, \ldots, \omega_{k}$. In a mutable BARG system, each proof string $\pi$ is a mutable encoding of original witnesses. Thus, a mutable BARG captures and enables computations over a batch proof $\pi$. We also study new privacy notions for mutable BARGs, guaranteeing that a mutated proof hides all non-trivial information. Such mutable BARGs are a naturally good fit for many privacy sensitive applications. Our main contributions can be summarized as introducing the general concept of mutable BARGs, identifying new non-trivial classes of feasible mutations over BARGs, designing new constructions for mutable BARGs satisfying mutation privacy for these classes from standard cryptographic assumptions, and developing applications of mutable BARGs to advanced signatures such as homomorphic signatures, redactable signatures, and aggregate signatures. Our results improve state-of-the-art known for many such signature systems either in terms of functionality, efficiency, security, or versatility (in terms of cryptographic assumptions).
Last updated:  2024-05-13
Secret Sharing with Certified Deletion
James Bartusek and Justin Raizes
Secret sharing allows a user to split a secret into many shares so that the secret can be recovered if, and only if, an authorized set of shares is collected. Although secret sharing typically does not require any computational hardness assumptions, its security does require that an adversary cannot collect an authorized set of shares. Over long periods of time where an adversary can benefit from multiple data breaches, this may become an unrealistic assumption. We initiate the systematic study of secret sharing with certified deletion in order to achieve security even against an adversary that eventually collects an authorized set of shares. In secret sharing with certified deletion, a (classical) secret $s$ is split into quantum shares that can be destroyed in a manner verifiable by the dealer. We put forth two natural definitions of security. No-signaling security roughly requires that if multiple non-communicating adversaries delete sufficiently many shares, then their combined view contains negligible information about $s$, even if the total set of corrupted parties forms an authorized set. Adaptive security requires privacy of $s$ against an adversary that can continuously and adaptively corrupt new shares and delete previously-corrupted shares, as long as the total set of corrupted shares minus deleted shares remains unauthorized. Next, we show that these security definitions are achievable: we show how to construct (i) a secret sharing scheme with no-signaling certified deletion for any monotone access structure, and (ii) a threshold secret sharing scheme with adaptive certified deletion. Our first construction uses Bartusek and Khurana's (CRYPTO 2023) 2-out-of-2 secret sharing scheme with certified deletion as a building block, while our second construction is built from scratch and requires several new technical ideas. For example, we significantly generalize the ``XOR extractor'' of Agarwal, Bartusek, Khurana, and Kumar (EUROCRYPT 2023) in order to obtain better seedless extraction from certain quantum sources of entropy, and show how polynomial interpolation can double as a high-rate randomness extractor in our context of threshold sharing with certified deletion.
Last updated:  2024-05-13
Secure Multiparty Computation in the Presence of Covert Adaptive Adversaries
Isheeta Nargis and Anwar Hasan
We design a new MPC protocol for arithmetic circuits secure against erasure-free covert adaptive adversaries with deterrence 1/2. The new MPC protocol has the same asymptotic communication cost, the number of PKE operations and the number of exponentiation operations as the most efficient MPC protocol for arithmetic circuits secure against covert static adversaries. That means, the new MPC protocol improves security from covert static security to covert adaptive adversary almost for free. For MPC problems where the number of parties n is much larger than the number of multiplication gates M, the new MPC protocol asymptotically improves communication complexity over the most efficient MPC protocol for arithmetic circuits secure against erasure-free active adaptive adversaries.
Last updated:  2024-05-13
Proof of Stake and Activity: Rewarding On-Chain Activity Through Consensus
Aram Jivanyan and Karen Terjanian
We are introducing a novel consensus protocol for blockchain, called Proof of Stake and Activity (PoSA) which can augment the traditional Proof of Stake methods by integrating a unique Proof of Activity system. PoSA offers a compelling economic model that promotes decentralization by rewarding validators based on their staked capital and also the business value they contribute to the chain. This protocol has been implemented already into a fully-fledged blockchain platform called Bahamut ( which boasts hundreds of thousands of active users already.
Last updated:  2024-05-13
Proxying is Enough: Security of Proxying in TLS Oracles and AEAD Context Unforgeability
Zhongtang Luo, Yanxue Jia, Yaobin Shen, and Aniket Kate
Show abstract
TLS oracles allow a TLS client to offer selective data provenance to an external (oracle) node such that the oracle node is ensured that the data is indeed coming from a pre-defined TLS server. Typically, the client/user supplies their credentials and reveals data in a zero-knowledge manner to demonstrate certain information to oracles while ensuring the privacy of the rest of the data. Conceptually, this is a standard three-party secure computation between the TLS server, TLS client (prover), and the oracle (verifier) node; however, the key practical requirement for TLS oracles to ensure that data provenance process remains transparent to the TLS server. Recent TLS oracle protocols such as DECO enforce the communication pattern of server-client-verifier and utilize a novel three-party handshake process during TLS to ensure data integrity against potential tempering by the client. However, this approach comes with a significant performance penalty on the client/prover and the verifier and raises the question if it is possible to improve the performance by putting the verifier (as a proxy) between the server and the client such that the correct TLS transcript is always available to the verifier. This work offers both positive and negative answers to this oracle proxy question: We first formalize the oracle proxy notion that allows the verifier to directly proxy client-server TLS communication, without entering a three-party handshake or interfering with the connection in any way. We then show that for common TLS-based higher-level protocols such as HTTPS, data integrity to the verifier proxy is ensured by the variable padding built into the HTTP protocol semantics. On the other hand, if a TLS-based protocol comes without variable padding, we demonstrate that data integrity cannot be guaranteed. In this context, we then study the case where the TLS response is pre-determined and cannot be tampered with during the connection. We propose the concept of context unforgeability and show allows overcoming the impossibility. We further show that ChaCha20-Poly1305 satisfies the concept while AES-GCM does not under the standard model.
Last updated:  2024-05-13
Compact Encryption based on Module-NTRU problems
Shi Bai, Hansraj Jangir, Hao Lin, Tran Ngo, Weiqiang Wen, and Jinwei Zheng
The Module-NTRU problem, introduced by Cheon, Kim, Kim, Son (IACR ePrint 2019/1468), and Chuengsatiansup, Prest, Stehlé, Wallet, Xagawa (ASIACCS ’20), generalizes the versatile NTRU assump- tion. One of its main advantages lies in its ability to offer greater flexibil- ity on parameters, such as the underlying ring dimension. In this work, we present several lattice-based encryption schemes, which are IND-CPA (or OW-CPA) secure in the standard model based on the Module-NTRU and Module-LWE problems. Leveraging the Fujisaki-Okamoto transfor- mations, one can obtain IND-CCA secure key encapsulation schemes. Our first encryption scheme is based on the Module-NTRU assumption, which uses the determinant of the secret matrix over the underlying ring for the decryption. Our second scheme is analogue to the Module-LWE encryption scheme, but uses only a matrix as the public key, based on a vectorial variant of the Module-NTRU problem. In the end, we conduct comprehensive analysis of known attacks and propose concrete parame- ters for the instantiations. In particular, our ciphertext size is about 614 (resp. 1228) bytes for NIST Level 1 (resp. Level 5) security and small decryption failure, placing it on par with the most recent schemes such as the one proposed by Zhang, Feng and Yan (ASIACRYPT ’23). We also present several competitive parameters for NIST Level 3, which has a ci- phertext size of 921 bytes. Moreover, our schemes do not require specific codes for plaintext encoding and decoding.
Last updated:  2024-05-13
Tight Security of Double-Block Nonce-Based MACs
Wonseok Choi, Jooyoung Lee, and Yeongmin Lee
In this paper, we study the security of MAC constructions among those classified by Chen et al. in ASIACRYPT '21. Precisely, $F^{\text{EDM}}_{B_2}$ (or $\mathsf{EWCDM}$ as named by Cogliati and Seurin in CRYPTO '16), $F^{\text{EDM}}_{B_3}$, $F^{\text{SoP}}_{B_2}$, $F^{\text{SoP}}_{B_3}$ (all as named by Chen et al.) are proved to be fully secure up to $2^n$ MAC queries in the nonce-respecting setting, improving the previous bound of $\frac{3n}{4}$-bit security. In particular, $F^{\text{SoP}}_{B_2}$ and $F^{\text{SoP}}_{B_3}$ enjoy graceful degradation as the number of queries with repeated nonces grows (when the underlying universal hash function satisfies a certain property called multi-xor-collision resistance). To do this, we develop a new tool, namely extended Mirror theory based on two independent permutations to a wide range of $\xi_{\max}$ including inequalities. Furthermore, we give a generic semi-black-box reduction from single-user security bound in the standard model to multi-user security bound in the ideal cipher model, yielding significantly better bounds than the naive hybrid argument. This reduction is applicable to all MAC construction we considered in this paper and even can be more generalized. We also present matching attacks on $F^{\text{EDM}}_{B_4}$ and $F^{\text{EDM}}_{B_5}$ using $O(2^{3n/4})$ MAC queries and $O(1)$ verification query without using repeated nonces.
Last updated:  2024-05-13
New Solutions to Delsarte's Dual Linear Programs
André Chailloux and Thomas Debris-Alazard
Understanding the maximum size of a code with a given minimum distance is a major question in computer science and discrete mathematics. The most fruitful approach for finding asymptotic bounds on such codes is by using Delsarte's theory of association schemes. With this approach, Delsarte constructs a linear program such that its maximum value is an upper bound on the maximum size of a code with a given minimum distance. Bounding this value can be done by finding solutions to the corresponding dual linear program. Delsarte's theory is very general and goes way beyond binary codes. In this work, we provide universal bounds in the framework of association schemes that generalize the Hamming bound and the Elias-Bassalygo bound, which can be applied to any association scheme constructed from a distance function. These bounds are obtained by constructing new solutions to Delsarte's dual linear program. We instantiate these results and we recover known bounds for $q$-ary codes and for constant-weight binary codes but which didn't come from the linear program method. Our other contribution is to recover, for essentially any $Q$-polynomial scheme, MRRW-type solutions to Delsarte's dual linear program which are inspired by the Laplacian approach of Friedman and Tillich instead of using the Christoffel-Darboux formulas. We show in particular how the second linear programming bound can be interpreted in this framework.
Last updated:  2024-05-13
Covert Adaptive Adversary Model: A New Adversary Model for Multiparty Computation
Isheeta Nargis and Anwar Hasan
In covert adversary model, the corrupted parties can behave in any possible way like active adversaries, but any party that attempts to cheat is guaranteed to get caught by the honest parties with a minimum fixed probability. That probability is called the deterrence factor of covert adversary model. Security-wise, covert adversary is stronger than passive adversary and weaker than active adversary. It is more realistic than passive adversary model. Protocols for covert adversaries are significantly more efficient than protocols for active adversaries. Covert adversary model is defined only for static corruption. Adaptive adversary model is more realistic than static adversaries. In this article, we define a new adversary model, the covert adaptive adversary model, by generalizing the definition of covert adversary model for the more realistic adaptive corruption. We prove security relations between the new covert adaptive adversary model with existing adversary models like passive adaptive adversary model, active adaptive adversary model and covert static adversary model. We prove the sequential composition theorem for the new adversary model which is necessary to allow modular design of protocols for this new adversary model.
Last updated:  2024-05-12
Relativized Succinct Arguments in the ROM Do Not Exist
Annalisa Barbara, Alessandro Chiesa, and Ziyi Guan
A relativized succinct argument in the random oracle model (ROM) is a succinct argument in the ROM that can prove/verify the correctness of computations that involve queries to the random oracle. We prove that relativized succinct arguments in the ROM do not exist. The impossibility holds even if the succinct argument is interactive, and even if soundness is computational (rather than statistical). This impossibility puts on a formal footing the commonly-held belief that succinct arguments require non-relativizing techniques. Moreover, our results stand in sharp contrast with other oracle models, for which a recent line of work has constructed relativized succinct non-interactive arguments (SNARGs). Indeed, relativized SNARGs are a powerful primitive that, e.g., can be used to obtain constructions of IVC (incrementally-verifiable computation) and PCD (proof-carrying data) based on falsifiable cryptographic assumptions. Our results rule out this approach for IVC and PCD in the ROM.
Last updated:  2024-05-12
Let Attackers Program Ideal Models: Modularity and Composability for Adaptive Compromise
Joseph Jaeger
We show that the adaptive compromise security definitions of Jaeger and Tyagi (Crypto '20) cannot be applied in several natural use-cases. These include proving multi-user security from single-user security, the security of the cascade PRF, and the security of schemes sharing the same ideal primitive. We provide new variants of the definitions and show that they resolve these issues with composition. Extending these definitions to the asymmetric settings, we establish the security of the modular KEM/DEM and Fujisaki-Okamoto approaches to public key encryption in the full adaptive compromise setting. This allows instantiations which are more efficient and standard than prior constructions.
Last updated:  2024-05-12
Challenger: Blockchain-based Massively Multiplayer Online Game Architecture
Boris Chan Yip Hon, Bilel Zaghdoudi, Maria Potop-Butucaru, Sébastien Tixeuil, and Serge Fdida
We propose Challenger a peer-to-peer blockchain-based middleware architecture for narrative games, and discuss its resilience to cheating attacks. Our architecture orchestrates nine services in a fully decentralized manner where nodes are not aware of the entire composition of the system nor its size. All these components are orchestrated together to obtain (strong) resilience to cheaters. The main contribution of the paper is to provide, for the first time, an architecture for narrative games agnostic of a particular blockchain that brings together several distinct research areas, namely distributed ledgers, peer-to-peer networks, multi-player-online games and resilience to attacks.
Last updated:  2024-05-12
Multi User Security of LightMAC and LightMAC_Plus
Nilanjan Datta, Shreya Dey, Avijit Dutta, and Devdutto Kanungo
In FSE'16, Luykx et al. have proposed $\textsf{LightMAC}$ that provably achieves a query length independent PRF security bound. To be precise, the construction achieves security roughly in the order of $O(q^2/2^n)$, when instantiated with two independently keyed $n$-bit block ciphers and $q$ is the total number of queries made by the adversary. Subsequently, in ASIACRYPT'17, Naito proposed a beyond-birthday-bound variant of the $\textsf{LightMAC}$ construction, dubbed as $\textsf{LightMAC_Plus}$, that is built on three independently keyed $n$-bit block ciphers and achieves $2n/3$-bits PRF security. Security analyses of these two constructions have been conducted in the single-user setting, where we assume that the adversary has the access to a single instance of the construction. In this paper, we investigate, for the first time, the security of the $\textsf{LightMAC}$ and the $\textsf{LightMAC_Plus}$ construction in the context of multi-user setting, where we assume that the adversary has access to more than one instances of the construction. In particular, we have shown that $\textsf{LightMAC}$ remains secure roughly up to $2^{n/2}$ construction queries and $2^k$ ideal-cipher queries in the ideal-cipher model and $\textsf{LightMAC_Plus}$ maintains security up to approximately $2^{2n/3}$ construction queries and $2^{2k/3}$ ideal-cipher queries in the ideal-cipher model, where $n$ denotes the block size and $k$ denotes the key size of the block cipher.
Last updated:  2024-05-13
zkSNARKs in the ROM with Unconditional UC-Security
Alessandro Chiesa and Giacomo Fenzi
The universal composability (UC) framework is a “gold standard” for security in cryptography. UC-secure protocols achieve strong security guarantees against powerful adaptive adversaries, and retain these guarantees when used as part of larger protocols. Zero knowledge succinct non-interactive arguments of knowledge (zkSNARKs) are a popular cryptographic primitive that are often used within larger protocols deployed in dynamic environments, and so UC-security is a highly desirable, if not necessary, goal. In this paper we prove that there exist zkSNARKs in the random oracle model (ROM) that unconditionally achieve UC-security. Here, “unconditionally” means that security holds against adversaries that make a bounded number of queries to the random oracle, but are otherwise computationally unbounded. Prior work studying UC-security for zkSNARKs obtains transformations that rely on computational assumptions and, in many cases, lose most of the succinctness property of the zkSNARK. Moreover, these transformations make the resulting zkSNARK more expensive and complicated. In contrast, we prove that widely used zkSNARKs in the ROM are UC-secure without modifications. We prove that the Micali construction, which is the canonical construction of a zkSNARK, is UC-secure. Moreover, we prove that the BCS construction, which many zkSNARKs deployed in practice are based on, is UC-secure. Our results confirm the intuition that these natural zkSNARKs do not need to be augmented to achieve UC-security, and give confidence that their use in larger real-world systems is secure.
Last updated:  2024-05-11
$\mathsf{OPA}$: One-shot Private Aggregation with Single Client Interaction and its Applications to Federated Learning
Harish Karthikeyan and Antigoni Polychroniadou
Our work aims to minimize interaction in secure computation due to the high cost and challenges associated with communication rounds, particularly in scenarios with many clients. In this work, we revisit the problem of secure aggregation in the single-server setting where a single evaluation server can securely aggregate client-held individual inputs. Our key contribution is One-shot Private Aggregation ($\mathsf{OPA}$) where clients speak only once (or even choose not to speak) per aggregation evaluation. Since every client communicates just once per aggregation, this streamlines the management of dropouts and dynamic participation of clients, contrasting with multi-round state-of-the-art protocols for each aggregation. We initiate the study of $\mathsf{OPA}$ in several ways. First, we formalize the model and present a security definition. Second, we construct $\mathsf{OPA}$ protocols based on class groups, DCR, and LWR assumptions. Third, we demonstrate $\mathsf{OPA}$ with two applications: private stream aggregation and privacy-preserving federated learning. Specifically, $\mathsf{OPA}$ can be used as a key building block to enable privacy-preserving federated learning and critically, where client speaks once. This is a sharp departure from prior multi-round protocols whose study was initiated by Bonawitz et al. (CCS, 2017). Moreover, unlike the YOSO (You Only Speak Once) model for general secure computation, $\mathsf{OPA}$ eliminates complex committee selection protocols to achieve adaptive security. Beyond asymptotic improvements, $\mathsf{OPA}$ is practical, outperforming state-of-the-art solutions. We leverage $\mathsf{OPA}$ to develop a streaming variant named $\mathsf{SOPA}$, serving as the building block for privacy-preserving federated learning. We utilize $\mathsf{SOPA}$ to construct logistic regression classifiers for two datasets. A new distributed key homomorphic PRF is at the core of our construction of $\mathsf{OPA}$. This key component addresses shortcomings observed in previous works that relied on DDH and LWR in the work of Boneh et al. (CRYPTO, 2013), marking it as an independent contribution to our work. Moreover, we also present new distributed key homomorphic PRFs based on class groups or DCR or the LWR assumption.
Last updated:  2024-05-10
Ultrametric integral cryptanalysis
Tim Beyne and Michiel Verbauwhede
A systematic method to analyze \emph{divisibility properties} is proposed. In integral cryptanalysis, divisibility properties interpolate between bits that sum to zero (divisibility by two) and saturated bits (divisibility by $2^{n - 1}$ for $2^n$ inputs). From a theoretical point of view, we construct a new cryptanalytic technique that is a non-Archimedean multiplicative analogue of linear cryptanalysis. It lifts integral cryptanalysis to characteristic zero in the sense that, if all quantities are reduced modulo two, then one recovers the algebraic theory of integral cryptanalysis. The new technique leads to a theory of trails. We develop a tool based on off-the-shelf solvers that automates the analysis of these trails and use it to show that many integral distinguishers on PRESENT and SIMON are stronger than expected.
Last updated:  2024-05-10
Real-world Universal zkSNARKs are non-malleable
Antonio Faonio, Dario Fiore, and Luigi Russo
Simulation extractability is a strong security notion of zkSNARKs that guarantees that an attacker who produces a valid proof must know the corresponding witness, even if the attacker had prior access to proofs generated by other users. Notably, simulation extractability implies that proofs are non-malleable and is of fundamental importance for applications of zkSNARKs in distributed systems. In this work, we study sufficient and necessary conditions for constructing simulation-extractable universal zkSNARKs via the popular design approach based on compiling polynomial interactive oracle proofs (PIOP). Our main result is the first security proof that popular universal zkSNARKs, such as PLONK and Marlin, as deployed in the real world, are simulation-extractable. Our result fills a gap left from previous work (Faonio et al. TCC’23, and Kohlweiss et al. TCC’23) which could only prove the simulation extractability of the “textbook” versions of these schemes and does not capture their optimized variants, with all the popular optimization tricks in place, that are eventually implemented and deployed in software libraries.
Last updated:  2024-05-13
Multivariate Blind Signatures Revisited
Ward Beullens
In 2017, Petzoldt, Szepieniec, and Mohamed proposed a blind signature scheme, based on multivariate cryptography. This construction has been expanded on by several other works. This short paper shows that their construction is susceptible to an efficient polynomial-time attack. The problem is that the authors implicitly assumed that for a random multivariate quadratic map $\mathcal{R}:\mathbb{F}_q^m \rightarrow \mathbb{F}_q^m$ and a collision-resistant hash function $H: \{0,1\}^* \rightarrow \mathbb{F}_q^m$, the function $\mathsf{Com}(m;\mathbf{r}) := H(m) - \mathcal{R}(\mathbf{r})$ is a binding commitment, which is not the case. There is a "folklore" algorithm that can be used to, given any pair of messages, efficiently produce a commitment that opens to both of them. We hope that by pointing out that multivariate quadratic maps are not binding, similar problems can be avoided in the future.
Last updated:  2024-05-18
Client-Efficient Online-Offline Private Information Retrieval
Hoang-Dung Nguyen, Jorge Guajardo, and Thang Hoang
Private Information Retrieval (PIR) permits clients to query entries from a public database hosted on untrusted servers in a privacy-preserving manner. Traditional PIR model suffers from high computation and/or bandwidth cost due to entire database processing for privacy. Recently, Online-Offline PIR (OO-PIR) has been suggested to improve the practicality of PIR, where query-independent materials are precomputed beforehand to accelerate online access. While state-of-the-art OO-PIR schemes (e.g., S&P’24, CRYPTO’23) successfully reduce the online processing overhead to sublinear, they still impose sustainable bandwidth and storage burdens on the client, especially when operating on large databases. In this paper, we propose Pirex, a new OO-PIR scheme with eminent client performance while maintaining the sublinear server processing efficiency. Specifically, Pirex offers clients with sublinear processing, minimal inbound bandwidth, and low storage requirements. Our Pirex design is fairly simple yet efficient, where the majority of operations are naturally low-cost and streamlined (e.g., XOR, PRF, modular arithmetic). We have fully implemented Pirex and evaluated its real-world performance using commodity hardware. Our experimental results demonstrated that Pirex outperforms existing OO-PIR schemes by at least two orders of magnitude. Concretely, with a 1 TB database, Pirex only takes 0.8s to query a 256-KB entry, compared with 30-220s by the state-of-the-art.
Last updated:  2024-05-10
PAC-Private Algorithms
Mayuri Sridhar, Hanshen Xiao, and Srinivas Devadas
Provable privacy typically requires involved analysis and is often associated with unacceptable accuracy loss. While many empirical verification or approximation methods, such as Membership Inference Attacks (MIA) and Differential Privacy Auditing (DPA), have been proposed, these do not offer rigorous privacy guarantees. In this paper, we apply recently-proposed Probably Approximately Correct (PAC) Privacy to give formal, mechanized, simulation-based proofs for a range of practical, black-box algorithms: K-Means, Support Vector Machines (SVM), Principal Component Analysis (PCA) and Random Forests. To provide these proofs, we present a new simulation algorithm that efficiently determines anisotropic noise perturbation required for any given level of privacy. We provide a proof of correctness for this algorithm and demonstrate that anisotropic noise has substantive benefits over isotropic noise. Stable algorithms are easier to privatize, and we demonstrate privacy amplification resulting from introducing regularization in these algorithms; meaningful privacy guarantees are obtained with small losses in accuracy. We also propose new techniques in order to canonicalize algorithmic output and convert intractable geometric stability verification into efficient deterministic stability verification. Thorough experiments are included, and we validate our provable adversarial inference hardness against state-of-the-art empirical attacks.
Last updated:  2024-05-09
An Improved Threshold Homomorphic Cryptosystem Based on Class Groups
Lennart Braun, Guilhem Castagnos, Ivan Damgård, Fabien Laguillaumie, Kelsey Melissaris, Claudio Orlandi, and Ida Tucker
We present distributed key generation and decryption protocols for an additively homomorphic cryptosystem based on class groups, improving on a similar system proposed by Braun, Damgård, and Orlandi at CRYPTO '23. Our key generation is similarly constant round but achieves lower communication complexity than the previous work. This improvement is in part the result of relaxing the reconstruction property required of the underlying integer verifiable secret sharing scheme. This eliminates the reliance on potentially costly proofs of knowledge in unknown order groups. We present a new method to batch zero-knowledge proofs in unknown order groups which strengthens these improvements. We also present a protocol which is proven secure against adaptive adversaries in the single inconsistent player (SIP) model. Our protocols are secure in the universal composability (UC) framework and provide guaranteed output delivery. We demonstrate the relative efficiency of our techniques by presenting the running times and communication costs associated with our implementation of the statically secure protocol and provide a direct comparison with alternate state of the art constructions.
Last updated:  2024-05-09
Unclonable Secret Sharing
Prabhanjan Ananth, Vipul Goyal, Jiahui Liu, and Qipeng Liu
Unclonable cryptography utilizes the principles of quantum mechanics to addresses cryptographic tasks that are impossible classically. We introduce a novel unclonable primitive in the context of secret sharing, called unclonable secret sharing (USS). In a USS scheme, there are $n$ shareholders, each holding a share of a classical secret represented as a quantum state. They can recover the secret once all parties (or at least $t$ parties) come together with their shares. Importantly, it should be infeasible to copy their own shares and send the copies to two non-communicating parties, enabling both of them to recover the secret. Our work initiates a formal investigation into the realm of unclonable secret sharing, shedding light on its implications, constructions, and inherent limitations. ** Connections: We explore the connections between USS and other quantum cryptographic primitives such as unclonable encryption and position verification, showing the difficulties to achieve USS in different scenarios. **Limited Entanglement: In the case where the adversarial shareholders do not share any entanglement or limited entanglement, we demonstrate information-theoretic constructions for USS. **Large Entanglement: If we allow the adversarial shareholders to have unbounded entanglement resources (and unbounded computation), we prove that unclonable secret sharing is impossible. On the other hand, in the quantum random oracle model where the adversary can only make a bounded polynomial number of queries, we show a construction secure even with unbounded entanglement. Furthermore, even when these adversaries possess only a polynomial amount of entanglement resources, we establish that any unclonable secret sharing scheme with a reconstruction function implementable using Cliffords and logarithmically many T-gates is also unattainable.
Last updated:  2024-05-09
A New Cryptographic Algorithm
Ali Mahdoum
The advent of quantum computing technology will compromise many of the current cryptographic algorithms, especially public-key cryptography, which is widely used to protect digital information. Most algorithms on which we depend are used worldwide in components of many different communications, processing, and storage systems. Once access to practical quantum computers becomes available, all public-key algorithms and associated protocols will be vulnerable to criminals, competitors, and other adversaries. It is critical to begin planning for the replacement of hardware, software, and services that use public-key algorithms now so that information is protected from future attacks.” [1]. For this purpose, we have developed a new algorithm that contributes to deal with the aforementioned problem. Instead to use a classical scheme of encoding / decoding methods (keys, prime numbers, etc.), our algorithm is rather based on a combination of functions. Because the cardinality of the set of functions is infinite, it would be impossible for a third party (e.g. a hacker) to decode the secret information transmitted by the sender (Bob) to the receiver (Alice).
Last updated:  2024-05-09
Learning with Quantization, Polar Quantizer, and Secure Source Coding
Shanxiang Lyu, Ling Liu, and Cong Ling
This paper presents a generalization of the Learning With Rounding (LWR) problem, initially introduced by Banerjee, Peikert, and Rosen, by applying the perspective of vector quantization. In LWR, noise is induced by rounding each coordinate to the nearest multiple of a fraction, a process inherently tied to scalar quantization. By considering a new variant termed Learning With Quantization (LWQ), we explore large-dimensional fast-decodable lattices with superior quantization properties, aiming to enhance the compression performance over conventional scalar quantization. We identify polar lattices as exemplary structures, effectively transforming LWQ into a problem akin to Learning With Errors (LWE), where the distribution of quantization noise is statistically close to discrete Gaussian. Furthermore, we develop a novel ``quancryption'' scheme for secure source coding. Notably, the scheme achieves near-optimal rate-distortion ratios for bounded rational signal sources, and can be implemented efficiently with quasi-linear time complexity. Python code of the polar-lattice quantizer is available at
Last updated:  2024-05-17
Analyzing Pump and jump BKZ algorithm using dynamical systems
Leizhang Wang
The analysis of the reduction effort of the lattice reduction algorithm is important in estimating the hardness of lattice-based cryptography schemes. Recently many lattice challenge records have been cracked by using the Pnj-BKZ algorithm which is the default lattice reduction algorithm used in G6K, such as the TU Darmstadt LWE and SVP Challenges. However, the previous estimations of the Pnj-BKZ algorithm are simulator algorithms rather than theoretical upper bound analyses. In this work, we present the first dynamic analysis of Pnj-BKZ algorithm. More precisely, our analysis results show that let $L$ is the lattice spanned by $(\mathbf{a}_i)_{i\leq d}$. The shortest vector $\mathbf{b}_1$ output by running $\Omega \left ( \frac{2Jd^2}{\beta(\beta-J)}\left ( \ln_{}{d} +\ln_{} \ln_{}{\max_{i}\frac{\left \| \mathbf{a}_i^{*} \right \| }{(\mathrm{det}L )^{1/d} } } \right ) \right ) $ tours reduction of pnj-BKZ$(\beta,J)$, $\mathbf{b}_1$ satisfied that $\left \| \mathbf{b}_1 \right \| \le {\gamma}_{\beta}^{\frac{d-1}{2(\beta-J)}+2 } \cdot \left ( \mathrm{det}L \right ) ^{\frac{1}{d} } $.
Last updated:  2024-05-15
Quantum NV Sieve on Grover for Solving Shortest Vector Problem
Hyunji Kim, Kyungbae Jang, Hyunjun Kim, Anubhab Baksi, Sumanta Chakraborty, and Hwajeong Seo
Quantum computers can efficiently model and solve several challenging problems for classical computers, raising concerns about potential security reductions in cryptography. NIST is already considering potential quantum attacks in the development of post-quantum cryptography by estimating the quantum resources required for such quantum attacks. In this paper, we present quantum circuits for the NV sieve algorithm to solve the Shortest Vector Problem (SVP), which serves as the security foundation for lattice-based cryptography, achieving a quantum speedup of the square root. Although there has been extensive research on the application of quantum algorithms for lattice-based problems at the theoretical level, specific quantum circuit implementations for them have not been presented yet. Notably, this work demonstrates that the required quantum complexity for the SVP in the lattice of rank 70 and dimension 70 is $2^{43}$ (a product of the total gate count and the total depth) with our optimized quantum implementation of the NV sieve algorithm. This complexity is significantly lower than the NIST post-quantum security standard, where level 1 is $2^{157}$, corresponding to the complexity of Grover's key search for AES-128.
Last updated:  2024-05-10
Non-Transferable Anonymous Tokens by Secret Binding
F. Betül Durak, Laurane Marco, Abdullah Talayhan, and Serge Vaudenay
Non-transferability (NT) is a security notion which ensures that credentials are only used by their intended owners. Despite its importance, it has not been formally treated in the context of anonymous tokens (AT) which are lightweight anonymous credentials. In this work, we consider a client who "buys" access tokens which are forbidden to be transferred although anonymously redeemed. We extensively study the trade-offs between privacy (obtained through anonymity) and security in AT through the notion of non-transferability. We formalise new security notions, design a suite of protocols with various flavors of NT, prove their security, and implement the protocols to assess their efficiency. Finally, we study the existing anonymous credentials which offer NT, and show that they cannot automatically be used as AT without security and complexity implications.
Last updated:  2024-05-08
BUFFing FALCON without Increasing the Signature Size
Samed Düzlü, Rune Fiedler, and Marc Fischlin
This work shows how FALCON can achieve the Beyond UnForgeability Features (BUFF) introduced by Cremers et al. (S&P'21) more efficiently than by applying the generic BUFF transform. Specifically, we show that applying a transform of Pornin and Stern (ACNS'05), dubbed PS-3 transform, already suffices for FALCON to achieve BUFF security. For FALCON, this merely means to include the public key in the hashing step in signature generation and verification, instead of hashing only the nonce and the message; the other signature computation steps and the signature output remain untouched. In comparison to the BUFF transform, which appends a hash value to the final signature, the PS-3 transform therefore achieves shorter signature sizes, without incurring additional computations.
Last updated:  2024-05-08
Masked Computation the Floor Function and its Application to the FALCON Signature
Justine Paillet, Pierre-Augustin Berthet, and Cédric Tavernier
FALCON is candidate for standardization of the new Post Quantum Cryptography (PQC) primitives by the National Institute of Standards and Technology (NIST). However, it remains a challenge to define efficient countermeasures against side-channel attacks (SCA) for this algorithm. FALCON is a lattice-based signature that relies on rational numbers which is unusual in the cryptography field. While recent work proposed a solution to mask the addition and the multiplication, some roadblocks remain, most noticeably how to protect the floor function. We propose in this work to complete the existing first trials of hardening FALCON against SCA. We perform the mathematical proofs of our methods as well as formal security proof in the probing model using the Non-Interference concepts.
Last updated:  2024-05-07
Automated Generation of Fault-Resistant Circuits
Nicolai Müller and Amir Moradi
Fault Injection (FI) attacks, which involve intentionally introducing faults into a system to cause it to behave in an unintended manner, are widely recognized and pose a significant threat to the security of cryptographic primitives implemented in hardware, making fault tolerance an increasingly critical concern. However, protecting cryptographic hardware primitives securely and efficiently, even with well-established and documented methods such as redundant computation, can be a time-consuming, error-prone, and expertise-demanding task. In this research, we present a comprehensive and fully-automated software solution for the Automated Generation of Fault-Resistant Circuits (AGEFA). Our application employs a generic and extensively researched methodology for the secure integration of countermeasures based on Error-Correcting Codes (ECCs) into cryptographic hardware circuits. Our software tool allows designers without hardware security expertise to develop fault-tolerant hardware circuits with pre-defined correction capabilities under a comprehensive fault adversary model. Moreover, our tool applies to masked designs without violating the masking security requirements, in particular to designs generated by the tool AGEMA. We evaluate the effectiveness of our approach through experiments on various block ciphers and demonstrate its ability to produce fault-tolerant circuits. Additionally, we assess the security of examples generated by AGEFA against Side-Channel Analysis (SCA) and FI using state-of-the-art leakage and fault evaluation tools.
Last updated:  2024-05-07
Towards a Polynomial Instruction Based Compiler for Fully Homomorphic Encryption Accelerators
Sejun Kim, Wen Wang, Duhyeong Kim, Adish Vartak, Michael Steiner, and Rosario Cammarota
Fully Homomorphic Encryption (FHE) is a transformative technology that enables computations on encrypted data without requiring decryption, promising enhanced data privacy. However, its adoption has been limited due to significant performance overheads. Recent advances include the proposal of domain-specific, highly-parallel hardware accelerators designed to overcome these limitations. This paper introduces PICA, a comprehensive compiler framework designed to simplify the programming of these specialized FHE accelerators and integration with existing FHE libraries. PICA leverages a novel polynomial Instruction Set Architecture (p-ISA), which abstracts polynomial rings and their arithmetic operations, serving as a fundamental data type for the creation of compact, efficient code embracing high-level operations on polynomial rings, referred to as kernels, e.g., encompassing FHE primitives like arithmetic and ciphertext management. We detail a kernel generation framework that translates high-level FHE operations into pseudo-code using p-ISA, and a subsequent tracing framework that incorporates p-ISA functionalities and kernels into established FHE libraries. Additionally, we introduce a mapper to coordinate multiple FHE kernels for optimal application performance on targeted hardware accelerators. Our evaluations demonstrate PICA's efficacy in creation of compact and efficient code, when compared with an x64 architecture. Particularly in managing complex FHE operations such as relinearization, where we observe a 25.24x instruction count reduction even when a large batch size (8192) is taken into account.
Last updated:  2024-05-07
Linicrypt in the Ideal Cipher Model
Zahra Javar and Bruce M. Kapron
We extend the Linicrypt framework for characterizing hash function security as proposed by McQuoid, Swope, and Rosulek (TCC 2018) to support constructions in the ideal cipher model. In this setting, we give a characterization of collision- and second-preimage-resistance in terms of a linear-algebraic condition on Linicrypt programs, and present an efficient algorithm for determining whether a program satisfies the condition. As an application, we consider the case of the block cipherbased hash functions proposed by Preneel, Govaerts, and Vandewall (Crypto 1993), and show that the semantic analysis of PGV given by Black et. al. (J. Crypto. 2010) can be captured as a special case of our characterization. In addition, We model hash functions constructed through the Merkle-Damgård transformation within the Linicrypt framework. Finally, we appy this model to an analysis of how various attacks on the underlying compression functions can compromise the collision resistance of the resulting hash function.
Last updated:  2024-05-07
Large-Scale MPC: Scaling Private Iris Code Uniqueness Checks to Millions of Users
Remco Bloemen, Daniel Kales, Philipp Sippl, and Roman Walch
In this work we tackle privacy concerns in biometric verification systems that typically require server-side processing of sensitive data (e.g., fingerprints and Iris Codes). Concretely, we design a solution that allows us to query whether a given Iris Code is similar to one contained in a given database, while all queries and datasets are being protected using secure multiparty computation (MPC). Addressing the substantial performance demands of operational systems like World ID and aid distributions by the Red Cross, we propose new protocols to improve performance by more than three orders of magnitude compared to the recent state-of-the-art system Janus (S&P 24). Our final protocol can achieve a throughput of over a million Iris Code comparisons per second on a single CPU core, while protecting the privacy of both the query and database Iris Codes. We additionally investigate GPU acceleration for some building blocks of our protocol, which results in further speedups of over 38x compared to the respective multi-threaded CPU implementation.
Last updated:  2024-05-07
Fully Automated Selfish Mining Analysis in Efficient Proof Systems Blockchains
Krishnendu Chatterjee, Amirali Ebrahim-Zadeh, Mehrdad Karrabi, Krzysztof Pietrzak, Michelle Yeo, and Djordje Zikelic
We study selfish mining attacks in longest-chain blockchains like Bitcoin, but where the proof of work is replaced with efficient proof systems -- like proofs of stake or proofs of space -- and consider the problem of computing an optimal selfish mining attack which maximizes expected relative revenue of the adversary, thus minimizing the chain quality. To this end, we propose a novel selfish mining attack that aims to maximize this objective and formally model the attack as a Markov decision process (MDP). We then present a formal analysis procedure which computes an $\epsilon$-tight lower bound on the optimal expected relative revenue in the MDP and a strategy that achieves this $\epsilon$-tight lower bound, where $\epsilon>0$ may be any specified precision. Our analysis is fully automated and provides formal guarantees on the correctness. We evaluate our selfish mining attack and observe that it achieves superior expected relative revenue compared to two considered baselines. In concurrent work [Sarenche FC'24] does an automated analysis on selfish mining in predictable longest-chain blockchains based on efficient proof systems. Predictable means the randomness for the challenges is fixed for many blocks (as used e.g., in Ouroboros), while we consider unpredictable (Bitcoin-like) chains where the challenge is derived from the previous block.
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