Quantum computers have the potential to solve hard problems that are nearly impossible to solve by classical computers, this has sparked a surge of research to apply quantum technology and algorithm against the cryptographic systems to evaluate for its quantum resistance. In the process of selecting post-quantum standards, NIST categorizes security levels based on the complexity that quantum computers would require to crack AES encryption (levels 1, 3 and 5) and SHA-2 or SHA-3 (levels 2 and...

The SHA-2 family including SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224 and SHA512/256 is a U.S. federal standard pub- lished by NIST. Especially, there is no doubt that SHA-256 is one of the most important hash functions used in real-world applications. Due to its complex design compared with SHA-1, there is almost no progress in collision attacks on SHA-2 after ASIACRYPT 2015. In this work, we retake this challenge and aim to significantly improve collision attacks on the SHA-2...

Hashing algorithms are one-way functions that are used in cryptographic protocols as Pseudo Random Functions (PRF), to assess data integrity or to create a Hash-based Message Authentication Code (HMAC). In many cryptographic constructions, secret data is processed with hashing functions. In these cases, recovering the input given to the hashing algorithm allows retrieving secret data. In this paper, we investigate the application of Soft Analytical Side-Channel Attacks (SASCA), based on a...

ZK-SNARKs, a fundamental component of privacy-oriented payment systems, identity protocols, or anonymous voting systems, are advanced cryptographic protocols for verifiable computation: modern SNARKs allow to encode the invariants of a program, expressed as an arithmetic circuit, in an appropriate constraint language from which short, zero-knowledge proofs for correct computations can be constructed. One of the most important computations that is run through SNARK systems is the...

Hash functions are a crucial component in incrementally verifiable computation (IVC) protocols and applications. Among those, recursive SNARKs and folding schemes require hash functions to be both fast in native CPU computations and compact in algebraic descriptions (constraints). However, neither SHA-2/3 nor newer algebraic constructions, such as Poseidon, achieve both requirements. In this work we overcome this problem in several steps. First, for certain prime field domains we propose a...

Cryptographic hash functions map data of arbitrary size to a fixed size digest, and are one of the most commonly used cryptographic objects. As it is infeasible to design an individual hash function for every input size, variable-input length hash functions are built by designing and bootstrapping a single fixed-input length function that looks sufficiently random. To prevent trivial preprocessing attacks, applications often require not just a single hash function but rather a family of...

We introduce the notion of a universal random oracle. Analogously to a classical random oracle it idealizes hash functions as random functions. However, as opposed to a classical random oracle which is created freshly and independently for each adversary, the universal random oracle should provide security of a cryptographic protocol against all adversaries simultaneously. This should even hold if the adversary now depends on the random function. This reflects better the idea that the strong...

Zero-knowledge (ZK) applications form a large group of use cases in modern cryptography, and recently gained in popularity due to novel proof systems. For many of these applications, cryptographic hash functions are used as the main building blocks, and they often dominate the overall performance and cost of these approaches. Therefore, in the last years several new hash functions were built in order to reduce the cost in these scenarios, including Poseidon and Rescue among others. These...

First of all we take a thorough look at an error in a paper by Daemen et al. (ToSC 2018) which looks at minimal requirements for tree-based hashing based on multiple primitives, including block ciphers. This reveals that the error is more fundamental than previously shown by Gunsing et al. (ToSC 2020), which is mainly interested in its effect on the security bounds. It turns out that the cause for the error is due to an essential oversight in the interaction between the different oracles...

In this work, we focus on collision attacks against instances of SHA-3 hash family in both classical and quantum settings. Since the 5-round collision attacks on SHA3-256 and other variants proposed by Guo et al. at JoC~2020, no other essential progress has been published. With a thorough investigation, we identify that the challenges of extending such collision attacks on SHA-3 to more rounds lie in the inefficiency of differential trail search. To overcome this obstacle, we develop a...

Side-channel attacks are a major threat to the security of cryptographic implementations, particularly for small devices that are under the physical control of the adversary. While several strategies for protecting against side-channel attacks exist, these often fail in practice due to unintended interactions between values deep within the CPU. To detect and protect from side-channel attacks, several automated tools have recently been proposed; one of their common limitations is that they...

We provide a modified version of the Ligero sublinear zero knowledge proof system for arithmetic circuits provided by Ames et. al. (CCS ‘17). Our modification "BooLigero" tailors Ligero for use in Boolean circuits to achieve a significant improvement in proof size. Although the original Ligero system could be used for Boolean circuits, Ligero generally requires allocating an entire field element to represent a single bit on a wire in a Boolean circuit. In contrast, our system performs...

The Fiat-Shamir transform is a general method for reducing interaction in public-coin protocols by replacing the random verifier messages with deterministic hashes of the protocol transcript. The soundness of this transformation is usually heuristic and lacks a formal security proof. Instead, to argue security, one can rely on the random oracle methodology, which informally states that whenever a random oracle soundly instantiates Fiat-Shamir, a hash function that is ``sufficiently...

Since Keccak was selected as the SHA-3 standard, more and more permutation-based primitives have been proposed. Different from block ciphers, there is no round key in the underlying permutation for permutation-based primitives. Therefore, there is a higher risk for a differential characteristic of the underlying permutation to become incompatible when considering the dependency of difference transitions over different rounds. However, in most of the MILP or SAT based models to search for...

We present a new methodology for building formally verified cryptographic libraries that are optimized for multiple architectures. In particular, we show how to write and verify generic crypto code in the F* programming language that exploits single-instruction multiple data (SIMD) parallelism. We show how this code can be compiled to platforms that supports vector instructions, including ARM Neon and Intel AVX, AVX2, and AVX512. We apply our methodology to obtain verified vectorized...

SNEIK is a family of lightweight cryptographic algorithms derived from a single 512-bit permutation. The SNEIGEN ``entropy distribution function'' was designed to speed up certain functions in post-quantum and lattice-based public key algorithms. We implement and evaluate SNEIK algorithms on popular 8-bit AVR and 32-bit ARMv7-M (Cortex M3/M4) microcontrollers, and also describe an implementation for the open-source RISC-V (RV32I) Instruction Set Architecture (ISA). Our results demonstrate...

The need for high-quality randomness in cryptography makes random-number generation one of its most fundamental tasks. A recent important line of work (initiated by Dodis et al., CCS ’13) focuses on the notion of *robustness* for *pseudorandom number generators (PRNGs) with inputs*—these are primitives that use various sources to accumulate sufficient entropy into a state, from which pseudorandom bits are extracted. Robustness ensures that PRNGs remain secure even under state compromise and...

A cryptographic function with a fixed-length output, such as a block cipher, hash function, or message authentication code (MAC), should behave as a random mapping. The mapping's randomness can be evaluated with statistical tests. Statistical test suites typically used to evaluate cryptographic functions, such as the NIST test suite, are not well-suited for testing fixed-output-length cryptographic functions. Also, these test suites employ a frequentist approach, making it difficult to...

Quantum computing threatens conventional public-key cryptography. In response, standards bodies such as NIST increasingly focus on post-quantum cryptography. In particular, hash-based signature schemes are notable candidates for deployment. No rigorous side-channel analysis of hash-based signature schemes has been conducted so far. This work bridges this gap. We analyse the stateful hash-based signature schemes XMSS and XMSS^MT, which are currently undergoing standardisation at IETF, as well...

Performance of cryptanalytic quantum search algorithms is mainly inferred from query complexity which hides overhead induced by an implementation. To shed light on quantitative complexity analysis removing hidden factors, we provide a framework for estimating time-space complexity, with carefully accounting for characteristics of target cryptographic functions. Processor and circuit parallelization methods are taken into account, resulting in the time-space trade-off curves in terms of depth...

We investigate the cost of Grover's quantum search algorithm when used in the context of pre-image attacks on the SHA-2 and SHA-3 families of hash functions. Our cost model assumes that the attack is run on a surface code based fault-tolerant quantum computer. Our estimates rely on a time-area metric that costs the number of logical qubits times the depth of the circuit in units of surface code cycles. As a surface code cycle involves a significant classical processing stage, our cost...

In 2012, NIST standardized SHA-512/224 and SHA-512/256, two truncated variants of SHA-512, in FIPS 180-4. These two hash functions are faster than SHA-224 and SHA-256 on 64-bit platforms, while maintaining the same hash size and claimed security level. So far, no third-party analysis of SHA-512/224 or SHA-512/256 has been published. In this work, we examine the collision resistance of step-reduced versions of SHA-512/224 and SHA-512/256 by using differential cryptanalysis in combination with...

Differential and linear cryptanalysis are the general purpose tools to analyze various cryptographic primitives. Both techniques have in common that they rely on the existence of good differential or linear characteristics. The difficulty of finding such characteristics depends on the primitive. For instance, AES is designed to be resistant against differential and linear attacks and therefore, provides upper bounds on the probability of possible linear characteristics. On the other hand, we...

In this paper, we focus on the construction of semi-free-start collisions for SHA-256, and show how to turn them into collisions. We present a collision attack on 28 steps of the hash function with practical complexity. Using a two-block approach we are able to turn a semi-free-start collision into a collision for 31 steps with a complexity of at most $2^{65.5}$. The main improvement of our work is to extend the size of the local collisions used in these attacks. To construct differential...

SHA-2 (SHA-224, SHA-256, SHA-384 and SHA-512) is hash function family issued by the National Institute of Standards and Technology (NIST) in 2002 and is widely used all over the world. In this work, we analyze the security of SHA-512 with respect to boomerang attack. Boomerang distinguisher on SHA-512 compression function reduced to 48 steps is proposed, with a practical complexity of $2^{51}$. A practical example of the distinguisher for 48-step SHA-512 is also given. As far as we know, it...

The security of HMAC (and more general hash-based MACs) against state-recovery and universal forgery attacks was very recently shown to be suboptimal, following a series of surprising results by Leurent \emph{et al.} and Peyrin \emph{et al.}. These results have shown that such powerful attacks require much less than $2^{\ell}$ computations, contradicting the common belief (where $\ell$ denotes the internal state size). In this work, we revisit and extend these results, with a focus on...

In this work, we present practical semi-free-start collisions for SHA-512 on up to 38 (out of 80) steps with complexity $2^{40.5}$. The best previously published result was on 24 steps. The attack is based on extending local collisions as proposed by Mendel et al. in their Eurocrypt 2013 attack on SHA-256. However, for SHA-512, the search space is too large for direct application of these techniques. We achieve our result by improving the branching heuristic of the guess-and-determine...

There exists a broad range of RFID protocols in literature that propose hash functions as cryptographic primitives. Since Keccak has been selected as the winner of the NIST SHA-3 competition in 2012, there is the question of how far we can push the limits of Keccak to fulfill the stringent requirements of passive low-cost RFID. In this paper, we address this question by presenting a hardware implementation of Keccak that aims for lowest power and lowest area. Our smallest (full-state) design...

The question of compatibility of differential paths plays a central role in second order collision attacks on hash functions. In this context, attacks typically proceed by starting from the middle and constructing the middle-steps quartet in which the two paths are enforced on the respec- tive faces of the quartet structure. Finding paths that can fit in such a quartet structure has been a major challenge and the currently known compatible paths extend over a suboptimal number of steps for...

In this paper we present a comprehensive comparison of all Round 3 SHA-3 candidates and the current standard SHA-2 from the point of view of hardware performance in modern FPGAs. Each algorithm is implemented using multiple architectures based on the concepts of iteration, folding, unrolling, pipelining, and circuit replication. Trade-offs between speed and area are investigated, and the best architecture from the point of view of the throughput to area ratio is identified. Finally, all...

A hash function maps a variable length input into a fixed length output. The hash functions that are used in the information security related applications are referred as cryptographic hash functions. Hash functions are being used as building blocks of many complex cryptographic mechanisms and protocols. Construction of a hash function consists of two components. First component is a compression function and the second component is a domain extender. The various hash function design...

SM3 is a hash function designed by Xiaoyun Wang et al., and published by the Chinese Commercial Cryptography Administration Office for the use of electronic authentication service system. The design of SM3 builds upon the design of the SHA-2 hash function, but introduces additional strengthening features. In this paper, using a higher order differential cryptanalysis approach, we present a practical 4-sum distinguisher against the compression function of SM3 reduced to 32 rounds. In...

On Nov 2007, NIST announced the SHA-3 competition to select a new hash standard as a replacement of SHA-2. On Dec 2010, five submissions have been selected as the final round candidates, including Skein, which have components based on ARX. In this paper, a new related-key boomerang distinguishing attack is proposed on 31-round Threefish-256 with a time complexity of about $2^{234}$. Our improved attack is based on the efficient algorithms for calculating differentials of modular addition.

We present the new concept of biclique as a tool for preimage attacks, which employs many powerful techniques from differential cryptanalysis of block ciphers and hash functions. The new tool has proved to be widely applicable by inspiring many authors to publish new results of the full versions of AES, KASUMI, IDEA, Square, and others. In this paper, we demonstrate how our concept results in the first cryptanalysis of the Skein hash function, and describe an attack on the SHA-2 hash...

In this short note we give an observation about the SHA- 3 candidate Keccak[r,c,d], where the parameters r,c and d receive values from the formal proposal for the Keccak hash function (with the hash output of n = c bits). We show how an attacker that will spend a one-time effort to find a second preimage for the value z0 = Keccak[r, c, d](0^r) will actually get infinite number of second preimages for free, for any message M. Our observation is an adaptation of similar attacks that have been...

Performance in hardware has been demonstrated to be an important factor in the evaluation of candidates for cryptographic standards. Up to now, no consensus exists on how such an evaluation should be performed in order to make it fair, transparent, practical, and acceptable for the majority of the cryptographic community. In this report, we formulate a proposal for a fair and comprehensive evaluation methodology, and apply it to the comparison of hardware performance of 14 Round~2 SHA-3...

In this note we show a consequence of the recent observation that narrow-pipe hash designs manifest an abberation from ideal random functions for finding collisions for those functions with complexities much lower than the so called generic birthday paradox lower bound. The problem is generic for narrow-pipe designs including classic Merkle-Damgard designs but also recent narrow-pipe SHA-3 candidates. Our finding does not reduces the generic collision security of n/2 bits that narrow-pipe...

In a recent note to the NIST hash-forum list, the following observation was presented: narrow-pipe hash functions differ significantly from ideal random functions $H:\{0,1\}^{N} \rightarrow \{0,1\}^n$ that map bit strings from a big domain where $N=n+m,\ m\geq n$ ($n=256$ or $n=512$). Namely, for an ideal random function with a big domain space $\{0,1\}^{N}$ and a finite co-domain space $Y=\{0,1\}^n$, for every element $y \in Y$, the probability $Pr\{H^{-1}(y) = \varnothing\} \approx...

The SHA-3 competition organized by NIST aims to find a new hash standard as a replacement of SHA-2. Till now, 14 submissions have been selected as the second round candidates, including Skein and BLAKE, both of which have components based on modular addition, rotation and bitwise XOR (ARX). In this paper, we propose improved near-collision attacks on the reduced-round compression functions of Skein and a variant of BLAKE. The attacks are based on linear differentials of the modular...

We revisit narrow-pipe designs that are in practical use, and their security against preimage attacks. Our results are the best known preimage attacks on Tiger, MD4, and reduced SHA-2, with the result on Tiger being the first cryptanalytic shortcut attack on the full hash function. Our attacks runs in time $2^{188.8}$ for finding preimages, and $2^{188.2}$ for second-preimages. Both have memory requirement of order $2^{8}$, which is much less than in any other recent preimage attacks on...

In this paper, we propose preimage attacks on 41-step SHA-256 and 46-step SHA-512, which drastically increase the number of attacked steps compared to the best previous preimage attack working for only 24 steps. The time complexity for 41-step SHA-256 is $2^{253.5}$ compression function operations and the memory requirement is $2^{16}\times 10$ words. The time complexity for 46-step SHA-512 is $2^{511.5}$ compression function operations and the memory requirement is $2^{3}\times 10$...

In this paper, we present a preimage attack for 42 step-reduced SHA-256 with time complexity $2^{251.7}$ and memory requirements of order $2^{12}$. The same attack also applies to 42 step-reduced SHA-512 with time complexity $2^{502.3}$ and memory requirements of order $2^{22}$. Our attack is meet-in-the-middle preimage attack.

The weakening of the widely used SHA-1 hash function has also cast doubts on the strength of the related algorithms of the SHA-2 family. The US NIST has therefore initiated the SHA-3 competition in order to select a modern hash function algorithm as a ``backup'' for SHA-2. This algorithm should be efficiently implementable both in software and hardware under different constraints. In this paper, we present hardware implementations of the four SHA-3 candidates ARIRANG, BLAKE, Grøstl, and...

This specification describes a modification of a candidate for SHA-3, named MeshHash. The first version had a flaw in it, it was possible to mount a second preimage attack [Tho08]. So MeshHash has not fulfilled the requirements for SHA-3 anymore and hence was conceded broken. Furthermore there was a bug in the reference implementation: The macro for rotation of a word computed an undefined value if it should rotate a word by 0 bit. But since the flaw can be easily fixed, which was already...

In this paper, we analyze the hash functions Dynamic SHA and Dynamic SHA2, which have been selected as first round candidates in the NIST hash function competition. These hash functions rely heavily on data-dependent rotations, similar to certain block ciphers, e.g., RC5. Our analysis suggests that in the case of hash functions, where the attacker has more control over the rotations, this approach is less favorable than in block ciphers. We present practical, or close to practical,...

This is a technical report describing a new hash algorithm called Khichidi-1 and has been written in response to a Hash competition (SHA-3) called by National Institute of Standards and Technology (NIST), USA. This algorithm generates a condensed representation of a message called a Message Digest. A group of functions used in the development of Khichidi-1 is described, followed by a detailed explanation of preprocessing approach. Differences between Khichidi-1 and NIST SHA-2, the algorithm...

In this work, we study several properties of the SHA-2 design which have been utilized in recent collision attacks against reduced round SHA-2. Small modifications to the SHA-2 design are suggested to thwart these attacks. The modified round function provides the same resistance to linearization attacks as the original SHA-2 round function, but, provides better resistance to non-linear attacks. Our next contribution is to introduce the general idea of ``multiple feed-forward" for the...

We perform a combinatorial analysis of SHA-2 compression function. This analysis explains in a unified way the recent attacks against reduced round SHA-2. We start with a general class of local collisions and show that the previously used local collision by Nikolić and Biryukov (NB) and Sanadhya and Sarkar (SS) are special cases. The study also clarifies several advantages of the SS local collision over the NB local collision. Deterministic constructions of up to 22-round SHA-2 collisions...

In this work, we provide new and improved attacks against 22, 23 and 24-step SHA-2 family using a local collision given by Sanadhya and Sarkar (SS) at ACISP '08. The success probability of our 22-step attack is 1 for both SHA-256 and SHA-512. The computational efforts for the 23-step and 24-step SHA-256 attacks are respectively $2^{11.5}$ and $2^{28.5}$ calls to the corresponding step reduced SHA-256. The corresponding values for the 23 and 24-step SHA-512 attack are respectively $2^{16.5}$...

Most of the attacks against (reduced) SHA-2 family in literature have used local collisions which are valid for linearized version of SHA-2 hash functions. Recently, at FSE '08, an attack against reduced round SHA-256 was presented by Nikolić and Biryukov which used a local collision which is valid for the actual SHA-256 function. It is a 9-step local collision which starts by introducing a modular difference of 1 in the two messages. It succeeds with probability roughly 1/3. We build on the...

In this paper I describe the construction of Dynamic SHA-2 family of cryptographic hash functions. They are built with design components from the SHA-2 family, but I use the bits in message as parameters of function G, R and ROTR operation in the new hash functionh. It enabled us to achieve a novel design principle: When message is changed, the calculation will be different. It make the system can resistant against all extant attacks.

In this paper we don't examine security of Turbo SHA-2 completely; we only show new collision attacks on it, with smaller complexity than it was considered by Turbo SHA-2 authors. In [1] they consider Turbo SHA-224/256-r and Turbo SHA-384/512-r with variable number of rounds r from 1 to 8. The authors of [1] show collision attack on Turbo SHA-256-1 with one round which has the complexity of 2^64. For other r from 2 to 8 they don't find better attack than with the complexity of 2^128....

In this paper I describe the construction of Dynamic SHA family of cryptographic hash functions. They are built with design components from the SHA-2 family, but there is function R in the new hash functionh. It enabled us to achieve a novel design principle: When message is changed, different rotate right operation maybe done. It make the system can resistant against all extant attacks.

In this paper we describe the construction of Turbo SHA-2 family of cryptographic hash functions. They are built with design components from the SHA-2 family, but the new hash function has three times more chaining variables, it is more robust and resistant against generic multi-block collision attacks, its design is resistant against generic length extension attacks and it is 2 - 8 times faster than the original SHA-2. It uses two novel design principles in the design of hash functions:...

The starting point for collision attacks on practical hash functions is a local collision. In this paper, we make a systematic study of local collisions for the SHA-2 family. The possible linear approximations of the constituent Boolean functions are considered and certain impossible conditions for such approximations are identified. Based on appropriate approximations, we describe a general method for finding local collisions. Applying this method, we obtain several local collisions and...

A wide-sweeping multi-dimensional analysis and comparison between VEST and the hardware implementations of the AES, AES-HMAC and SHA-2 primitives.

The Secure Hash Standard (SHS) [3] includes hashing algorithms denoted SHA-n, (n in {224, 256, 384, 512}) for producing message digests of length n. These algorithms are based on a common design, sometimes known as SHA-2, that consists of a message schedule and a register. The most successful attacks on the SHA algorithms are Chabaud-Joux differential collisions [1, 2, 4, 5, 7], which are based on finding a corrective pattern for the register. Previous analysis of the SHA-2 algoritms [4]...