International Association
for Cryptologic Research

The area is one of the most important criteria for an S-box in hardware implementation when designing lightweight cryptography primitives. The area can be well estimated by the number of gate equivalent (GE). However, to our best knowledge, there is no efficient method to search for an S-box implementation with the least GE. Previous approaches can be classified into two categories, one is a heuristic that aims at finding an implementation with a satisfying but not necessarily the smallest GE number; the other one is SAT-based focusing on only the smallest number of gates while it ignored that the areas of different gates vary. Implementation with the least gates would usually not lead to the smallest number of GE. In this paper, we propose an improved SAT-based tool targeting optimizing the number of GE of an S-box implementation. Given an S-box, our tool can return the implementation of this S-box with the smallest number of GE. We speed up the search process of the tool by bit-sliced technique. Additionally, our tool supports 2-, 3-, and 4-input gates, while the previous tools cover only 2-input gates. To highlight the strength of our tool, we apply it to some 4-bit and 5-bit S-boxes of famous ciphers. We obtain a better implementation of RECTANGLE's S-box with the area of 18.00GE. What's more, we prove that the implementations of S-boxes of PICCOLO, SKINNY, and LBLOCK in the current literature have been optimal. When using the DC synthesizer on the circuits produced by our tool, the area are much better than the circuits converted by DC synthesizers from the lookup tables (LUT). At last, we use our tool to find implementations of 5-bit S-boxes, such as those used in KECCAK and ASCON.

We revisit decentralized random beacons with a focus on practical distributed applications. Decentralized random beacons (Beaver and So, Eurocrypt 1993) provide the functionality for $n$ parties to generate an unpredictable sequence of bits in a way that cannot be biased, which is useful for any decentralized protocol requiring trusted randomness.

Existing beacon constructions are highly inefficient in practical settings where protocol parties need to rejoin after crashes or disconnections, and more significantly where smart contracts may rely on arbitrary index points in high-volume streams. For this, we introduce a new notion of history-generating decentralized random beacons (HGDRBs).

Roughly, the history-generation property of HGDRBs allows for previous beacon outputs to be efficiently generated knowing only the current value and the public key. At application layers, history-generation supports registering a sparser set of on-chain values if desired, so that apps like lotteries can utilize on-chain values without incurring high-frequency costs, enjoying all the benefits of DRBs implemented off-chain or with decoupled, special-purpose chains. Unlike rollups, HG is tailored specifically to recovering and verifying pseudorandom bit sequences and thus enjoys unique optimizations investigated in this work.

We introduce STROBE: an efficient HGDRB construction which generalizes the original squaring-based RSA approach of Beaver and So. STROBE enjoys several useful properties that make it suited for practical applications that use beacons:

- history-generating: it can regenerate and verify high-throughput beacon streams, supporting sparse (thus cost-effective) ledger entries;

- concisely self-verifying: NIZK-free, with state and validation employing a single ring element;

- eco-friendly: stake-based rather than work based;

- unbounded: refresh-free, addressing limitations of Beaver and So;

- delay-free: results are immediately available.

Today's data-intensive applications increasingly suffer from significant performance bottlenecks due to the limited memory bandwidth of the classical von Neumann architecture. Near-Data Processing (NDP) has been proposed to perform computation near memory or data storage to reduce data movement for improving performance and energy consumption. However, the untrusted NDP processing units (PUs) bring in new threats to workloads that are private and sensitive, such as private database queries and private machine learning inferences. Meanwhile, most existing secure hardware designs do not consider off-chip components trustworthy. Once data leaving the processor, they must be protected, e.g., via block cipher encryption. Unfortunately, current encryption schemes do not support computation over encrypted data stored in memory or storage, hindering the adoption of NDP techniques for sensitive workloads.

In this paper, we propose SecNDP, a lightweight encryption and verification scheme for untrusted NDP devices to perform computation over ciphertext and verify the correctness of linear operations. Our encryption scheme leverages arithmetic secret sharing in secure Multi-Party Computation (MPC) to support operations over ciphertext, and uses counter-mode encryption to reduce the decryption latency. The security of the scheme is formally proven. Compared with a non-NDP baseline, secure computation with SecNDP significantly reduces the memory bandwidth usage while providing security guarantees. We evaluate SecNDP for two workloads of distinct memory access patterns. In the setting of eight NDP units, we show a speedup up to 7.46x and energy savings of 18% over an unprotected non-NDP baseline, approaching the performance gain attained by native NDP without protection.Furthermore, SecNDP does not require any security assumption on NDP to hold, thus, using the same threat model as existing secure processors. SecNDP can be implemented without changing the NDP protocols and their inherent hardware design.

WARP is an energy-efficient lightweight block cipher that is currently the smallest 128-bit block cipher in terms of hardware. It was proposed by Banik et al. in SAC 2020 as a lightweight replacement for AES-128 without changing the mode of operation. This paper proposes key-recovery attacks on WARP based on differential cryptanalysis in single and related-key settings. We searched for differential trails for up to 20 rounds of WARP, with the first 19 having optimal differential probabilities. We also found that the cipher has a strong differential effect, whereby 16 to 20-round differentials have substantially higher probabilities than their corresponding individual trails. A 23-round key-recovery attack was then realized using an 18-round differential distinguisher. Next, we formulated an automatic boomerang search using SMT that relies on the Feistel Boomerang Connectivity Table to identify valid switches. We designed the search as an add-on to the CryptoSMT tool, making it applicable to other Feistel-like ciphers such as TWINE and LBlock-s. For WARP, we found a 21-round boomerang distinguisher which was used in a 24-round rectangle attack. In the related-key setting, we describe a family of 2-round iterative differential trails, which we used in a practical related-key attack on the full 41-round WARP.

BORON is a 64-bit lightweight block cipher based on the substitution-permutation network that supports an 80-bit (BORON-80) and 128-bit (BORON-128) secret key. In this paper, we revisit the use of differential cryptanalysis on BORON in the single-key model. Using an SAT/SMT approach, we look for differentials that consist of multiple differential characteristics with the same input and output differences. Each characteristic that conforms to a given differential improves its overall probability. We also implemented the same search using Matsui's algorithm for verification and performance comparison purposes. We identified high-probability differentials which were then used in key recovery attacks against BORON-80/128. We first show that the previous differential cryptanalysis attack against 9-round of BORON was at most an 8.5 round attack due to the omission of the final block XOR layer. Then, we used 8-round differentials with a probability of $2^{-58.156}$ and $2^{-62.415}$ in key recovery attacks against 9 and 10 rounds of BORON-80 and BORON-128 with time/data/memory complexities of {$2^{63.63}/2^{62}/2^{55}$ and $2^{100.28}/2^{64}/2^{71}$} respectively. Our key recovery framework provides a more accurate estimate of the attack complexity as compared to previous work. The attacks proposed in this paper are the best differential attacks against BORON-80/128 in the single-key model to date.

This article discusses a simple deterministic algorithm for solving quadratic Boolean systems which is essentially a special case of more sophisticated methods. The main idea fits in a single sentence: guess enough variables so that the remaining quadratic equations can be solved by linearization (i.e. by considering each remaining monomial as an independent variable and solving the resulting linear system) and restart until the solution is found. Under strong heuristic assumptions, this finds all the solutions of $m$ quadratic polynomials in $n$ variables with $\mathcal{\tilde O}({2^{n-\sqrt{2m}}})$ operations. Although the best known algorithms require exponentially less time, the present technique has the advantage of being simpler to describe and easy to implement. In strong contrast with the state-of-the-art, it is also quite efficient in practice.

What is the funniest number in cryptography (Episode 2 )? 0 . The reason is that ∀x, x ∗ 0 = 0, i.e., the equation is always satisfied no matter what x is. We’ll use zero to attack zero-knowledge proof (ZKP). In particular, we’ll discuss a critical issue in a cutting-edge ZKP PLONK C++ implementation which allows an attacker to create a forged proof that all verifiers will accept. We’ll show how theory guides the attack’s direction. In practice, the attack works like a charm and we’ll show how the attack falls through a chain of perfectly aligned software cracks.

In the same codebase, there is an independent critical ECDSA bug where (r, s) = (0, 0) is a valid signature for arbitrary keys and messages, but we won’t discuss it further because it’s a known ECDSA attack vector in the Google Wycheproof project that I worked on a few years ago.

All bugs have been responsibly disclosed through the vendor’s bug bounty program with total reward ~ $15,000 (thank you).

The cryptographic algorithms that we rely on for Internet trust and security are based on the computational difficulty of solving particular mathematical problems. Sufficiently powerful quantum computers could solve those problems in a day or less, rendering their protection largely useless. When this hypothetical future is on the horizon, Internet software suppliers should undertake the massive project of changing the fundamental cryptographic algorithms to completely different kinds of computations. This paper calls attention to how today's algorithms could be vulnerable, to the factors that impede the realization of quantum computing, and to how technologists might measure the distance to the quantum horizon.

The emergence of cloud-computing has raised important privacy questions about the data that users share with remote servers. While data in transit is protected using standard techniques like Transport Layer Security (TLS), most cloud providers have unrestricted plaintext access to user data at the endpoint. Fully Homomorphic Encryption (FHE) offers one solution to this problem by allowing for arbitrarily complex computations on encrypted data without ever needing to decrypt it. Unfortunately, all known implementations of FHE require the addition of noise during encryption which grows during computation. As a result, sustaining deep computations requires a periodic noise reduction step known as bootstrapping. The cost of the bootstrapping operation is one of the primary barriers to the wide-spread adoption of FHE.In this paper, we present an in-depth architectural analysis of the bootstrapping step in FHE. First, we observe that se-cure implementations of bootstrapping exhibit a low arithmetic intensity (<1Op/byte), require large caches (>100MB) and as such, are heavily bound by the main memory bandwidth.Consequently, we demonstrate that existing workloads observe marginal performance gains from the design of bespoke high-throughput arithmetic units tailored to FHE. Secondly, we propose several cache-friendly algorithmic optimizations that improve the throughput in FHE bootstrapping by enabling upto3.2×higher arithmetic intensity and4.6×lower memory bandwidth. Our optimizations apply to a wide range of structurally similar computations such as private evaluation and training of machine learning models. Finally, we incorporate these optimizations into an architectural tool which, given a cache size, memory subsystem, the number of functional units and a desired security level, selects optimal cryptosystem parameters to maximize the bootstrapping throughput.Our optimized bootstrapping implementation represents a best-case scenario for compute acceleration of FHE. We show that despite these optimizations, bootstrapping (as well as other applications with similar computational structure) continue to remain bottlenecked by main memory bandwidth. We thus conclude that secure FHE implementations need to look beyond accelerated compute for further performance improvements and to that end, we propose new research directions to address the underlying memory bottleneck. In summary, our answer to the titular question is: yes, but only after addressing the memory bottleneck!

Distributed key generation (DKG) is an important building block in designing many efficient distributed protocols. In this work, we initiate the study of communication complexity and latency of distributed key generation protocols under a synchronous network in a point-to-point network. Our key result is the first synchronous DKG protocol for discrete log-based cryptosystems with $O(\kappa n^3)$ communication complexity ($\kappa$ denotes a security parameter) that tolerates $t < n/2$ Byzantine faults among $n$ parties. We show two variants of the protocol: a deterministic protocol with $O(t\Delta)$ latency and randomized protocol with $O(\Delta)$ latency in expectation where $\Delta$ denotes the bounded synchronous delay. In the process of achieving our results, we design (1) a gradecast protocol with optimal communication complexity of $O(\kappa n^2)$ for linear-sized inputs and latency of $O(\Delta)$, (2) a primitive called ``recoverable set of shares'' for ensuring recovery of shared secrets, (3) an oblivious leader election protocol with $O(\kappa n^3)$ communication and $O(\Delta)$ latency, and (4) a multi-valued validated Byzantine agreement (MVBA) protocol with $O(\kappa n^3)$ communication complexity for linear-sized inputs and $O(\Delta)$ latency in expectation. Each of these primitives may be of independent interest.

With the recent shift to post-quantum algorithms it becomes increasingly important to provide precise bit-security estimates for code-based cryptography such as McEliece and quasi-cyclic schemes like BIKE and HQC. While there has been significant progress on information set decoding (ISD) algorithms within the last decade, it is still unclear to which extent this affects current cryptographic security estimates.

We provide the first concrete implementations for representation-based ISD, such as May-Meurer-Thomae (MMT) or Becker-Joux-May-Meurer (BJMM), that are parameter-optimized for the McEliece and quasi-cyclic setting. Although MMT and BJMM consume more memory than naive ISD algorithms like Prange, we demonstrate that these algorithms lead to significant speedups for practical cryptanalysis on medium-sized instances (around 60 bit). More concretely, we provide data for the record computations of McEliece-1223 and McEliece-1284 (old record: 1161), and for the quasi-cyclic setting up to code length 2918 (before: 1938).

Based on our record computations we extrapolate to the bit-security level of the proposed BIKE, HQC and McEliece parameters in NIST's standardization process. For BIKE/HQC, we also show how to transfer the Decoding-One-Out-of-Many (DOOM) technique to MMT/BJMM. Although we achieve significant DOOM speedups, our estimates confirm the bit-security levels of BIKE and HQC.

For the proposed McEliece round-3 parameter sets of 192 and 256 bit, however, our extrapolation indicates a security level overestimate by roughly 20 and 10 bits, respectively, i.e., the high-security McEliece instantiations may be a bit less secure than desired.

We are witnessing the emergence of decentralized AI pipelines wherein different organisations are involved in the different steps of the pipeline. In this paper, we introduce a comprehensive framework for verifiable provenance for decentralized AI pipelines with support for confidentiality concerns of the owners of data and model assets. Although some of the past works address different aspects of provenance, verifiability, and confidentiality, none of them address all the aspects under one uniform framework. We present an efficient and scalable approach for verifiable provenance for decentralized AI pipelines with support for confidentiality based on zero-knowledge proofs (ZKPs). Our work is of independent interest to the fields of verifiable computation (VC) and verifiable model inference. We present methods for basic computation primitives like read only memory access and operations on datasets that are an order of magnitude better than the state of the art. In the case of verifiable model inference, we again improve the state of the art for de- cision tree inference by an order of magnitude. We present an extensive experimental evaluation of our system.

We consider four variants of the RSA cryptosystem with an RSA modulus $N=pq$ where the public exponent $e$ and the private exponent $d$ satisfy an equation of the form $ed-k\left(p^2-1\right)\left(q^2-1\right)=1$. We show that, if the prime numbers $p$ and $q$ share most significant bits, that is, if the prime difference $|p-q|$ is sufficiently small, then one can solve the equation for larger values of $d$, and factor the RSA modulus, which makes the systems insecure.

The pseudo-random sampling of constant weight word, as it is currently implemented in schemes like BIKE or HQC, is prone to the leakage of information on the seed being used. This creates a vulnerability when the semantic security conversion requires a deterministic re-encryption. This observation was first made in [HLS21] about HQC, and a timing attack was presented to recover the secret key. As suggested in [HLS21] a similar attack applies to BIKE and an instance of such an attack is presented here, as well as countermeasures similar to those suggested in [HLS21] for HQC. A new approach for fixing the issue is also proposed. It is first remarked that, contrary to what is done currently, the sampling of constant weight words doesn’t need to produce a uniformly distributed output. If the distribution is close to uniform in the appropriate metric, the impact on security is negligible. Also, a new variant of Fisher-Yates shuffle is proposed which is (1) very well suited for secure implementations against timing and cache attacks, and (2) produces constant weight words with a distribution close enough to uniform.

The RSA cryptosystem comprises of two important features that are needed for encryption process known as the public parameter $e$ and the modulus $N$. In 1999, a cryptanalysis on RSA which was described by Boneh and Durfee focused on the key equation $ed-k\phi(N)=1$ and $e$ of the same magnitude to $N$. Their method was applicable for the case of $d

The public parameters of the RSA cryptosystem are represented by the pair of integers $N$ and $e$. In this work, first we show that if $e$ satisfies the Diophantine equation of the form $ex^2-\phi(N)y^2=z$ for appropriate values of $x, y$ and $z$ under certain specified conditions, then one is able to factor $N$. That is, the unknown $\frac{y}{x}$ can be found amongst the convergents of $\frac{\sqrt{e}}{\sqrt{N}}$ via continued fractions algorithm. Consequently, Coppersmith's theorem is applied to solve for prime factors $p$ and $q$ in polynomial time. We also report a second weakness that enabled us to factor $k$ instances of RSA moduli simultaneously from the given $(N_i,e_i)$ for $i=1,2,\cdots,k$ and a fixed $x$ that fulfills the Diophantine equation $e_{i}x^{2}-y_{i}^{2}\phi(N_{i})=z_{i}$. This weakness was identified by solving the simultaneous Diophantine approximations using the lattice basis reduction technique. We note that this work extends the bound of insecure RSA decryption exponents.

Front-running is the malicious, and often illegal, act of both manipulating the order of pending trades and injecting additional trades to make a profit at the cost of other users. In decentralized finance (DeFi), front-running strategies exploit both public knowledge of user trades from transactions pending on the network and the miner's ability to determine the final transaction order. Given the financial loss and increased transaction load resulting from adversarial front-running in decentralized finance, novel cryptographic protocols have been proposed to mitigate such attacks in the permission-less blockchain setting. We systematize and discuss the state-of-the-art of front-running mitigation in decentralized finance, and illustrate remaining attacks and open challenges.

The Transport Layer Security (TLS) protocol is a fundamental building block for ensuring security on Internet. It provides an easy to use framework for the purposes of establishing an authenticated and secure channel between two parties that have never physically met. Nevertheless, TLS only provides a simple cryptographic functionality compared to more advanced protocols such as protocols for secure multiparty computation (MPC).

In this work, we provide a framework for efficiently establishing channels for MPC over the Internet. We focus on MPC protocols in the oblivious transfer (OT) hybrid model such that it is sufficient to establish OT correlations for such a channel. We revisit and combine different notions of UC security proposed in both the MPC and authenticated key exchange settings. Through this work, we show how an OT protocol can be composed with a secure authenticator to ensure the authenticity of messages sent during the OT.

In addition, we adapt and analyse non-interactive OTs based on dense key encapsulation mechanisms (KEMs) in the random oracle model, where the first message, i.e. public key, can be reused. These KEMs can be instantiated based on CDH, RSA and LWE and after a performance and security evaluation, it turns out that the resulting OT protocols are very competitive with the state of the art and are able to leverage existing PKIs.

We present the application of a known subfield lattice attack on a fully homomorphic encryption scheme based on NTRU. We show that the scheme is vulnerable to the attack due to a particular parameter having to satisfy a derived lower bound. We also show that, due to the structure of the scheme, the attack is successful in all practical instantiations of the scheme.

Quantum computers provide a new way of solving problems even in cryptography in which digital signature make an important role. In this paper, we describe a comparison between the spectral test in classical mode and quantum mode through Fourier Transform. A comparison of the results in the two cases was made. Applications of the proposed techniques are from the field of statistical testing of the pseudorandom bit generators used for cryptographic applications. The proposed statistical test is an extension of the Discrete Fourier Transform statistical test proposed in NIST SP 800-22.