SQISign is an isogeny-based signature scheme that has short keys and signatures and is expected to be a post-quantum scheme. Its security depends on the hardness of the problem to find an isogeny between given two elliptic curves over $\mathbb{F}_{p^2}$, where $p$ is a large prime. For efficiency reasons, a public key in SQISign is taken from a set of supersingular elliptic curves with a particular property. In this paper, we investigate the security related to public keys in SQISign. First, we show some properties of the set of public keys. Next, we show that a key generation procedure used in implementing SQISign could not generate all public keys and propose a modification for the procedure. In addition, we confirm the latter result through an experiment.

Private function evaluation (PFE) is a special type of MPC protocols that, in addition to the input privacy, can preserve the function privacy. In this work, we propose a PFE scheme for RAM. In particular, we first design an efficient 4-server distributed ORAM scheme with amortized communication $O(\log n)$ per access (both reading and writing). We then simulate a RISC RAM machine over the MPC platform, hiding (i) the memory access pattern, (ii) the machine state (including registers, program counter, condition flag, etc.), and (iii) the executed instructions. Our scheme can naturally support a simplified TinyRAM instruction set; if a public RAM program $P$ with given inputs $x$ needs to execute $z$ instruction cycles, our PFE scheme is able to securely evaluate $P(x)$ on private $P$ and $x$ within $5z+1$ online rounds. We prototype and benchmark our system for set intersection, binary search, quicksort, and heapsort algorithms. For instance, to obliviously perform the binary search algorithm on a $2^{10}$ array takes $5.81s$ with function privacy.

In this paper, we present the first chosen-ciphertext (CC) cache-timing attacks on the reference implementation of HQC. We build a cache-timing based distinguisher for implementing a plaintext-checking (PC) oracle. The PC oracle uses side-channel information to check if a given ciphertext decrypts to a given message. This is done by identifying a vulnerability during the generating process of two vectors in the reference implementation of HQC. We also propose a new method of using PC oracles for chosen-ciphertext side-channel attacks against HQC, which may have independent interest. We show a general proof-of-concept attack, where we use the Flush&Reload technique and also derive, in more detail, a practical attack on an HQC execution on Intel SGX, where the Prime&Probe technique is used. We show the exact path to do key recovery by explaining the detailed steps, using the PC oracle. In both scenarios, the new attack requires $53,857$ traces on average with much fewer PC oracle calls than the timing attack of Guo et al. CHES 2022 on an HQC implementation.

In CRYPTO 2012, Zhandry developed generic semi-constant oracle technique and proved security of an identity-based encryption scheme, GPV-IBE, and full domain hash (FDH) signature scheme in the quantum random oracle model (QROM). However, the reduction provided by Zhandry incurred a quadratic reduction loss. In this work, we provide a much tighter proof, with linear reduntion loss, for the FDH, probabilistc FDH (PFDH), and GPV-IBE in the QROM. Our proof is based on the measure-and-reprogram technique developed by Don, Fehr, Majenz and Schaffner.

Micciancio and Sorrel (ICALP 2018) proposed a bootstrapping algorithm that can refresh many messages at once with sublinearly many homomorphic operations per message. However, despite the attractive asymptotic cost, it is unclear if their algorithm could ever be practical, which reduces the impact of their results. In this work, we follow their general framework, but propose an amortized bootstrapping that is conceptually simpler and asymptotically cheaper. We reduce the number of homomorphic operations per refreshed message from $O(3^\rho \cdot n^{1/\rho} \cdot \log n)$ to $O(\rho \cdot n^{1/\rho})$, and the noise overhead from $\tilde{O}(n^{2 + 3 \cdot \rho})$ to $\tilde{O}(n^{1 + \rho})$. We also make it more general, by handling non-binary messages and applying programmable bootstrapping. To obtain a concrete instantiation of our bootstrapping algorithm, we propose a double-CRT (aka RNS) version of the GSW scheme, including a new operation, called shrinking, used to speed-up homomorphic operations by reducing the dimension and ciphertext modulus of the ciphertexts. We also provide a C++ implementation of our algorithm, thus showing for the first time the practicability of the amortized bootstrapping. Moreover, it is competitive with existing bootstrapping algorithms, being even around 3.4 times faster than an equivalent non-amortized version of our bootstrapping.

Automatic methods for differential and linear characteristic search are well-established at the moment. Typically, the designers of novel ciphers also give preliminary analytical findings for analysing the differential and linear properties using automatic techniques. However, neither MILP-based nor SAT/SMT-based approaches have fully resolved the problem of searching for actual differential and linear characteristics of ciphers with large S-boxes. To tackle the issue, we present three strategies for developing SAT models for 8-bit S-boxes that are geared toward differential probabilities and linear correlations. While these approaches cannot guarantee a minimum model size, the time needed to obtain models is drastically reduced. The newly proposed SAT model for large S-boxes enables us to establish that the upper bound on the differential probability for 14 rounds of SKINNY-128 is 2^{-131}, thereby completing the unsuccessful work of Abdelkhalek et al. We also analyse the seven AES-based constructions C1 - C7 designed by Jean and Nikolic and compute the minimum number of active S-boxes necessary to cause an internal collision using the SAT method. For two constructions C3 and C5, the current lower bound on the number of active S-boxes is increased, resulting in a more precise security analysis for these two structures.

We introduce Grotto, a framework and C++ library for space- and time-efficient $(2+1)$-party piecewise polynomial (i.e., spline) evaluation on secrets additively shared over $\mathbb{Z}_{2^{n}}$. Grotto improves on the state-of-the-art approaches based on distributed comparison functions (DCFs) in almost every metric, offering asymptotically superior communication and computation costs with the same or lower round complexity. At the heart of Grotto is a novel observation about the structure of the ``tree'' representation underlying the most efficient distributed point functions (DPFs) from the literature, alongside an efficient algorithm that leverages this structure to do with a single DPF what state-of-the-art approaches require many DCFs to do. Our open-source Grotto implementation supports evaluating dozens of useful functions out of the box, including trigonometric and hyperbolic functions (and their inverses); various logarithms; roots, reciprocals, and reciprocal roots; sign testing and bit counting; and over two dozen of the most common (univariate) activation functions from the deep-learning literature.

This paper specifies a new arithmetization-oriented hash function called Tip5. It uses the SHARK design strategy with low-degree power maps in combination with lookup tables, and is tailored to the field with $p=2^{64}-2^{32}+1$ elements. The context motivating this design is the recursive verification of STARKs. This context imposes particular design constraints, and therefore the hash function's arithmetization is discussed at length.

Constructing a supersingular elliptic curve whose endomorphism ring is isomorphic to a given quaternion maximal order (one direction of the Deuring correspondence) is known to be polynomial-time assuming the generalized Riemann hypothesis [KLPT14; Wes21], but notoriously daunting in practice when not working over carefully selected base fields. In this work, we speed up the computation of the Deuring correspondence in general characteristic, i.e., without assuming any special form of the characteristic. Our algorithm follows the same overall strategy as earlier works, but we add simple (yet effective) optimizations to multiple subroutines to significantly improve the practical performance of the method. To demonstrate the impact of our improvements, we show that our implementation achieves highly practical running times even for examples of cryptographic size. One implication of these findings is that cryptographic security reductions based on KLPT-derived algorithms (such as [EHLMP18; Wes22]) have become tighter, and therefore more meaningful in practice. Another is the pure bliss of fast(er) computer algebra: We provide a Sage implementation which works for general primes and includes many necessary tools for computational number theorists' and cryptographers' needs when working with endomorphism rings of supersingular elliptic curves. This includes the KLPT algorithm, translation of ideals to isogenies, and finding supersingular elliptic curves with known endomorphism ring for general primes. Finally, the Deuring correspondence has recently received increased interest because of its role in the SQISign signature scheme [DeF+20]. We provide a short and self-contained summary of the state-of-the-art algorithms without going into any of the cryptographic intricacies of SQISign.

Streamlined NTRU Prime is a lattice-based Key Encapsulation Mechanism (KEM) that is, together with X25519, currently the default algorithm in OpenSSH 9. Being based on lattice assumptions, it is assumed to be secure also against attackers with access to large-scale quantum computers. While Post-Quantum Cryptography (PQC) schemes have been subject to extensive research in the recent years, challenges remain with respect to protection mechanisms against attackers that have additional side-channel information such as the power consumption of a device processing secret data. As a countermeasure to such attacks, masking has been shown to be a promising and effective approach. For public-key schemes, including any recent PQC schemes, usually a mixture of Boolean and arithmetic approaches are applied on an algorithmic level. Our generic hardware implementation of Streamlined NTRU Prime decapsulation, however, follows an idea that until now was assumed to be only applicable to symmetric cryptography: gate-level masking. There, a hardware design that consists of logic gates is transformed into a secure implementation by replacing each gate with a composably secure gadget that operates on uniform random shares of secret values. In our work, we show the feasibility of applying this approach also to PQC schemes and present the first Public-Key Cryptography (PKC) – pre- and post-quantum – implementation masked at gate level considering several trade-offs and design choices. We synthesize our implementation both for Artix-7 Field-Programmable Gate Arrays (FPGAs) and 45 nm Application-Specific Integrated Circuits (ASICs), yielding practically feasible results regarding area, randomness demand and latency. Finally, we also analyze the applicability of our concept to Kyber which will be standardized by the National Institute of Standards and Technology (NIST).

In this work, we investigate the BGV scheme as implemented in HElib. We begin by performing an implementation-specific noise analysis of BGV. This allows us to derive much tighter bounds than what was previously done. To confirm this, we compare our bounds against the state of the art. We find that, while our bounds are at most $1.8$ bits off the experimentally observed values, they are as much as $29$ bits tighter than previous work. Finally, to illustrate the importance of our results, we propose new and optimised parameters for HElib. In HElib, the special modulus is chosen to be $k$ times larger than the current ciphertext modulus $Q_i$. For a ratio of subsequent ciphertext moduli $\log\left( \frac{Q_i}{Qi−1}\right) = 54$ (a very common choice in HElib), we can optimise $k$ by up to $26$ bits. This means that we can either enable more multiplications without having to switch to larger parameters, or reduce the size of the evaluation keys, thus reducing on communication costs in relevant applications. We argue that our results are near-optimal.

In $1$-out-of-$q$ Oblivious Transfer (OT) protocols, a sender Alice is able to send one of $q\ge 2$ messages to a receiver Bob, all while being oblivious to which message was transferred. Moreover, the receiver learns only one of these messages. Oblivious Transfer combiners take $n$ instances of OT protocols as input, and produce an OT protocol that is secure if sufficiently many of the $n$ original OT instances are secure. We present new $1$-out-of-$q$ OT combiners that are perfectly secure against active adversaries. Our combiners arise from secret sharing techniques. We show that given an $\mathbb{F}_q$-linear secret sharing scheme on a set of $n$ participants and adversary structure $\mathcal{A}$, we can construct $n$-server, $1$-out-of-$q$ OT combiners that are secure against an adversary corrupting either Alice and a set of servers in $\mathcal{A}$, or Bob and a set of servers $B$ with $\bar{B}\notin\mathcal{A}$. If the normalized total share size of the scheme is $\ell$, then the resulting OT combiner requires $\ell$ calls to OT protocols, and the total amount of bits exchanged during the protocol is $(q^2+q+1)\ell\log q$. We also present a construction based on $1$-out-of-$2$ OT combiners that uses the protocol of Crépeau, Brassard and Robert (FOCS 1986). This construction provides smaller communication costs for certain adversary structures, such as threshold ones: For any prime power $q\geq n$, there are $n$-server, $1$-out-of-$q$ OT combiners that are perfectly secure against active adversaries corrupting either Alice or Bob, and a minority of the OT candidates, exchanging $O(qn\log q)$ bits in total.

An important cryptographic operation on elliptic curves is hashing to a point on the curve. When the curve is not of prime order, the point is multiplied by the cofactor so that the result has a prime order. This is important to avoid small subgroup attacks for example. A second important operation, in the composite-order case, is testing whether a point belongs to the subgroup of prime order. A pairing is a bilinear map e : G1 × G2 → GT where G1 and G2 are distinct subgroups of prime order r of an elliptic curve, and GT is a multiplicative subgroup of the same prime order r of a finite field extension. Pairing-friendly curves are rarely of prime order. We investigate cofactor clearing and subgroup membership testing on these composite-order curves. First, we generalize a result on faster cofactor clearing for BLS curves to other pairing-friendly families of a polynomial form from the taxonomy of Freeman, Scott and Teske. Second, we investigate subgroup membership testing for G1 and G2. We fix a proof argument for the G2 case that appeared in a preprint by Scott in late 2021 and has recently been implemented in different cryptographic libraries. We then generalize the result to both G1 and G2 and apply it to different pairing-friendly families of curves. This gives a simple and shared framework to prove membership tests for both cryptographic subgroups.

Encryption satisfying CCA2 security is commonly known to be unnecessarily strong for realizing secure channels. Moreover, CCA2 constructions in the standard model are far from being competitive practical alternatives to constructions via random oracle. A promising research area to alleviate this problem are weaker security notions—like IND-RCCA secure encryption or IND-atag-wCCA secure tag-based encryption—which are still able to facilitate secure message transfer (SMT) via authenticated channels. In this paper we introduce the concept of sender-binding encryption (SBE), unifying prior approaches of SMT construction in the universal composability (UC) model. We furthermore develop the corresponding non-trivial security notion of IND-SB-CPA and formally prove that it suffices for realizing SMT in conjunction with authenticated channels. Our notion is the weakest so far in the sense that it generically implies the weakest prior notions—RCCA and atag-wCCA—without additional assumptions, while the reverse is not true. A direct consequence is that IND-stag-wCCA, which is strictly weaker than IND-atag-wCCA but stronger than our IND-SB-CPA, can be used to construct a secure channel. Finally, we give an efficient IND-SB-CPA secure construction in the standard model from IND-CPA secure double receiver encryption (DRE) based on McEliece. This shows that IND-SB-CPA security yields simpler and more efficient constructions in the standard model than the weakest prior notions, i.e., IND-atag-wCCA and IND-stag-wCCA.

Thesecurityofmanyprotocolssuchasvotingandblockchains relies on a secure source of randomness. Decentralised Randomness Beacon (DRB) has been considered as a promising approach, where a set of participants jointly generates a sequence of random outputs. While the DRBs have been extensively studied, they failed to capture the advantage that some participants learn random outputs earlier than other participants. In time-sensitive protocols whose execution depends on the randomness from a DRB, such an advantage allows the adversary to behave adaptively according to random outputs, compromising the fairness and/or security in these protocols. In this paper, we formalise a new property, delivery-fairness, to quantify the advantage. In particular, we distinguish two aspects of delivery-fairness, namely length-advantage, i.e., how many random outputs an adversary can learn earlier than correct participants, and time-advantage, i.e., how much time an adversary can learn a given random output earlier than correct participants. In addition, we prove the lower bound of delivery-fairness showing optimal guarantee. We further analyse the delivery-fairness guarantee of state-of-the-art DRBs and discuss insights, which, we show through case studies, could help improve delivery-fairness of existing systems to its optimal.

This paper combines techniques from several previous papers with some modifications to improve the previous cryptanalysis of 3-round Keccak-256. Furthermore, we propose a fast rebuilding method to improve the efficiency of solving equation systems. As a result, the guessing times of finding a preimage for 3-round Keccak-256 are decreased from $2^{65}$ to $2^{52}$, and the solving time of each guess is decreased from $2^{9}$ 3-round Keccak calls to $2^{5.3}$ 3-round Keccak calls. We identify a preimage of all '0' digest for 3-round Keccak-256 to support the effectiveness of our methodology.

State-separating proofs (SSP) is a recent methodology for structuring game-based cryptographic proofs in a modular way, by using algebraic laws to exploit the modular structure of composed protocols. While promising, this methodology was previously not fully formalized and came with little tool support. We address this by introducing SSProve, the first general verification framework for machine-checked state-separating proofs. SSProve combines high-level modular proofs about composed protocols, as proposed in SSP, with a probabilistic relational program logic for formalizing the lower-level details, which together enable constructing fully machine-checked cryptographic proofs in the Coq proof assistant. Moreover, SSProve is itself formalized in Coq, including the algebraic laws of SSP, the soundness of the program logic, and the connection between these two verification styles. To illustrate SSProve we use it to mechanize the simple security proofs of ElGamal and PRF-based encryption. We also validate the SSProve approach by conducting two more substantial case studies: First, we mechanize an SSP security proof of the KEM-DEM public key encryption scheme, which led to the discovery of an error in the original paper proof that has since been fixed. Second, we use SSProve to formally prove security of the sigma-protocol zero-knowledge construction, and we moreover construct a commitment scheme from a sigma-protocol to compare with a similar development in CryptHOL. We instantiate the security proof for sigma-protocols to give concrete security bounds for Schnorr's sigma-protocol.

Secure neural network inference has been a promising solution to private Deep-Learning-as-a-Service, which enables the service provider and user to execute neural network inference without revealing their private inputs. However, the expensive overhead of current schemes is still an obstacle when applied in real applications. In this work, we present \textsc{Meteor}, an online communication-efficient and fast secure 3-party computation neural network inference system aginst semi-honest adversary in honest-majority. The main contributions of \textsc{Meteor} are two-fold: \romannumeral1) We propose a new and improved 3-party secret sharing scheme stemming from the \textit{linearity} of replicated secret sharing, and design efficient protocols for the basic cryptographic primitives, including linear operations, multiplication, most significant bit extraction, and multiplexer. \romannumeral2) Furthermore, we build efficient and secure blocks for the widely used neural network operators such as Matrix Multiplication, ReLU, and Maxpool, along with exploiting several specific optimizations for better efficiency. Our total communication with the setup phase is a little larger than SecureNN (PoPETs'19) and \textsc{Falcon} (PoPETs'21), two state-of-the-art solutions, but the gap is not significant when the online phase must be optimized as a priority. Using \textsc{Meteor}, we perform extensive evaluations on various neural networks. Compared to SecureNN and \textsc{Falcon}, we reduce the online communication costs by up to $25.6\times$ and $1.5\times$, and improve the running-time by at most $9.8\times$ (resp. $8.1\times$) and $1.5\times$ (resp. $2.1\times$) in LAN (resp. WAN) for the online inference.

TLS termination, which is essential to network and security infrastructure providers, is an extremely latency sensitive operation that benefits from access to sensitive key material close to the edge. However, increasing regulatory concerns prompt customers to demand sophisticated controls on where their keys may be accessed. While traditional access-control solutions rely on a highly available centralized process to enforce access, the round-trip latency and decreased fault tolerance make this approach unappealing. Furthermore, the desired level of customer control is at odds with customizing the distribution process for each key. To solve this dilemma, we have designed and implemented Portunus, a cryptographic storage and access control system built using a variant of public-key cryptography called attribute-based encryption (ABE). Using Portunus, TLS keys are protected using ABE under a policy chosen by the customer. Each server is issued unique ABE keys based on its attributes, allowing it to decrypt only the TLS keys for which it satisfies the policy. Thus, the encrypted keys can be stored at the edge, with access control enforced passively through ABE. If a server receives a TLS connection but is not authorized to decrypt the necessary TLS key, the request is forwarded directly to the nearest authorized server, further avoiding the need for a centralized coordinator. In comparison, a trivial instantiation of this system using standard public-key cryptography might wrap each TLS key with the key of every authorized data center. This strategy, however, multiplies the storage overhead by the number of data centers. We have deployed Portunus on Cloudflare's global network of over 400 data centers. Our measurements indicate that we can handle millions of requests per second globally, making it one of the largest deployments of ABE.

Multiparty garbling is the most popular approach for constant-round secure multiparty computation (MPC). Despite being the focus of significant research effort, instantiating prior approaches to multiparty garbling results in constant-round MPC that can not realistically accommodate large numbers of parties. In this work we present the first global-scale multiparty garbling protocol. The per-party communication complexity of our protocol decreases as the number of parties participating in the protocol increases---for the first time matching the asymptotic communication complexity of non-constant round MPC protocols. Our protocol achieves malicious security in the honest-majority setting and relies on the hardness of the Learning Party with Noise assumption.

FUTURE is a recently proposed, lightweight block cipher. It has an AES-like, SP-based, 10-round encryption function, where, unlike most other lightweight constructions, the diffusion layer is based on an MDS matrix. Despite its relative complexity, it has a remarkable hardware performance due to careful design decisions. In this paper, we conducted a MILP-based analysis of the cipher, where we incorporated exact probabilities rather than just the number of active S-boxes into the model. Through the MILP analysis, we were able to find differential and linear distinguishers for up to 5 rounds of FUTURE, extending the known distinguishers of the cipher by one round.

Recent years have witnessed a push to bring multi-party computation (MPC) to practice and make it accessible to the end user/programmer. Despite novel ideas, on frontend language design (e.g., Wysteria, Viaduct), backend protocol design and implementation (e.g., ABY, MOTION), or both (e.g., SPDZ), classical compiler optimizations remain largely under-utilized (if not completely unused) in MPC programming. A likely reason is that such optimizations are often applied on a middle-end intermediate representation such as SSA. We put forth a methodology for an MPC programming compilation toolchain, which by mimicking the compilation methodology of standard imperative languages enables middle-end optimizations on MPC, yielding significant improvements. To this direction we devise an MPC circuit compiler that allows MPC programming in what is essentially Python, and inherits the structure (and therefore optimization opportunities) of the classical compilation pipeline. Our key conceptual contribution is advancing an intermediate language, which we call MPC-IR, that can be viewed as the analogue, in an MPC program’s compilation, of (enriched) SSA form. MPC-IR is a particularly appealing intermediate language as it allows backend-independent optimizations, a close analogy to machine independent optimizations in classical compilers. Demonstrating the power of our approach, we focus on a specific backend-independent optimization, SIMD-vectorization: We devise a novel classical-compiler-inspired automatic SIMD-vectorization on MPC-IR, which we show leads to significant speedup in circuit generation time and running time, as well as significant reduction in communication size and number of gates over the corresponding iterative schedule. We implement and benchmark our compiler from a Python-like program to an optimized circuit that can be fed into an MPC backend (for our benchmarks we make use of the MOTION backend for MPC). We view our exhaustive benchmarks as both a way to validate our optimization and end-to-end compiler, and as a contribution, by itself, to a more complete benchmarks suite for MPC programming—such benchmarks suites are common in classical compilers.

We present a new construction for secure logistic regression training, which enables two parties to train a model on private secret-shared data. Our goal is to minimize online communication and round complexity, while still allowing for an efficient offline phase. As part of our construction we develop many building blocks of independent interest. These include a new approximation technique for the sigmoid function, which results in a secure protocol with better communication; secure spline evaluation and secure powers computation protocols for fixed-point values; and a new comparison protocol that optimizes online communication. We also present a new two-party protocol for generating keys for distributed point functions (DPFs) over arithmetic sharing, where previous constructions do this only for Boolean outputs. We implement our protocol in an end-to-end system and benchmark its efficiency. We can securely evaluate a sigmoid in $18$ ms online time and $0.5$ KB of online communication. Our system can train a model over a database with $70,000$ samples and $15$ features with online communication of $208.09$ MB and online time of $2.24$ hours at the cost of $6.11$c over WAN. Our benchmarks demonstrate that we reduce online communication over state of the art by $\approx 10 \times$ for sigmoid and $\approx38\times$ for logistic regression training.

In LWE-based KEMs, observed decryption errors leak information about the secret key in the form of equations or inequalities. Several practical fault attacks have already exploited such leakage by either directly applying a fault or enabling a chosen-ciphertext attack using a fault. When the leaked information is in the form of inequalities, the recovery of the secret key is not trivial. Recent methods use either statistical or algebraic methods (but not both), with some being able to handle incorrect information. We answer this question positively by proposing an error-tolerant combination of statistical and algebraic methods that make use of the advantages of both approaches. The combination enables us to improve upon existing methods -- we use both fewer inequalities and are more resistant to errors. We further provide precise security estimates based on the number of available inequalities. Our recovery method applies to several types of implementation attacks in which decryption errors are used in a chosen-ciphertext attack. We practically demonstrate the improved performance of our approach in a key-recovery attack against Kyber with fault-induced decryption errors.

A Password-Authenticated Key Exchange (PAKE) protocol allows two parties to agree upon a cryptographic key, when the only information shared in advance is a low-entropy password. The standard security notion for PAKE (Canetti et al., Eurocrypt 2005) is in the Universally Composable (UC) framework. We show that unlike most UC security notions, UC PAKE does not imply correctness. While Canetti et al. has briefly noticed this issue, we present the first comprehensive study of correctness in UC PAKE. Our contributions are four-fold: 1. We show that TrivialPAKE, a no-message protocol that does not satisfy correctness, is a UC PAKE; 2. We propose nine approaches to guaranteeing correctness in the UC security notion of PAKE, and show that seven of them are equivalent, whereas the other two are unachievable; 3. We prove that a direct solution, namely changing the UC PAKE functionality to incorporate correctness, is impossible; 4. Finally, we show how to naturally incorporate correctness by changing the model — we view PAKE as a three-party protocol, with the man-in-the-middle adversary as the third party. In this way, we hope to shed some light on the very nature of UC-security in the man-in-the-middle setting.

This note describes two pairing-friendly curves that embed ed25519, of different bit security levels. Our search is not novel; it follows the standard recipe of the Cocks-Pinch method. We implemented these two curves on arkworks-rs. This note is intended to document how the parameters are being generated and how to implement these curves in arkworks-rs 0.4.0, for further reference. We name the two curves as Yafa-108 and Yafa-146: - Yafa-108 is estimated to offer 108-bit security, which we parameterized to match the 103-bit security of BN254 - Yafa-146 is estimated to offer 146-bit security, which we parameterized to match the 132-bit security of BLS12-446 or 123-bit security of BLS12-381 We use these curves as an example to demonstrate two things: - The "elastic" zero-knowledge proof, Gemini (EUROCRYPT '22), is more than being elastic, but it is more curve-agnostic and hardware-friendly. - The cost of nonnative field arithmetics can be drastic, and the needs of application-specific curves may be inherent. This result serves as evidence of the necessity of EIP-1962, and the insufficiency of EIP-2537.

Non-interactive zero-knowledge proofs (NIZKs) and in particular succinct NIZK arguments of knowledge (so called zk-SNARKs) increasingly see real-world adoption in large and complex systems. A requirement that turns out to be important for NIZKs is ensuring non-malleability of proofs, which can be achieved via the property of simulation extractability (SE). Moreover, many zk-SNARKs require a trusted setup, i.e., a common reference string (CRS), and in practice it is desirable to reduce the trust in the CRS generation. Latter can be achieved via the notions of subversion or updatable CRS. Another important property when deployed in large and complex systems is the secure composition of protocols, e.g., via using the Universal Composability (UC) framework. Relying on the UC frameworks allows to arbitrarily and securely compose protocols in a modular way. In this work, we are interested in whether zk-SNARKs can provide all these desired properties. This is a tricky task as the UC framework rules out several natural techniques for such a construction. Our main result is to show that achieving these properties is indeed possible in a generic and modular way when slightly relaxing the succinctness properties of zk-SNARKs to those of a circuit-succinct NIZK which is not witness-succinct, i.e., by increasing the proof size of the underlying zk-SNARK by the size of the witness $w$. We will argue that for various practical applications of zk-SNARKs this overhead is perfectly tolerable. Our starting point is a framework by Abdolmaleki et al. called Lamassu (ACM CCS'20) which we extend in several directions. Moreover, we implement our compiler on top of Sonic (ACM CCS'19) and provide benchmarks as well as a discussion on the choice of the required primitives.

While the efficiency of secure multi-party computation protocols has greatly increased in the last few years, these improvements and protocols are often based on rather unrealistic, idealised, assumptions about how technology is deployed in the real world. In this work we examine multi-party computation protocols in the presence of two major constraints present in deployed systems. Firstly, we consider the situation where the parties are connected not by direct point-to-point connections, but by a star-like topology with a few central post-office style relays. Secondly, we consider MPC protocols with a strong honest majority ($n \gg t/2$) in which we have stragglers (some parties are progressing slower than others). We model stragglers by allowing the adversary to delay messages to and from some parties for a given length of time. We first show that having only a single honest rely is enough to ensure consensus of the messages sent within a protocol; secondly, we show that special care must be taken to describe multiplication protocols in the case of relays and stragglers and that some well known protocols do not guarantee privacy and correctness in this setting; thirdly, we present an efficient honest-majority MPC protocol which can be run on top of the relays and which provides active-security with abort in the case of a strong honest majority, even when run with stragglers. We back up our protocol presentation with both experimental evaluations and simulations of the effect of the relays and delays on our protocol.

The TLS (Transport Layer Security) protocol is the most important, most attacked, most analysed and most used cryptographic protocol in the world today. TLS is critical to the integrity of the Internet, and if it were to be broken e-commerce would become impossible, with very serious implications for the global economy. Furthermore TLS is likely to assume even greater significance in the near future with the rapid growth of an Internet of Things (IoT) -- a multiplicity of internet connected devices all engaged in secure inter-communication. However the impending invention of a Cryptographically Relevant Quantum Computer (CRQC) would represent an existential threat to TLS in its current form. As it stands the latest version TLS1.3, benefiting as it does from years of research and study, provides effective security, but it must soon be updated to resist this new threat. In this research we first undertake a new clean-room implementation of a small-footprint open source TLS1.3, written in C++ and Rust, and suitable for IoT applications. Our implementation is designed to be cryptographically agile, so that it can easily accomodate new post-quantum cryptographic primitives. Next we use this new implementation as a vehicle to study the impact of going post-quantum, with a particular emphasis on the impact on the Internet of Things. Finally we showcase the flexibility of our implementation by proposing an implementation of TLS that uses identity-based encryption to mitigate this impact.

Learning parity with noise (LPN) has been widely studied and used in cryptography. It was recently brought to new prosperity since Boyle et al. (CCS'18), putting LPN to a central role in designing secure multi-party computation, zero-knowledge proofs, private set intersection, and many other protocols. In this paper, we thoroughly studied the concrete security of LPN problems in these settings. We found that many conclusions from classical LPN cryptanalysis do not apply to this new setting due to the low noise rates, extremely high dimensions, various types (in addition to $\mathbb{F}_2$) and noise distributions. 1. For LPN over field $\mathbb{F}_q$, we give a parameterized reduction from an exact noise distribution to a regular one that not only generalizes the recent result by Feneuil, Joux and Rivain (Crypto'22), but also significantly reduces the security loss by paying only an additive price in dimension and number of samples. 2. We analyze the security of LPN over a ring $\mathbb{Z}_{2^\lambda}$. Although existing protocols based on LPN over integer rings use parameters as if they are over fields, we found an attack that effectively reduces the weight of a noise by half compared to LPN over fields. Consequently, prior works that use LPN over $\mathbb{Z}_{2^\lambda}$ overestimate up to 40 bits of security. 3. We provide a complete picture of the hardness of LPN over integer rings by showing: 1) the equivalence between its search and decisional versions; 2) an efficient reduction from LPN over $\mathbb{F}_2$ to LPN over $\mathbb{Z}_{2^\lambda}$; and 3) generalization of our results to any integer ring. 4. For LPN over finite fields, we found that prior analysis ignored some important differences between classical LPN cryptanalysis and the new setting, leading to overly conservative parameters. We show that even after bringing all classical LPN cryptanalysis, including the latest SD $2.0$ analysis (Asiacrypt'22), to the setting over finite fields, much less weight of noises is needed for the same level of security. To improve the use of LPN assumptions for a wide range of cryptographic protocols, we provide an open-sourced script that estimates the concrete security of LPN over integer rings and finite fields.

The usage of convolutional neural networks (CNNs) to break cryptographic systems through hardware side-channels has enabled fast and adaptable attacks on devices like smart cards and TPMs. Current literature proposes fixed CNN architectures designed by domain experts to break such systems, which is time-consuming and unsuitable for attacking a new system. Recently, an approach using neural architecture search (NAS), which is able to acquire a suitable architecture automatically, has been explored. These works use the secret key information in the attack dataset for optimization and only explore two different search strategies using one-dimensional CNNs. We propose a NAS approach that relies only on using the profiling dataset for optimization, making it fully black-box. Using a large-scale experimental parameter study, we explore which choices for NAS, such as 1-D or 2-D CNNs and search strategy, produce the best results on 10 state-of-the-art datasets for Hamming weight and identity leakage models. We show that applying the random search strategy on 1-D inputs results in a high success rate and retrieves the correct secret key using a single attack trace on two of the datasets. This combination matches the attack efficiency of fixed CNN architectures, outperforming them in 4 out of 10 datasets. Our experiments also point toward the need for repeated attack evaluations of machine learning-based solutions in order to avoid biased performance estimates.

The bottleneck in the proving algorithm of most of elliptic-curve-based SNARK proof systems is the Multi-Scalar-Multiplication (MSM) algorithm. In this paper we give an overview of a variant of the Pippenger MSM algorithm together with a set of optimizations tailored for curves that admit a twisted Edwards form. This is the case for SNARK-friendly chains and cycles of elliptic curves, which are useful for recursive constructions. Accelerating the MSM over these curves on mobile devices is critical for deployment of recursive proof systems on mobile applications. This work is implemented in Go and uses hand-written arm64 assembly for accelerating the finite field arithmetic (bigint). This work was implemented as part of a submission to the ZPrize competition in the open division “Accelerating MSM on Mobile” (https://www.zprize.io/). We achieved a 78% speedup over the ZPrize baseline implementation in Rust.

Evaluating exact computational resources necessary for factoring large integers by Shor algorithm using an ideal quantum computer is difficult because simplified circuits were used in past experiments, in which qubits and gates were reduced as much as possible by using the features of the integers, though 15 and 21 were factored on quantum computers. In this paper, we implement Shor algorithm for general composite numbers, and factored 96 RSA-type composite numbers up to 9-bit using a quantum computer simulator. In the largest case, $N=511$ was factored within 2 hours. Then, based on these experiments, we estimate the number of gates and the depth of Shor's quantum circuits for factoring 1024-bit and 2048-bit integers. In our estimation, Shor's quantum circuit for factoring 1024-bit integers requires $2.78 \times 10^{11}$ gates, and with depth $2.24 \times 10^{11}$, while $2.23 \times 10^{12}$ gates, and with depth $1.80 \times 10^{12}$ for 2048-bit integers.

We study satisfiability modulo the theory of finite fields and give a decision procedure for this theory. We implement our procedure for prime fields inside the cvc5 SMT solver. Using this theory, we construct SMT queries that verify the correctness of various zero knowledge proof compilers on various input programs. Our experiments show that our implementation is vastly superior to previous approaches (which encode field arithmetic using integers or bit-vectors).

Because of the rapid growth of Internet of Things (IoT), embedded systems have become an interesting target for experienced attackers. ESP32~\cite{tech-ref-man} is a low-cost and low-power system on chip (SoC) series created by Espressif Systems. The firmware extraction of such embedded systems is a real threat to the manufacturer as it breaks its intellectual property and raises the risk of creating equivalent systems with less effort and resources. In 2019, LimitedResults~\cite{LimitedResultsPown} published power glitch attacks which resulted in dumping secure boot and flash encryption keys stored in the eFuses of ESP32. Therefore, Espressif patched this vulnerability and then advised its customers to use ESP32-V3, which is an updated SoC revision. This new version is hardened against fault injection attacks in hardware and software as announced by Espressif~\cite{ESPpatch}. In this paper, we present for the first time a deep hardware security evaluation for ESP32-V3. The main goal of this evaluation is to extract the firmware encryption key stored in the eFuses. This evaluation includes Fault Injection (FI) and Side-Channel (SC) attacks. First, we use Electromagnetic FI (EMFI) in order to show that ESP32-V3 doesn't resist EMFI. However, by experimental results, we show that this version contains a revised bootloader compared to ESP32-V1, which hardens dumping the eFuse keys by FI. Second, we perform a full SC analysis on the AES accelerator of ESP32-V3. We show that an attacker with a physical access to the device can extract all the keys of the hardware AES-256 after collecting 60K power measurements during the execution of the AES block. Third, we present another SC analysis for the firmware decryption mechanism, by targeting the decryption operation during the power up. Using this knowledge, we demonstrate that the full 256-bit AES firmware encryption key, which is stored in the eFuses, can be recovered by SC analysis using 300K power measurements. Finally, we apply practically the firmware encryption attack on Jade hardware wallet \cite{jade}.

We initiate a formal study of individual cryptography Informally speaking, an algorithm Alg is individual if in every implementation of Alg there always exists an individual user that has full knowledge of the cryptographic secrets S used by Alg. In particular, it should be infeasible to design implementations of this algorithm that would hide the secret S by distributing it between a group of parties using an MPC protocol, or via outsourcing it to a trusted execution environment.

Cryptographic voting protocols have recently seen much interest from practitioners due to their (planned) use in countries such as Estonia, Switzerland, France, and Australia. Practical protocols usually rely on tested designs such as the mixing-and-decryption paradigm. There, multiple servers verifiably shuffle encrypted ballots, which are then decrypted in a distributed manner. While several efficient protocols implementing this paradigm exist from discrete log-type assumptions, the situation is less clear for post-quantum alternatives such as lattices. This is because the design ideas of the discrete log-based voting protocols do not carry over easily to the lattice setting, due to specific problems such as noise growth and approximate relations. In this work, we propose a new verifiable secret shuffle for BGV ciphertexts and a compatible verifiable distributed decryption protocol. The shuffle is based on an extension of a shuffle of commitments to known values which is combined with an amortized proof of correct re-randomization. The verifiable distributed decryption protocol uses noise drowning, proving the correctness of decryption steps in zero-knowledge. Both primitives are then used to instantiate the mixing-and-decryption electronic voting paradigm from lattice-based assumptions. We give concrete parameters for our system, estimate the size of each component and provide implementations of all important sub-protocols. Our experiments show that the shuffle and decryption protocol is suitable for use in real-world e-voting schemes.

This paper describes a formalization of the specification and the algorithm of the public key encryption scheme CRYSTALS-KYBER as well as the verification of its $\delta$-correctness and indistinguishability under chosen plaintext attack (IND-CPA) security proof. The algorithms and proofs were formalized with only minimal assumptions in a modular way to verify the proofs for all possible parameter sets. During the formalization in this flexible setting, problems in the correctness proof were uncovered. Furthermore, the security of CRYSTALS-KYBER under IND-CPA was verified using a game-based approach. As the security property does not hold for the original version of CRYSTALS-KYBER, we only show the IND-CPA security for the latest versions. The security proof was verified under the hardness assumption of the module Learning-with-Errors Problem. The formalization was realized in the theorem prover Isabelle and is foundational.

As the number of blockchain projects grows, efficient cross-chain interoperability becomes more necessary. A common cross-chain protocol is the two-way peg, which is typically used to transfer assets between blockchains and their sidechains. The criticality of cross-chain protocols require that they are designed with strong security models, which can reduce usability in the form of long transfer times. In this paper, we present Flyover, a repayment protocol to speed up the transfer of bitcoins over federated pegs by allowing untrusted liquidity providers to advance funds for the users. Transfer times are reduced because liquidity providers do not have the same security requirements as the underlying cross-chain protocol. We illustrate the Flyover protocol on the cross-chain interoperability protocol that connects Bitcoin to the RSK sidechain and show how Flyover can reduce transfer times without reducing security. In addition to this, Flyover extends the cross-chain protocol by allowing liquidity providers to make smart contract calls on RSK on behalf of the user.

The ChaCha20-Poly1305 AEAD scheme is being increasingly widely deployed in practice. Practitioners need proven security bounds in order to set data limits and rekeying intervals for the scheme. But the formal security analysis of ChaCha20-Poly1305 currently lags behind that of AES-GCM. The only extant analysis (Procter, 2014) contains a flaw and is only for the single-user setting. We rectify this situation. We prove a multi-user security bound on the AEAD security of ChaCha20-Poly1305 and establish the tightness of each term in our bound through matching attacks. We show how our bound differs both qualitatively and quantitatively from the known bounds for AES-GCM, highlighting how subtle design choices lead to distinctive security properties. We translate our bound to the nonce-randomized setting employed in TLS 1.3 and elsewhere, and we additionally improve the corresponding security bounds for GCM. Finally, we provide a simple yet stronger variant of ChaCha20-Poly1305 that addresses the deficiencies highlighted by our analysis.

We give a construction of a 2-round blind signature scheme based on the hardness of standard lattice problems (Ring/Module-SIS/LWE and NTRU) with a signature size of 22 KB. The protocol is round-optimal and has a transcript size that can be as small as 60 KB. This blind signature is around $4$ times shorter than the most compact lattice-based scheme based on standard assumptions of del Pino and Katsumata (Crypto 2022) and around $2$ times shorter than the scheme of Agrawal et al. (CCS 2022) based on their newly-proposed one-more-SIS assumption. We also give a construction of a ``keyed-verification'' blind signature scheme in which the verifier and the signer need to share a secret key. The signature size in this case is only $48$ bytes, but more work needs to be done to explore the efficiency of the protocol which generates the signature.

Ring signatures enable a user to sign messages on behalf of an arbitrary set of users, called the ring. The anonymity property guarantees that the signature does not reveal which member of the ring signed the message. The notion of linkable ring signatures (LRS) is an extension of the concept of ring signatures such that there is a public way of determining whether two signatures have been produced by the same signer. Lattice-based LRS is an important and active research line since lattice-based cryptography has attracted more attention due to its distinctive features, especially the quantum-resistant. However, all the existing lattice-based LRS relied on random oracle heuristics, i.e., no lattice-based LRS in the standard model has been introduced so far. In this paper, we present a lattice-based LRS scheme in the standard model. Toward our goal, we present a lattice basis extending algorithm which is the key ingredient in our construction, that may be of indepen- dent interest

Since the invention of Bitcoin, cryptocurrencies have gained huge popularity. Crypto wallet, as the tool to store and manage the cryptographic keys, is the primary entrance for the public to access cryptocurrency funds. Deterministic wallet is an advanced wallet mech- anism that has been proposed to achieve some appealing virtues, such as low-maintenance, easy backup and recovery, supporting functionali- ties required by cryptocurrencies, and so on. But deterministic wallets still have a long way to be practical in quantum world, and there are also some gaps in the classic world, since there are the following prob- lems waiting to be solved. Firstly, the relying on the state, i.e., stateful. The stateful deterministic wallet scheme must internally maintain and keep refreshing synchronously a state which makes the implementation in practice become more complex. And once one of the states is leaked, thereafter the security notion of unlinkability is cannot be guaranteed (referred to as the weak security notion of forward unlinkability). The second problem is vulnerable. There are security shortfalls in previous works, they suffer a vulnerability when a minor fault happens (say, one derived key is compromised somehow), then the damage is not limited to the leaked derived key, instead, it spreads to the master key and the whole system collapses. Thirdly, the falling short in supporting hot/cold setting. The hot/cold setting is a widely adopted method to effectively reduce the exposure chance of secret keys and hence improving the se- curity of the deterministic wallet system. The last problem is the relying on the weak security notion of unforgeability, in which the adversary is only allowed to query and forge the signatures w.r.t. the public keys that were assigned by the challenger. In this work, we present a new deterministic wallet scheme in quantum world, which is stateless, supports hot/cold setting, satisfiies stronger security notions, and is more efficient. In particular, we reformalize the syntax and security models for deterministic wallets, capturing the func- tionality and security requirements imposed by the practice in cryptocur- rency. Then we propose a deterministic wallet construction and prove its security in the quantum random oracle model. Finally, we show our wal- let scheme is more practicable by analyzing an instantiation of our wallet scheme based on the signature scheme Falcon.

The Secure-Boot is a critical security feature in modern devices based on System-on-Chips (SoC). It ensures the authenticity and integrity of the code before its execution, avoiding the SoC to run malicious code. To the best of our knowledge, this paper presents the first bypass of an Android Secure-Boot by using an Electromagnetic Fault Injection (EMFI). Two hardware characterization methods are combined to conduct this experiment. A real-time Side-Channel Analysis (SCA) is used to synchronize an EMFI during the Linux Kernel authentication step of the Android Secure-Boot of a smartphone-grade SoC. This new synchronization method is called Synchronization by Frequency Detection (SFD). It is based on the detection of the activation of a characteristic frequency in the target electromagnetic emanations. In this work we present a proof-of-concept of this new triggering method. By triggering the attack upon the activation of this characteristic frequency, we successfully bypassed this security feature, effectively running Android OS with a compromised Linux Kernel with one success every 15 minutes.

We propose a single-tiered hybrid Proof-of-Work consensus protocol to encourage decentralization in bitcoin. Our new mechanism comprises coupled puzzles of which properties differ from each other; the one is the extant outsourceable bitcoin puzzle while the other is non-outsourceable. Our new protocol enables miners to solve either puzzle as they want; therefore, blocks can be generated by either puzzle. Our hybrid consensus can be successfully implemented in bitcoin, because it is backward-compatible with existing bitcoin mining equipment(more precisely, existing bitcoin mining ASICs)

Oblivious RAM (ORAM), introduced by Goldreich and Ostrovsky (J. ACM '96), is a primitive that allows a client to perform RAM computations on an external database without revealing any information through the access pattern. For a database of size $N$, well-known lower bounds show that a multiplicative overhead of $\Omega(\log N)$ in the number of RAM queries is necessary assuming $O(1)$ client storage. A long sequence of works culminated in the asymptotically optimal construction of Asharov, Komargodski, Lin, and Shi (CRYPTO '21) with $O(\log N)$ worst-case overhead and $O(1)$ client storage. However, this optimal ORAM construction is known to be secure only in the honest-but-curious setting, where an adversary is allowed to observe the access patterns but not modify the contents of the database. In the malicious setting, where an adversary is additionally allowed to tamper with the database, this construction and many others in fact become insecure. In this work, we construct the first maliciously secure ORAM protocol with worst-case $O(\log N)$ overhead and $O(1)$ client storage assuming one-way functions, which are also necessary. By the $\Omega(\log N)$ ORAM lower bound, our construction is asymptotically optimal. We can also interpret our construction as an online memory checker that matches the bandwidth of the best known online memory checkers while additionally hiding the access pattern. To achieve this, we intricately interleave the ORAM construction of Asharov et al. with online and offline memory checking techniques.

Flow is a high-throughput blockchain with a dedicated step for executing the transactions in a block and a subsequent verification step performed by Verification Nodes. To enforce integrity of the blockchain, the protocol requires a component that prevents Verification Nodes from approving execution results without checking. In our preceding work, we have sketched out an approach called Specialized Proof of Confidential Knowledge (SPoCK). Using SPoCK, nodes can provide evidence to a third party that they both executed the same transaction sequence without revealing the resulting execution trace. The previous Flow white paper presented a basic implementation of such scheme. In this note, we introduce a new SPoCK implementation that is more concise and more efficient than the previous proposal. We first provide a formal generic description of a SPoCK scheme as well as its security definition. Then we propose a new construction of SPoCK based on the BLS signature scheme. We support the new scheme with its proof of security under the appropriate computation assumptions.

Encryption alone is not enough for secure end-to-end encrypted messaging: a server must also honestly serve public keys to users. Key transparency has been presented as an efficient solution for detecting (and hence deterring) a server that attempts to dishonestly serve keys. Key transparency involves two major components: (1) a username to public key mapping, stored and cryptographically committed to by the server, and, (2) an out-of-band consistency protocol for serving short commitments to users. In the setting of real-world deployments and supporting production scale, new challenges must be considered for both of these components. We enumerate these challenges and provide solutions to address them. In particular, we design and implement a memory-optimized and privacy-preserving verifiable data structure for committing to the username to public key store. To make this implementation viable for production, we also integrate support for persistent and distributed storage. We also propose a future-facing solution, termed ''compaction'', as a mechanism for mitigating practical issues that arise from dealing with infinitely growing server data structures. Finally, we implement a consensusless solution that achieves the minimum requirements for a service that consistently distributes commitments for a transparency application, providing a much more efficient protocol for distributing small and consistent commitments to users. This culminates in our production-grade implementation of a key transparency system (Parakeet) which we have open-sourced, along with a demonstration of feasibility through our benchmarks.

We propose a novel methodology to obtain $B$lind signatures that is fundamentally based on the idea of hiding part of the underlying plain signatures under a $Z$ero-knowledge argument of knowledge of the whole signature (hence the shorthand, $BZ$). Our proposal is necessarily non-black-box and stated in the random oracle model. We illustrate the technique by describing two instantiations: a classical setting based on the traditional discrete logarithm assumption, and a post-quantum setting based on the commutative supersingular isogeny Diffie-Hellman (CSIDH) assumption.

The private heavy-hitters problem is a data-collection task where many clients possess private bit strings, and data-collection servers aim to identify the most popular strings without learning anything about the clients' inputs. The recent work of Poplar constructed a protocol for private heavy hitters but their solution was susceptible to additive attacks by a malicious server, compromising both the correctness and the security of the protocol. In this paper, we introduce PLASMA, a private analytics framework that addresses these challenges by using three data-collection servers and a novel primitive, called verifiable incremental distributed point function (VIDPF). PLASMA allows each client to non-interactively send a message to the servers as its input and then go offline. Our new VIDPF primitive employs lightweight techniques based on efficient hashing and allows the servers to non-interactively validate client inputs and preemptively reject malformed ones. PLASMA drastically reduces the communication overhead incurred by the servers using our novel batched consistency checks. Specifically, our server-to-server communication depends only on the number of malicious clients, as opposed to the total number of clients, yielding a $182\times$ and $235\times$ improvement over Poplar and other state-of-the-art sorting-based protocols respectively. Compared to recent works, PLASMA enables both client input validation and succinct communication, while ensuring full security. At runtime, PLASMA computes the 1000 most popular strings among a set of 1 million client-held 32-bit strings in 67 seconds and 256-bit strings in less than 20 minutes respectively.

The increasing popularity of blockchain technology has affected the way we view many fields related to computer science, with E-commerce being no exception. The distributed nature and transparency of blockchain-based systems is one of its main perks, but it also raises some issues when it comes to privacy. Zero-knowledge proofs are very powerful building blocks when it comes to building privacy-preserving protocols, so, naturally, they have attracted a lot of attention in the last years. Following the recent collapse of the very popular crypto exchange FTX, we believe it is important to analyse how such events can be prevented in the future. This paper aims to highlight solutions that use zero-knowledge to prove solvency.

Blockchain is a newly emerging technology, however, it has proven effective in many applications because it provides multiple advantages, mainly as it represents a trust system in which data is encrypted in a way that cannot be tampered with or forged. Because it contains many details such as smart contracts, consensus, authentication, etc. the blockchain is a fertile ground for researchers where they can continually improve previous versions of these concepts. This paper introduces a new multi-signature scheme based on RSA. This scheme is designed to reduce the blockchain's size and prevent known attacks and is also applicable in many other settings that require multi-signatures. Our scheme is in the plain public key model, which means nodes do not need to prove knowledge or possession of their private key. In which, whatever the number of signers, the final signature size is equal to $O(k)$ where $k$ is a security parameter and no interaction between signers is needed. To verify that a number of parties have signed a shared message $m$, a verifier needs the signature, list of signers, and the message $m$. The presented practical short accountable-subgroup multi-signature (ASM) scheme allows a valid signature to disclose which subset generated the signature. It is worth noting that our multi-signatures with public key aggregation is an interactive two-round protocol and a multi-signature model applied to the entire block and not to individual transactions.

Threshold Fully Homomorphic Encryption (ThFHE) enables arbitrary computation over encrypted data while keeping the decryption key to be distributed across multiple parties at all time. ThFHE is a key enabler for threshold cryptography and, more generally, secure distributed computing. Existing ThFHE schemes inherently require highly inefficient parameters and are unsuitable for practical deployment. In this paper, we take the first step towards to make ThFHE practically usable by (i) proposing a novel ThFHE scheme with a new analysis resulting in significantly improved parameters; (ii) and providing the first ThFHE implementation benchmark based on Torus FHE. • We propose the first ThFHE scheme with a polynomial modulus-to-noise ratio that supports practically efficient parameters while retaining provable security based on standard quantum-safe assumptions. We achieve this via a novel Rényi divergence-based security analysis of our proposed threshold decryption mechanism. • We present a highly optimized software implementation of our proposed ThFHE scheme that builds upon the existing Torus FHE library and supports (distributed) decryption on highly resource-constrained ARM-based handheld devices. To the best of our knowledge, this is the first practically efficient implementation of any ThFHE scheme. Along the way, we implement several extensions to the Torus FHE library, including a Torus-based linear integer secret sharing subroutine to support ThFHE key sharing and distributed decryption for any threshold access structure. We illustrate the efficacy of our proposal via an end-to-end use case involving encrypted computations over a real medical database, and distributed decryptions of the computed result on resource-constrained handheld devices.

Fully Homomorphic Encryption (FHE) promises to secure our data on the untrusted cloud, while allowing arbitrary computations. Recent research has shown two side channel attacks on the client side running a popular HE library. However, no side channel attacks have yet been reported on the server side in existing literature. The current paper shows that it is possible for adversaries to inject perturbations in the ciphertexts stored in the cloud to result in decryption errors. Most importantly, we highlight that when the client reports of such aberrations to the cloud service provider the complete secret key can be extracted in few attempts. Technically, this implies a break of the IND-CVA (Indistinguishability against Ciphertext Verification Attacks) security of the FHE schemes. The core idea of the attack is to extract the underlying error values for each homomorphically computed ciphertext and thereby construct an exact system of equations. As the security of the underlying Learning with Errors (LWE) collapse with the leakage of the errors, the adversary is capable of ascertaining the secret keys. We demonstrate this attack on two well-known FHE libraries, namely FHEW and TFHE. The objective of the server is to perform the attack in a stealthy manner, without raising any suspicion from the innocent client. Therefore in a practical scenario, the successful key retrieval from a client would require the server to perform the attack with as few queries as possible. Thus we craftily use timing information during homomorphic gate computations to optimise our attack and significantly reduce the required number of queries per ciphertext. More precisely, we need 8 and 23 queries to the client for each error recovery for FHEW and TFHE, respectively. We mount a full-key recovery attack 1 on TFHE (without and with bootstrapping) with key size of 630 bits and successfully faulted 739 and 930 ciphertexts to recover correct errors. This required a total of 19838 and 29200 client queries respectively. In case of FHEW with key size 500, we successfully faulted 766 ciphertexts to recover correct errors, which required 7565 client queries. The results serve as a stark reminder that FHE schemes need to be secured at the application level apart from being secure at the primitive level so that the security of participants against realistic attacks can be ensured.

Payment channel networks (PCNs) mitigate the scalability issues of current decentralized cryptocurrencies. They allow for arbitrarily many payments between users connected through a path of intermediate payment channels, while requiring interacting with the blockchain only to open and close the channels. Unfortunately, PCNs are (i) tailored to payments, excluding more complex smart contract functionalities, such as the oracle-enabling Discreet Log Contracts and (ii) their need for active participation from intermediaries may make payments unreliable, slower, expensive, and privacy-invasive. Virtual channels are among the most promising techniques to mitigate these issues, allowing two endpoints of a path to create a direct channel over the intermediaries without any interaction with the blockchain. After such a virtual channel is constructed, (i) the endpoints can use this direct channel for applications other than payments and (ii) the intermediaries are no longer involved in updates. In this work, we first introduce the Domino attack, a new DoS/griefing style attack that leverages virtual channels to destruct the PCN itself and is inherent to the design adopted by the existing Bitcoin-compatible virtual channels. We then demonstrate its severity by a quantitative analysis on a snapshot of the Lightning Network (LN), the most widely deployed PCN at present. We finally discuss other serious drawbacks of existing virtual channel designs, such as the support for only a single intermediary, a latency and blockchain overhead linear in the path length, or a non-constant storage overhead per user. We then present Donner, the first virtual channel construction that overcomes the shortcomings above, by relying on a novel design paradigm. We formally define and prove security and privacy properties in the Universal Composability framework. Our evaluation shows that Donner is efficient, reduces the on-chain number of transactions for disputes from linear in the path length to a single one, which is the key to prevent Domino attacks, and reduces the storage overhead from logarithmic in the path length to constant. Donner is Bitcoin-compatible and can be easily integrated in the LN.

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

Being capable of updating cryptographic algorithms is an inevitable and essential practice in cryptographic engineering. This cryptographic agility, as it has been called, is a fundamental desideratum for long term cryptographic system security that still poses significant challenges from a modeling perspective. For instance, current formulations of agility fail to express the fundamental security that is expected to stem from timely implementation updates, namely the fact that the system retains some of its security properties provided that the update is performed prior to the deprecated implementation becoming exploited. In this work we put forth a novel framework for expressing updateability in the context of cryptographic primitives within the universal composition model. Our updatable ideal functionality framework provides a general template for expressing the security we expect from cryptographic agility capturing in a fine-grained manner all the properties that can be retained across implementation updates. We exemplify our framework over two basic cryptographic primitives, digital signatures and non-interactive zero-knowledge (NIZK), where we demonstrate how to achieve updateability with consistency and backwards-compatibility across updates in a composable manner. We also illustrate how our notion is a continuation of a much broader scope of the concept of agility introduced by Acar, Belenkiy, Bellare, and Cash in Eurocrypt 2010 in the context of symmetric cryptographic primitives.

In recent years there have been several attempts to build white-box block ciphers whose implementation aims to be incompressible. This includes the weak white-box ASASA construction by Bouillaguet, Biryukov and Khovratovich from Asiacrypt 2014, and the recent space-hard construction by Bogdanov and Isobe at CCS 2016. In this article we propose the first constructions aiming at the same goal while offering provable security guarantees. Moreover we propose concrete instantiations of our constructions, which prove to be quite efficient and competitive with prior work. Thus provable security comes with a surprisingly low overhead.

Masking has become one of the most effective approaches for securing hardware designs against side-channel attacks. Irrespective of the effort put into correctly implementing masking schemes on a field programmable gate array (FPGA), leakage can be unexpectedly observed. This is due to the fact that the assumption underlying all masked designs, i.e., the leakages of different shares are independent of each other, may no longer hold in practice. In this regard, extreme temperatures have been shown to be an important factor in inducing leakage, even in correctly-masked designs. This has previously been verified using an external heat generator (i.e., a climate chamber). In this paper, we examine whether the leakage can be induced using the circuit components themselves. Specifically, we target masked neural networks (NNs) in FPGAs, with one of the main building blocks being block random access memory (BRAM) and flip-flops (FFs). In this respect, thanks to the inherent characteristics of NNs, our novel internal heat generators leverage solely the memories devoted to storing the user’s input, especially when frequently writing alternating patterns into BRAMs and FFs. The possibility of observing first-order leakage is evaluated by considering one of the most recent and successful first-order secure masked NNs, namely ModuloNET. ModuloNET is specifically designed for FPGAs, where BRAMs are used for storing the inputs and intermediate computations. Our experimental results demonstrate that undesirable first-order leakage can be observed by increasing the temperature when an alternating input is applied to the masked NN. To give a better understanding of the impact of extreme heat, we further perform a similar test on the design with FFs storing the input, where the same conclusion can be drawn.

The threat of chip-level tampering and its detection is a widely researched field. Hardware Trojan insertions are prominent examples of such tamper events. Altering the placement and routing of a design or removing a part of a circuit for side-channel leakage/fault sensitivity amplification are other instances of such attacks. While semi- and fully-invasive physical verification methods can confidently detect such stealthy tamper events, they are costly, time-consuming, and destructive. On the other hand, virtually all proposed non-invasive side-channel methods suffer from noise and, therefore, have low confidence. Moreover, they require activating the tampered part of the circuit (e.g., the Trojan trigger) to compare and detect the modification. In this work, we introduce a general non-invasive post-silicon tamper detection technique applicable to all sorts of tamper events at the chip level without requiring the activation of the malicious circuit. Our method relies on the fact that all classes of physical modifications (regardless of their physical, activation, or action characteristics) alter the impedance of the chip. Hence, characterizing the impedance can lead to the detection of the tamper events. To sense the changes in the impedance, we deploy known RF tools, namely, scattering parameters, in which we inject sine wave signals with high frequencies to the power distribution network (PDN) of the system and measure the “echo” of the signal. The reflected signals in various frequency bands reveal different tamper events based on their impact size on the die. To validate our claims, we performed extensive measurements on several proof-of-concept tampered hardware implementations realized on an FPGA manufactured with a 28 nm technology. Based on these groundbreaking results, we demonstrate that stealthy hardware Trojans, as well as sophisticated modifications of P&R, can be detected with high confidence.

We consider multi-party information-theoretic private computation. Such computation inherently requires the use of local randomness by the parties, and the question of minimizing the total number of random bits used for given private computations has received considerable attention in the literature. In this work we are interested in another question: given a private computation, we ask how many of the players need to have access to a random source, and how many of them can be deterministic parties. We are further interested in the possible interplay between the number of random sources in the system and the total number of random bits necessary for the computation. We give a number of results. We first show that, perhaps surprisingly, $t$ players (rather than $t+1$) with access to a random source are sufficient for the information-theoretic $t$-private computation of any deterministic functionality over $n$ players for any $t<n/2$; by a result of (Kushilevitz and Mansour, PODC'96), this is best possible. This means that, counter intuitively, while private computation is impossible without randomness, it is possible to have a private computation even when the adversary can control all parties who can toss coins (and therefore sees all random coins). For randomized functionalities we show that $t+1$ random sources are necessary (and sufficient). We then turn to the question of the possible interplay between the number of random sources and the necessary number of random bits. Since for only very few settings in private computation meaningful bounds on the number of necessary random bits are known, we consider the AND function, for which some such bounds are known. We give a new protocol to $1$-privately compute the $n$-player AND function, which uses a single random source and $6$ random bits tossed by that source. This improves, upon the currently best known results (Kushilevitz et al., TCC'19), at the same time the number of sources and the number of random bits (KOPRT19 gives a $2$-source, $8$-bits protocol). This result gives maybe some evidence that for $1$-privacy, using the minimum necessary number of sources one can also achieve the necessary minimum number of random bits. We believe however that our protocol is of independent interest for the study of randomness in private computation.

This Paper proposes FssNN, a communication-efficient secure two-party computation framework for evaluating privacy-preserving neural network via function secret sharing (FSS) in semi-honest adversary setting. In FssNN, two parties with input data in secret sharing form perform secure linear computations using additive secret haring and non-linear computations using FSS, and obtain secret shares of model parameters without disclosing their input data. To decrease communication cost, we split the protocol into online and offline phases where input-independent correlated randomness is generated in offline phase while only lightweight ``non-cryptographic'' computations are executed in online phase. Specifically, we propose $\mathsf{BitXA}$ to reduce online communication in linear computation, DCF to reduce key size of the FSS scheme used in offline phase for nonlinear computation. To further support neural network training, we enlarge the input size of neural network to $2^{32}$ via ``MPC-friendly'' PRG. We implement the framework in Python and evaluate the end-to-end system for private training between two parties on standard neural networks. FssNN achieves on MNIST dataset an accuracy of 98.0%, with communication cost of 27.52GB and runtime of 0.23h per epoch in the LAN settings. That shows our work advances the state-of-the-art secure computation protocol for neural networks.

We put forth a new cryptographic primitive for securely computing inner-products in a scalable, non-interactive fashion: any party can broadcast a public (computationally hiding) encoding of its input, and store a secret state. Given their secret state and the other party's public encoding, any pair of parties can non-interactively compute additive shares of the inner-product between the encoded vectors. We give constructions of this primitive from a common template, which can be instantiated under either the LPN (with non-negligible correctness error) or the LWE (with negligible correctness error) assumptions. Our construction uses a novel twist on the standard non-interactive key exchange based on the Alekhnovich cryptosystem, which upgrades it to a non-interactive inner product protocol almost for free. In addition to being non-interactive, our constructions have linear communication (with constants smaller than all known alternatives) and small computation: using LPN or LWE with quasi-cyclic codes, we estimate that encoding a length-$2^{20}$ vector over a 32-bit field takes less that 2s on a standard laptop; decoding amounts to a single cheap inner-product. We show how to remove the non-negligible error in our LPN instantiation using a one-time, logarithmic-communication preprocessing. Eventually, we show to to upgrade its security to the malicious model using new sublinear-communication zero-knowledge proofs for low-noise LPN samples, which might be of independent interest.

In any real-life setting, side-channel secure implementations of public-key cryptography must be able to load and store their secret keys in a side-channel secure way. We describe WrapQ, a masking-friendly key management technique and compact encoding format for Kyber and Dilithium Critical Security Parameters (CSPs). WrapQ protects secret key integrity and confidentiality with a Key-Encrypting Key (KEK) and allows the keys to be stored on an untrusted medium. Importantly, its encryption and decryption processes avoid temporarily collapsing the masked asymmetric secret keys (which are plaintext payloads from the viewpoint of the wrapping primitive) into an unmasked format. We demonstrate that a masked Kyber or Dilithium private key can be loaded in a leakage-free fashion from a compact WrapQ format without updating the encoding in non-volatile memory. WrapQ has been implemented in a side-channel secure hardware module. Kyber and Dilithium wrapping and unwrapping functions were validated with 100K traces of TVLA-type leakage assessment.

This paper aims to provide a security analysis comparison between three popular instant messaging apps: Signal, WhatsApp and Telegram. The analysis will focus on the encryption protocols used by each app and the security features they offer. The paper will evaluate the strengths and weaknesses of each app, and provide a summary of their overall security posture. Additionally, this paper will discuss other considerations such as user base, data collection and usage policies, and other features which may impact the security of the apps. The results of this analysis will provide insights for individuals and organizations looking to choose a secure instant messaging app for their communication needs. In this paper we reviewed the main encryption standards and we compared the features, traffic analysis, protocols, performance and recent security breaches for WhatsApp, Signal and Telegram. The paper includes packet sniffing using Wireshark and Fiddler.

The purpose of this article is to present,illustrate and to put in evidence a new side- channel attack on RSA cryptosystem based on the generation of prime numbers. The vulnerability of the cryptosystem is spotted during the execution of the key generation step.The probability of success of the attack is around 10-15% in the case of realistic parameters

Public-key quantum money is a cryptographic proposal for using highly entangled quantum states as currency that is publicly verifiable yet resistant to counterfeiting due to the laws of physics. Despite significant interest, constructing provably-secure public-key quantum money schemes based on standard cryptographic assumptions has remained an elusive goal. Even proposing plausibly-secure candidate schemes has been a challenge. These difficulties call for a deeper and systematic study of the structure of public-key quantum money schemes and the assumptions they can be based on. Motivated by this, we present the first black-box separation of quantum money and cryptographic primitives. Specifically, we show that collision-resistant hash functions cannot be used as a black-box to construct public-key quantum money schemes where the banknote verification makes classical queries to the hash function. Our result involves a novel combination of state synthesis techniques from quantum complexity theory and simulation techniques, including Zhandry's compressed oracle technique.

The use of data as a product and service has given momentum to the extensive uptake of complex machine learning algorithms that focus on performing prediction with popular tree-based methods such as decision trees classifiers. With increasing adoption over a wide array of sensitive applications, a significant need to protect the confidentiality of the classifier model and user data is identified. The existing literature safeguards them using interactive solutions based on expensive cryptographic approaches, where an encrypted classifier model interacts with the encrypted queries and forwards the encrypted classification to the user. Adding to that, the state-of-art protocols for protecting the privacy of the model do not contain model-extraction attacks. We design an efficient virtual black-box obfuscator for binary decision trees and use the random oracle paradigm to analyze the security of our construction. To thwart model-extraction attacks, we restrict to evasive decision trees, as black-box access to the classifier does not allow a PPT adversary to extract the model. While doing so, we present an encoder for hiding parameters in an interval-membership function. Our exclusive goal behind designing the obfuscator is that, not only will the solution increase the class of functions that has cryptographically secure obfuscators, but also address the open problem of non-interactive prediction in privacy-preserving classification using computationally inexpensive cryptographic hash functions.

We present mining-based techniques to reduce the size of various cryptographic outputs without loss of security. Our approach can be generalized for multiple primitives, such as cryptographic key generation, signing, hashing and encryption schemes, by introducing a brute-forcing step to provers/senders aiming at compressing submitted cryptographic material. Interestingly, mining can result in record-size cryptographic outputs, and we show that 5%-12% shorter hash digests and signatures are practically feasible even with commodity hardware. As a result, our techniques make compressing addresses and transaction signatures possible in order to pay less fees in blockchain applications while decreasing the demand for blockchain space, a major bottleneck for initial syncing, communication and storage. Also, the effects of "compressing once - then reuse'' at mass scale can be economically profitable in the long run for both the Web2 and Web3 ecosystems. Our paradigm relies on a brute-force search operation in order to craft the primitive's output such that it fits into fewer bytes, while the "missing" fixed bytes are implied by the system parameters and omitted from the actual communication. While such compression requires computational effort depending on the level of compression, this cost is only paid at the source (i.e. in blockchains, senders are rewarded by lowered transaction fees), and the benefits of the compression are enjoyed by the whole ecosystem. As a starting point, we show how our paradigm applies to some basic primitives commonly used in blockchain applications but also traditional Web2 transactions (such as shorter digital certificates), and show how security is preserved using a bit security framework. Surprisingly, we also identified cases where wise mining strategies require proportionally less effort than naive brute-forcing, shorter hash-based signatures being one of the best examples. We also evaluate our approach for several primitives based on different levels of compression. Our evaluation concretely demonstrates the benefits both in terms of financial cost and storage if adopted by the community, and we showcase how our technique can achieve up to 83.21% reduction in smart contract gas fees at a cost of less than 4 seconds of computation on a single core.

There is a line of 'lookup' protocols to show that all elements of a sequence $f\in{\mathbb F}^n$ are contained in a table $t\in{\mathbb F}^d$, for some field ${\mathbb F}$. Lookup has become an important primitive in Zero Knowledge Virtual Machines, and is used for range checks and other parts of the proofs of a correct program execution. In this note we give several variants of the protocol. We adapt it to the situation when there are multiple lookups with the same table (as is usually the case with range checks), and handle also 'bounded lookup' that caps the number of repetitions.

Fully Homomorphic Encryption enables arbitrary computations over encrypted data and it has a multitude of applications, e.g., secure cloud computing in healthcare or finance. Multi-Key Homomorphic Encryption (MKHE) further allows to process encrypted data from multiple sources: the data can be encrypted with keys owned by different parties. In this paper, we propose a new variant of MKHE instantiated with the TFHE scheme. Compared to previous attempts by Chen et al. and by Kwak et al., our scheme achieves computation runtime that is linear in the number of involved parties and it outperforms the faster scheme by a factor of 4.5-6.9x, at the cost of a slightly extended pre-computation. In addition, for our scheme, we propose and practically evaluate parameters for up to 128 parties, which enjoy the same estimated security as parameters suggested for the previous schemes (100 bits). It is also worth noting that our scheme—unlike the previous schemes—did not experience any error in any of our nine experiments, each running 1 000 trials.

We present several new heuristic algorithms to compute class polynomials and modular polynomials modulo a prime $P$. For that, we revisit the idea of working with supersingular elliptic curves. The best known algorithms to this date are based on ordinary curves, due to the supposed inefficiency of the supersingular case. While this was true a decade ago, the recent advances in the study of supersingular curves through the Deuring correspondence motivated by isogeny-based cryptography has provided all the tools to perform the necessary tasks efficiently. Our main ingredients are two new heuristic algorithms to compute the $j$-invariants of supersingular curves having an endomorphism ring contained in some set of isomorphism class of maximal orders. The first one is derived easily from the existing tools of isogeny-based cryptography, while the second introduces new ideas to perform that task efficiently for a big number of maximal orders. From there, we obtain two main results. First, we show that we can associate these two algorithms with some operations over the quaternion algebra ramified at $P$ and infinity to compute directly Hilbert and modular polynomials $\mod P$. In that manner, we obtain the first algorithms to compute Hilbert (resp. modular) polynomials modulo $P$ for a good portion of all (resp. all) primes $P$ with a complexity in $O(\sqrt{|D|})$ for the discriminant $D$ (resp. $O(\ell^2)$ for the level $\ell$). Due to the (hidden) complexity dependency on $P$, these algorithms do not outperform the best known algorithms for all prime $P$ but they still provide an asymptotic improvement for a range of prime going up to a bound that is sub-exponential in $|D|$ (resp. $\ell$). Second, we revisit the CRT method for both class and modular polynomials. We show that applying our second heuristic algorithm over supersingular curves to the CRT approach yields the same asymptotic complexity as the best known algorithms based on ordinary curves and we argue that our new approach might be more efficient in practice. The situation appears especially promising for modular polynomials, as our approach reduces the asymptotic cost of elliptic curve operations by a linear factor in the level $\ell$. We obtain an algorithm whose asymptotic complexity is now fully dominated by linear algebra and standard polynomial arithmetic over finite fields.

We introduce a new notion of {\em multiverse threshold signatures} (MTS). In an MTS scheme, multiple universes -- each defined by a set of (possibly overlapping) signers, their weights, and a specific security threshold -- can co-exist. A universe can be (adaptively) created via a non-interactive asynchronous setup. Crucially, each party in the multiverse holds constant-sized keys and releases compact signatures with size and computation time both independent of the number of universes. Given sufficient partial signatures over a message from the members of a specific universe, an aggregator can produce a short aggregate signature relative to that universe. We construct an MTS scheme building on BLS signatures. Our scheme is practical, and can be used to reduce bandwidth complexity and computational costs in decentralized oracle networks. As an example data point, consider a multiverse containing 2000 nodes and 100 universes (parameters inspired by Chainlink's use in the wild) each of which contains arbitrarily large subsets of nodes and arbitrary thresholds. Each node computes and outputs 1 group element as its partial signature; the aggregator performs under 0.7 seconds of work for each aggregate signature, and the final signature of size 192 bytes takes 6.4 ms (or 198K EVM gas units) to verify. For this setting, prior approaches when used to construct MTS, yield schemes that have one of the following drawbacks: (i) partial signatures that are 97$\times$ larger, (ii) have aggregation times 311$\times$ worse, or (iii) have signature size 39$\times$ and verification gas costs 3.38$\times$ larger. We also provide an open-source implementation and a detailed evaluation.

Multi-signature is a protocol where a set of signatures jointly sign a message so that the final signature is significantly shorter than concatenating individual signatures together. Recently, it finds applications in blockchain, where several users want to jointly authorize a payment through a multi-signature. However, in this setting, there is no centralized authority and it could suffer from a rogue key attack where the attacker can generate his own keys arbitrarily. Further, to minimize the storage on blockchain, it is desired that the aggregated public-key and the aggregated signature are both as short as possible. In this paper, we find a compiler that converts a kind of identification (ID) scheme (which we call a linear ID) to a multi-signature so that both the aggregated public-key and the aggregated signature have a size independent of the number of signers. Our compiler is provably secure. The advantage of our results is that we reduce a multi-party problem to a weakly secure two-party problem. We realize our compiler with two ID schemes. The first is Schnorr ID. The second is a new lattice-based ID scheme, which via our compiler gives the first regular lattice-based multi-signature scheme with key-and-signature compact without a restart during signing process.

This paper presents a new method for quantum identity authentication (QIA) protocols. The logic of classical zero-knowledge proofs (ZKPs) due to Schnorr is applied in quantum circuits and algorithms. This novel approach gives an exact way with which a prover $P$ can prove they know some secret by encapsulating it in a quantum state before sending to a verifier $V$ by means of a quantum channel - allowing for a ZKP wherein an eavesdropper or manipulation can be detected with a fail-safe design. This paper presents a method with which this can be achieved. With the anticipated advent of a 'quantum internet', such protocols and ideas may soon have utility and execution in the real world.

We consider the following strong variant of private information retrieval (PIR). There is a large database x that we want to make publicly available. To this end, we post an encoding X of x together with a short public key pk in a publicly accessible repository. The goal is to allow any client who comes along to retrieve a chosen bit x_i by reading a small number of bits from X, whose positions may be randomly chosen based on i and pk, such that even an adversary who can fully observe the access to X does not learn information about i. Towards solving the above problem, we study a weaker secret key variant where the data is encoded and accessed by the same party. This primitive, that we call an oblivious locally decodable code (OLDC), is independently motivated by applications such as searchable sym- metric encryption. We reduce the public-key variant of PIR to OLDC using an ideal form of obfuscation that can be instantiated heuristically with existing indistinguishability obfuscation candidates, or alternatively implemented with small and stateless tamper-proof hardware. Finally, a central contribution of our work is the first proposal of an OLDC candidate. Our candidate is based on a secretly permuted Reed-Muller code. We analyze the security of this candidate against several natural attacks and leave its further study to future work.

Multiparty randomized encodings (Applebaum, Brakerski, and Tsabary, SICOMP 2021) reduce the task of securely computing a complicated multiparty functionality $f$ to the task of securely computing a simpler functionality $g$. The reduction is non-interactive and preserves information-theoretic security against a passive (semi-honest) adversary, also referred to as privacy. The special case of a degree-2 encoding $g$ (2MPRE) has recently found several applications to secure multiparty computation (MPC) with either information-theoretic security or making black-box access to cryptographic primitives. Unfortunately, as all known constructions are based on information-theoretic MPC protocols in the plain model, they can only be private with an honest majority. In this paper, we break the honest-majority barrier and present the first construction of general 2MPRE that remains secure in the presence of a dishonest majority. Our construction encodes every $n$-party functionality $f$ by a 2MPRE that tolerates at most $t=\lfloor 2n/3\rfloor$ passive corruptions. We derive several applications including: (1) The first non-interactive client-server MPC protocol with perfect privacy against any coalition of a minority of the servers and up to $t$ of the $n$ clients; (2) Completeness of 3-party functionalities under non-interactive $t$-private reductions; and (3) A single-round $t$-private reduction from general-MPC to an ideal oblivious transfer (OT). These positive results partially resolve open questions that were posed in several previous works. We also show that $t$-private 2MPREs are necessary for solving (2) and (3), thus establishing new equivalence theorems between these three notions. Finally, we present a new approach for constructing fully-private 2MPREs based on multi-round protocols in the OT-hybrid model that achieve \emph{perfect privacy} against active attacks. Moreover, by slightly restricting the power of the active adversary, we derive an equivalence between these notions. This forms a surprising, and quite unique, connection between a non-interactive passively-private primitive to an interactive actively-private primitive.

Robust (fuzzy) extractors are very useful for, e.g., authenticated exchange from shared weak secret and remote biometric authentication against active adversaries. They enable two parties to extract the same uniform randomness with the ``helper'' string. More importantly, they have an authentication mechanism built in that tampering of the ``helper'' string will be detected. Unfortunately, as shown by Dodis and Wichs, in the information-theoretic setting, a robust extractor for an $(n,k)$-source requires $k>n/2$, which is in sharp contrast with randomness extractors which only require $k=\omega(\log n)$. Existing work either relies on random oracles or introduces CRS and works only for CRS-independent sources (even in the computational setting). In this work, we give a systematic study of robust (fuzzy) extractors for general CRS-dependent sources. We show in the information-theoretic setting, the same entropy lower bound holds even in the CRS model; we then show we can have robust extractors in the computational setting for general CRS-dependent source that is only with minimal entropy. At the heart of our construction lies a new primitive called $\kappa$-MAC that is unforgeable with a weak key and hides all partial information about the key (both against auxiliary input), by which we can compile any conventional randomness extractor into a robust one. We further augment $\kappa$-MAC to defend against ``key manipulation" attacks, which yields a robust fuzzy extractor for CRS-dependent sources.

Many applications in finance and healthcare need access to data from multiple organizations. While these organizations can benefit from computing on their joint datasets, they often cannot share data with each other due to regulatory constraints and business competition. One way mutually distrusting parties can collaborate without sharing their data in the clear is to use secure multiparty computation (MPC). However, MPC’s performance presents a serious obstacle for adoption as it is difficult for users who lack expertise in advanced cryptography to optimize. In this paper, we present Silph, a framework that can automatically compile a program written in a high-level language to an optimized, hybrid MPC protocol that mixes multiple MPC primitives securely and efficiently. Compared to prior works, our compilation speed is improved by up to 30000×. On various database analytics and machine learning workloads, the MPC protocols generated by Silph match or outperform prior work by up to 3.6×.

Two multivariate digital signature schemes, Rainbow and GeMSS, made it into the third round of the NIST PQC competition. However, either made its way to being a standard due to devastating attacks (in one case by Beullens, the other by Tao, Petzoldt, and Ding). How should multivariate cryptography recover from this blow? We propose that, rather than trying to fix Rainbow and HFEv- by introducing countermeasures, the better approach is to return to the classical Oil and Vinegar scheme. We show that, if parametrized appropriately, Oil and Vinegar still provides competitive performance compared to the new NIST standards by most measures (except for key size). At NIST security level 1, this results in either 128-byte signatures with 44 kB public keys or 96-byte signatures with 67 kB public keys. We revamp the state-of-the-art of Oil and Vinegar implementations for the Intel/AMD AVX2, the Arm Cortex-M4 microprocessor, the Xilinx Artix-7 FPGA, and the Armv8-A microarchitecture with the Neon vector instructions set.

We consider a scenario where two mutually distrustful parties, Alice and Bob, want to perform a payment conditioned on the outcome of some real-world event. A semi-trusted oracle (or a threshold number of oracles, in a distributed trust setting) is entrusted to attest that such an outcome indeed occurred, and only then the payment is successfully made. Such oracle-based conditional (ObC) payments are ubiquitous in many real-world applications, like financial adjudication, pre-scheduled payments or trading, and are a necessary building block to introduce information about real-world events into blockchains. In this work we show how to realize ObC payments with provable security guarantees and efficient instantiations. To do this, we propose a new cryptographic primitive that we call verifiable witness encryption based on threshold signatures (VweTS): Users can encrypt signatures on payments that can be decrypted if a threshold number of signers (e.g., oracles) sign another message (e.g., the description of an event outcome). We require two security notions: (1) one-wayness that guarantees that without the threshold number of signatures, the ciphertext hides the encrypted signature, and (2) verifiability, that guarantees that a ciphertext that correctly verifies can be successfully decrypted to reveal the underlying signature. We present provably secure and efficient instantiations of VweTS where the encrypted signature can be some of the widely used schemes like Schnorr, ECDSA or BLS signatures. Our main technical innovation is a new batching technique for cut-and-choose, inspired by the work of Lindell-Riva on garbled circuits. Our VweTS instantiations can be readily used to realize ObC payments on virtually all cryptocurrencies of today in a fungible, cost-efficient, and scalable manner. The resulting ObC payments are the first to support distributed trust (i.e., multiple oracles) without requiring any form of synchrony or coordination among the users and the oracles. To demonstrate the practicality of our scheme, we present a prototype implementation and our benchmarks in commodity hardware show that the computation overhead is less than 25 seconds even for a threshold of 4-of-7 and a payment conditioned on 1024 different real-world event outcomes, while the communication overhead is below 2.3 MB

We present SCALLOP: SCALable isogeny action based on Oriented supersingular curves with Prime conductor, a new group action based on isogenies of supersingular curves. Similarly to CSIDH and OSIDH, we use the group action of an imaginary quadratic order’s class group on the set of oriented supersingular curves. Compared to CSIDH, the main benefit of our construction is that it is easy to compute the class-group structure; this data is required to uniquely represent— and efficiently act by— arbitrary group elements, which is a requirement in, e.g., the CSI-FiSh signature scheme by Beullens, Kleinjung and Vercauteren. The index-calculus algorithm used in CSI-FiSh to compute the class-group structure has complexity L(1/2), ruling out class groups much larger than CSIDH-512, a limitation that is particularly problematic in light of the ongoing debate regarding the quantum security of cryptographic group actions. Hoping to solve this issue, we consider the class group of a quadratic order of large prime conductor inside an imaginary quadratic field of small discriminant. This family of quadratic orders lets us easily determine the size of the class group, and, by carefully choosing the conductor, even exercise significant control on it— in particular supporting highly smooth choices. Although evaluating the resulting group action still has subexponential asymptotic complexity, a careful choice of parameters leads to a practical speedup that we demonstrate in practice for a security level equivalent to CSIDH-1024, a parameter currently firmly out of reach of index-calculus-based methods. However, our implementation takes 35 seconds (resp. 12.5 minutes) for a single group-action evaluation at a CSIDH-512-equivalent (resp. CSIDH-1024-equivalent) security level, showing that, while feasible, the SCALLOP group action does not achieve realistically usable performance yet.

Critical and widely used cryptographic protocols have repeatedly been found to contain flaws in their design and their implementation. A prominent class of such vulnerabilities is logical attacks, i.e. attacks that solely exploit flawed protocol logic. Automated formal verification methods, based on the Dolev-Yao (DY) attacker, excel at finding such flaws, but operate only on abstract specification models. Fully automated verification of existing protocol implementations is today still out of reach. This leaves open whether widely used protocol implementations are secure. Unfortunately, this blind spot hides numerous attacks, notably recent logical attacks on widely used TLS implementations introduced by implementation bugs. We answer by proposing a novel and effective technique that we call DY model-guided fuzzing, which precludes logical attacks against protocol implementations. The main idea is to consider as possible test cases the set of abstract DY executions of the DY attacker, and use a mutation-based fuzzer to explore this set. The DY fuzzer concretizes each abstract execution to test it on the program under test. This approach enables reasoning at a more structural and security-related level of messages (e.g. decrypt a message and re-encrypt it with a different key) as opposed to random bit-level modifications that are much less likely to produce relevant logical adversarial behaviors. We implement a full-fledged and modular DY protocol fuzzer. We demonstrate its effectiveness by fuzzing three popular TLS implementations, resulting in the discovery of four novel vulnerabilities.

Bilinear pairings have been used in different cryptographic applications and demonstrated to be a key building block for a plethora of constructions. In particular, some Succinct Non-interactive ARguments of Knowledge (SNARKs) have very short proofs and very fast verifi- cation thanks to a multi-pairing computation. This succinctness makes pairing-based SNARKs suitable for proof recursion, that is proofs veri- fying other proofs. In this scenario one requires to express efficiently a multi-pairing computation as a SNARK arithmetic circuit. Other com- pelling applications such as verifying Boneh–Lynn–Shacham (BLS) sig- natures or Kate–Zaverucha–Goldberg (KZG) polynomial commitment opening in a SNARK fall into the same requirement. The implementation of pairings is challenging but the literature has very detailed approaches on how to reach practical and optimized implementations in different contexts and for different target environments. However, to the best of our knowledge, no previous publication has addressed the question of ef- ficiently implementing a pairing as a SNARK arithmetic circuit. In this work, we consider efficiently implementing pairings in Rank-1 Constraint Systems (R1CS), a widely used model to express SNARK statements. We implement our techniques in the gnark open-source ecosystem and show that the arithmetic circuit depth can be almost halved compared to the previously best known pairing implementation on a Barreto–Lynn–Scott (BLS) curve of embedding degree 12, resulting in a significantly faster proving time. We also investigate and implement the case of BLS curves of embedding degree 24.

A hash-and-sign signature based on preimage-sampleable function (PSF) (Gentry et al. [STOC 2008]) is secure in the Quantum Random Oracle Model (QROM) if the PSF is collision-resistant (Boneh et al. [ASIACRYPT 2011]) or one-way (Zhandry [CRYPTO 2012]). However, trapdoor functions (TDFs) in code-based and multivariate-quadratic-based (MQ-based) signatures are not PSFs; for example, underlying TDFs of the Courtois-Finiasz-Sendrier (CFS), Unbalanced Oil and Vinegar (UOV), and Hidden Field Equations (HFE) signatures are not surjection. Thus, such signature schemes adopt probabilistic hash-and-sign with retry. This paradigm is secure in the (classical) Random Oracle Model (ROM), assuming that the underlying TDF is non-invertible; that is, it is hard to find a preimage of a given random value in the range (e.g., Sakumoto et al. [PQCRYPTO 2011] for the modified UOV/HFE signatures). Unfortunately, there is no known security proof for the probabilistic hash-and-sign with retry in the QROM. We give the first security proof for the probabilistic hash-and-sign with retry in the QROM, assuming that the underlying non-PSF TDF is non-invertible. Our reduction from the non-invertibility is tighter than the existing ones that apply to only signature schemes based on PSFs. We apply the security proof to code-based and MQ-based signatures. Moreover, we extend the proof into the multi-key setting by using prefix hashing (Duman et al. [ACM CCS 2021]).

In recent works of Li the noisy subset product problem (also known as subset product with errors) was invented and applied to cryptography. To better understand its hardness, we give a quantum annealing algorithm for it. Our algorithm is the first algorithm for the problem. We also give the first quantum annealing algorithm for the subset product problem. The efficiencies of both algorithms rely on the fundamental efficiency of quantum annealing. At the end we give two lattice algorithms for both problems via solving the closest vector problem. The complexities of the lattice algorithms depend on the complexities of solving the closest vector problem in two special lattices. They are efficient when the special closest vector problems fall into the regime of bounded distance decoding problems that can be efficiently solved using existing methods based on the LLL algorithm or Babai's nearest plane algorithm.

The celebrated PCP Theorem states that any language in NP can be decided via a verifier that reads $O(1)$ bits from a polynomially long proof. Interactive oracle proofs (IOP), a generalization of PCPs, allow the verifier to interact with the prover for multiple rounds while reading a small number of bits from each prover message. While PCPs are relatively well understood, the power captured by IOPs (beyond NP) has yet to be fully explored. We present a generalization of the PCP theorem for interactive languages. We show that any language decidable by a $k(n)$-round IP has a $k(n)$-round public-coin IOP, where the verifier makes its decision by reading only $O(1)$ bits from each (polynomially long) prover message and $O(1)$ bits from each of its own (random) messages to the prover. Our result and the underlying techniques have several applications. We get a new hardness of approximation result for a stochastic satisfiability problem, we show IOP-to-IOP transformations that previously were known to hold only for IPs, and we formulate a new notion of PCPs (index-decodable PCPs) that enables us to obtain a commit-and-prove SNARK in the random oracle model for nondeterministic computations.

Voting mechanisms allow the expression of the elections by a democratic approach. Any voting scheme must ensure, preferably in an efficient way, a series of safety measures such as confidentiality, integrity and anonymity. Since the 1980s, the concept of electronic voting became more and more of interest, being an advantageous or even necessary alternative for the organization of secure elections. In this paper, we give an overview for the e-voting mechanisms together with the security features they must fulfill. Then we focus on the blind signature paradigm, specifically on the Pairing Free Identity-Based Blind Signature Scheme with Message Recovery (PF-IDBS-MR). Our goal is to give a better understanding on the PF-IDBS-MR scheme by offering an adaptation on the standard voting protocol’s phases. More important, we analyze if the general security requirements and the recommendations proposed by the Council of Europe are met by the scheme.

Public random beacons publish random numbers at regular intervals, which anyone can obtain and verify. The design of public distributed random beacons has been an exciting research direction with significant implications for blockchains, voting, and beyond. Distributed random beacons, in addition to being bias-resistant and unpredictable, also need to have low communication overhead and latency, high resilience to faults, and ease of reconfigurability. Existing synchronous random beacon protocols sacrifice one or more of these properties. In this work, we design an efficient unpredictable synchronous random beacon protocol, OptRand, with quadratic (in the number n of system nodes) communication complexity per beacon output. First, we innovate by employing a novel combination of bilinear pairing based publicly verifiable secret-sharing and non-interactive zero-knowledge proofs to build a linear (in n) sized publicly verifiable random sharing. Second, we develop a state machine replication protocol with linear-sized inputs that is also optimistically responsive, i.e., it can progress responsively at actual network speed during optimistic conditions, despite the synchrony assumption, and thus incur low latency. In addition, we present an efficient reconfiguration mechanism for OptRand that allows nodes to leave and join the system. Our experiments show our protocols perform significantly better compared to state-of-the-art protocols under optimistic conditions and on par with state-of-the-art protocols in the normal case. We are also the first to implement a reconfiguration mechanism for distributed beacons and demonstrate that our protocol continues to be live during reconfigurations.

We introduce incoercible digital signature schemes, a variant of a standard digital signature. Incoercible signatures enable signers, when coerced to produce a signature for a message chosen by an attacker, to generate fake signatures that are indistinguishable from real signatures, even if the signer is compelled to reveal their full history (including their secret signing keys and any randomness used to produce keys/signatures) to the attacker. Additionally, we introduce an authenticator that can detect fake signatures, which ensures that coercion is identified. We present a formal security model for incoercible signature schemes that comprises an established definition of unforgeability and captures new notions of weak receipt-freeness, strong receipt-freeness and coercion-resistance. We demonstrate that an incoercible signature scheme can be viewed as a transformation of any generic signature scheme. Indeed, we present two incoercible signature scheme constructions that are built from a standard signature scheme and a sender-deniable encryption scheme. We prove that our first construction satisfies coercion-resistance, and our second satisfies strong receipt-freeness. We conclude by presenting an extension to our security model: we show that our security model can be extended to the designated verifier signature scheme setting in an intuitive way as the designated verifier can assume the role of the authenticator and detect coercion during the verification process.

In practical operational networks, it is essential to validate path integrity, especially when untrusted intermediate nodes are from numerous network infrastructures operated by several network authorities. Current solutions often reveal the entire path to all parties involved, which may potentially expose the network structures to malicious intermediate attackers. Additionally, there is no prior work done to provide a systematic approach combining the complete lifecycle of packet delivery, i.e., path slicing, path validation and path rerouting, leaving these highly-intertwined modules completely separated. In this work, we present a decentralized privacy-preserving path validation system 𝑃3𝑉 that integrates our novel path validation protocol with an efficient path slicing algorithm and a malice-resilient path rerouting mechanism. Specifically, leveraging Non-Interactive Zero-Knowledge proofs, our path validation protocol XOR-Hash-NIZK protects the packet delivery tasks against information leakage about multi-hop paths and potentially the underlying network infrastructures. We implemented and evaluated our system on a state-of-the-art 5G Dispersed Computing Testbed simulating a multi-authority network. Our results show that while preserving the privacy of paths and nodes and enhancing the security of network service, our system optimizes the performance trade-off between network service quality and security/privacy.

Nonces are a fact of life for achieving semantic security. Generating a uniformly random nonce can be costly and may not always be feasible. Using anything other than uniformly random bits can result in information leakage; e.g., a timestamp can deanonymize a communication and a counter can leak the quantity of transmitted messages. Ideally, we would like to be able to efficiently encrypt the nonce to 1) avoid needing uniformly random bits and 2) avoid information leakage. This paper presents new modes built on top of Farfalle that achieve nonce and redundancy encryption in the AEAD and onion AE settings.

Modern digital signature schemes can provide more guarantees than the standard notion of (strong) unforgeability, such as offering security even in the presence of maliciously generated keys, or requiring to know a message to produce a signature for it. The use of signature schemes that lack these properties has previously enabled attacks on real-world protocols. In this work we revisit several of these notions beyond unforgeability, establish relations among them, provide the first formal definition of non re-signability, and two generic transformations that can provide these properties for a given signature scheme in a provable and efficient way. Our results are not only relevant for established schemes: for example, the ongoing NIST PQC competition towards standardizing post-quantum signature schemes had six candidates in its third round of which three are to be standardized. We perform an in-depth analysis of all the candidates with respect to their security properties beyond unforgeability. We show that many of them do not yet offer these stronger guarantees, which implies that the security guarantees of these post-quantum schemes are not strictly stronger than, but instead incomparable to, classical signature schemes. We show how applying our transformations would efficiently solve this, paving the way for the standardized schemes to provide these additional guarantees and thereby making them harder to misuse.

In [Optimal Collision Side-Channel Attacks] we studied collision side-channel attacks, and derived an optimal distinguisher for key ranking. In this note we propose a heuristic estimation procedure for key ranking based on this distinguisher, and provide estimates of lower bounds for secret key ranks in collision side-channel attacks. The procedure employs nonuniform sampling introduced in [MCRank: Monte Carlo Key Rank Estimation for Side-Channel Security Evaluations], and it is more efficient than the subset uniform sampling procedure [A Note on Key Ranking for Optimal Collision Side-Channel Attacks].

An important research direction in secure multi-party computation (MPC) is to improve the efficiency of the protocol. One idea that has recently received attention is to consider a slightly weaker security model than full malicious security -- the so-called setting of $\textit{covert security}$. In covert security, the adversary may cheat but only is detected with certain probability. Several works in covert security consider the offline/online approach, where during a costly offline phase correlated randomness is computed, which is consumed in a fast online phase. State-of-the-art protocols focus on improving the efficiency by using a covert offline phase, but ignore the online phase. In particular, the online phase is usually assumed to guarantee security against malicious adversaries. In this work, we take a fresh look at the offline/online paradigm in the covert security setting. Our main insight is that by weakening the security of the online phase from malicious to covert, we can gain significant efficiency improvements during the offline phase. Concretely, we demonstrate our technique by applying it to the online phase of the well-known TinyOT protocol (Nielsen et al., CRYPTO '12). The main observation is that by reducing the MAC length in the online phase of TinyOT to $t$ bits, we can guarantee covert security with a detection probability of $1- \frac{1}{2^t}$. Since the computation carried out by the offline phase depends on the MAC length, shorter MACs result in a more efficient offline phase and thus speed up the overall computation. Our evaluation shows that our approach reduces the communication complexity of the offline protocol by at least 35% for a detection rate up to $\frac{7}{8}$. In addition, we present a new generic composition result for analyzing the security of online/offline protocols in terms of concrete security.

Applying the pothole method on the factors of numbers of the form $2^n-1$, we prove the inequality $$\iota(2^n-1)\leq n-1+\iota(n)$$ where $\iota(n)$ denotes the length of the shortest addition chain producing $n$.

This paper presents a new profiling side-channel attack on the signature scheme CRYSTALS-Dilithium, which has been selected by the NIST as the new primary standard for quantum-safe digital signatures. This algorithm has a constant-time implementation with consideration for side-channel resilience. However, it does not protect against attacks that exploit intermediate data leakage. We exploit such a leakage on a vector generated during the signing process and whose costly protection by masking is a matter of debate. We design a template attack that enables us to efficiently predict whether a given coefficient in one coordinate of this vector is zero or not. Once this value has been completely reconstructed, one can recover, using linear algebra methods, part of the secret key that is sufficient to produce universal forgeries. While our paper deeply discusses the theoretical attack path, it also demonstrates the validity of the assumption regarding the required leakage model, from practical experiments with the reference implementation on an ARM Cortex-M4.

Deep neural networks (DNN) have become a significant threat to the security of cryptographic implementations with regards to side-channel analysis (SCA), as they automatically combine the leakages without any preprocessing needed, leading to a more efficient attack. However, these DNNs for SCA remain mostly black-box algorithms that are very difficult to interpret. Benamira \textit{et al.} recently proposed an interpretable neural network called Truth Table Deep Convolutional Neural Network (TT-DCNN), which is both expressive and easier to interpret. In particular, a TT-DCNN has a transparent inner structure that can entirely be transformed into SAT equations after training. In this work, we analyze the SAT equations extracted from a TT-DCNN when applied in SCA context, eventually obtaining the rules and decisions that the neural networks learned when retrieving the secret key from the cryptographic primitive (i.e., exact formula). As a result, we can pinpoint the critical rules that the neural network uses to locate the exact Points of Interest (PoIs). We validate our approach first on simulated traces for higher-order masking. However, applying TT-DCNN on real traces is not straightforward. We propose a method to adapt TT-DCNN for application on real SCA traces containing thousands of sample points. Experimental validation is performed on software-based ASCADv1 and hardware-based AES\_HD\_ext datasets. In addition, TT-DCNN is shown to be able to learn the exact countermeasure in a best-case setting.

Homomorphic encryption (HE) is one of the most promising techniques for privacy-preserving computations, especially the word-wise HE schemes that allow batched computations over ciphertexts. However, the high computational overhead hinders the deployment of HE in real-word applications. The GPUs are often used to accelerate the execution in such scenarios, while the performance of different HE schemes on the same GPU platform is still absent. In this work, we implement three word-wise HE schemes BGV, BFV, and CKKS on GPU, with both theoretical and engineering optimizations. We optimize the hybrid key-switching technique, reducing the computational and memory overhead of this procedure. We explore several kernel fusing strategies to reuse data, which reduces the memory access and IO latency, and improves the overall performance. By comparing with the state-of-the-art works, we demonstrate the effectiveness of our implementation. Meanwhile, we present a framework that finely integrates our implementation of the three schemes, covering almost all scheme functions and homomorphic operations. We optimize the management of pre-computation, RNS bases and memory in the framework, to provide efficient and low-latency data access and transfer. Based on this framework, we provide a thorough benchmark of the three schemes, which can serve as a reference for scheme selection and implementation in constructing privacy-preserving applications.

On-line/off-line encryption schemes enable the fast encryption of a message from a pre-computed coupon. The paradigm was put forward in the case of digital signatures. This work introduces a compact public-key additively homomorphic encryption scheme. The scheme is semantically secure under the decisional composite residuosity (DCR) assumption. Compared to Paillier cryptosystem, it merely requires one or two integer additions in the on-line phase and no increase in the ciphertext size. This work also introduces a compact on-line/off-line trapdoor commitment scheme featuring the same fast on-line phase. Finally, applications to chameleon signatures are presented.