Branching Heuristics in Differential Collision Search with Applications to SHA-512

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 approach to find differential characteristics and conforming message pairs. Experiments show that for smaller problems like 27 steps of SHA-512, the heuristic can also speed up the collision search by a factor of $2^{20}$

CDCL(Crypto) and Machine Learning based SAT Solvers for Cryptanalysis

Over the last two decades, we have seen a dramatic improvement in the efficiency of conflict-driven clause-learning Boolean satisfiability (CDCL SAT) solvers over industrial problems from a variety of applications such as verification, testing, security, and AI. The availability of such powerful general-purpose search tools as the SAT solver has led many researchers to propose SAT-based methods for cryptanalysis, including techniques for finding collisions in hash functions and breaking symmetric encryption schemes. A feature of all of the previously proposed SAT-based cryptanalysis work is that they are \textit{blackbox}, in the sense that the cryptanalysis problem is encoded as a SAT instance and then a CDCL SAT solver is invoked to solve said instance. A weakness of this approach is that the encoding thus generated may be too large for any modern solver to solve it efficiently. Perhaps a more important weakness of this approach is that the solver is in no way specialized or tuned to solve the given instance. Finally, very little work has been done to leverage parallelism in the context of SAT-based cryptanalysis. To address these issues, we developed a set of methods that improve on the state-of-the-art SAT-based cryptanalysis along three fronts. First, we describe an approach called \cdcl (inspired by the CDCL($T$) paradigm) to tailor the internal subroutines of the CDCL SAT solver with domain-specific knowledge about cryptographic primitives. Specifically, we extend the propagation and conflict analysis subroutines of CDCL solvers with specialized codes that have knowledge about the cryptographic primitive being analyzed by the solver. We demonstrate the power of this framework in two cryptanalysis tasks of algebraic fault attack and differential cryptanalysis of SHA-1 and SHA-256 cryptographic hash functions. Second, we propose a machine-learning based parallel SAT solver that performs well on cryptographic problems relative to many state-of-the-art parallel SAT solvers. Finally, we use a formulation of SAT into Bayesian moment matching to address heuristic initialization problem in SAT solvers

SAT-based preimage attacks on SHA-1

Hash functions are important cryptographic primitives which map arbitrarily long messages to fixed-length message digests in such a way that: (1) it is easy to compute the message digest given a message, while (2) inverting the hashing process (e.g. finding a message that maps to a specific message digest) is hard. One attack against a hash function is an algorithm that nevertheless manages to invert the hashing process. Hash functions are used in e.g. authentication, digital signatures, and key exchange. A popular hash function used in many practical application scenarios is the Secure Hash Algorithm (SHA-1). In this thesis we investigate the current state of the art in carrying out preimage attacks against SHA-1 using SAT solvers, and we attempt to find out if there is any room for improvement in either the encoding or the solving processes. We run a series of experiments using SAT solvers on encodings of reduced-difficulty versions of SHA-1. Each experiment tests one aspect of the encoding or solving process, such as e.g. determining whether there exists an optimal restart interval or determining which branching heuristic leads to the best average solving time. An important part of our work is to use statistically sound methods, i.e. hypothesis tests which take sample size and variation into account. Our most important result is a new encoding of 32-bit modular addition which significantly reduces the time it takes the SAT solver to find a solution compared to previously known encodings. Other results include the fact that reducing the absolute size of the search space by fixing bits of the message up to a certain point actually results in an instance that is harder for the SAT solver to solve. We have also identified some slight improvements to the parameters used by the heuristics of the solver MiniSat; for example, contrary to assertions made in the literature, we find that using longer restart intervals improves the running time of the solver

New Records in Collision Attacks on RIPEMD-160 and SHA-256

RIPEMD-160 and SHA-256 are two hash functions used to generate the bitcoin address. In particular, RIPEMD-160 is an ISO/IEC standard and SHA-256 has been widely used in the world. Due to their complex designs, the progress to find (semi-free-start) collisions for the two hash functions is slow. Recently at EUROCRYPT 2023, Liu et al. presented the first collision attack on 36 steps of RIPEMD-160 and the first MILP-based method to find collision-generating signed differential characteristics. We continue this line of research and implement the MILP-based method with a SAT/SMT-based method. Furthermore, we observe that the collision attack on RIPEMD-160 can be improved to 40 steps with different message differences. We have practically found a colliding message pair for 40-step RIPEMD-160 in 16 hours with 115 threads. Moreover, we also report the first semi-free-start (SFS) colliding message pair for 39-step SHA-256, which can be found in about 3 hours with 120 threads. These results update the best (SFS) collision attacks on RIPEMD-160 and SHA-256. Especially, we have made some progress on SHA-256 since the last update on (SFS) collision attacks on it at EUROCRYPT 2013, where the first practical SFS collision attack on 38-step SHA-256 was found

Analysis of SHA-512/224 and SHA-512/256

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 sophisticated search tools. We are able to generate practical examples of free-start collisions for 44-step SHA-512/224 and 43-step SHA-512/256. Thus, the truncation performed by these variants on their larger state allows us to attack several more rounds compared to the untruncated family members. In addition, we improve upon the best published collisions for 24-step SHA-512 and present practical collisions for 27 steps of SHA-512/224, SHA-512/256, and SHA-512

New Records in Collision Attacks on SHA-2

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 family. First, we observe from many existing attacks on SHA-2 that the current advanced tool to search for SHA-2 characteristics has reached the bottleneck. Specifically, longer differential characteristics could not be found, and this causes that the collision attack could not reach more steps. To address this issue, we adopt Liu et al.’s MILP-based method and implement it with SAT/SMT for SHA-2, where we also add more techniques to detect contradictions in SHA-2 characteristics. This answers an open problem left in Liu et al.’s paper to apply the technique to SHA-2. With this SAT/SMT-based tool, we search for SHA-2 charac- teristics by controlling its sparsity in a dedicated way. As a result, we successfully find the first practical semi-free-start (SFS) colliding message pair for 39-step SHA-256, improving the best 38-step SFS collision attack published at EUROCRYPT 2013. In addition, we also report the first practical free-start (FS) collision attack on 40-step SHA-224, while the previously best theoretic 40-step attack has time complexity 2110. More- over, for the first time, we can mount practical and theoretic collision attacks on 28-step and 31-step SHA-512, respectively, which improve the best collision attack only reaching 27 steps of SHA-512 at ASIACRYPT 2015. In a word, with new techniques to find SHA-2 characteristics, we have made some notable progress in the analysis of SHA-2 after the major achievements made at EUROCRYPT 2013 and ASIACRYPT 2015

Quantum Collision Attacks on Reduced SHA-256 and SHA-512

In this paper, we study dedicated quantum collision attacks on SHA-256 and SHA-512 for the first time. The attacks reach 38 and 39 steps, respectively, which significantly improve the classical attacks for 31 and 27 steps. Both attacks adopt the framework of the previous work that converts many semi-free-start collisions into a 2-block collision, and are faster than the generic attack in the cost metric of time-space tradeoff. We observe that the number of required semi-free-start collisions can be reduced in the quantum setting, which allows us to convert the previous classical 38 and 39 step semi-free-start collisions into a collision. The idea behind our attacks is simple and will also be applicable to other cryptographic hash functions

Logical Reasoning to Detect Weaknesses About SHA-1 and MD4/5

In recent years, studies about the SATisfiability Problem (short for SAT) were more and more numerous because of its conceptual simplicity and ability to express a large set of various problems. Within a practical framework, works highlighting SAT impli- cations in real world problems had grown significantly. In this way, a new field called logical cryptanalysis appears in the 2000s and consists in an algebraic cryptanalysis in a binary context thanks to SAT solving. This paper deals with this concept applied to cryptographic hash functions. We first present the logical cryptanalysis principle, and provide details about our encoding approach. In a second part, we put the stress on the contribution of SAT to analyze the generated problem thanks to the discover of logical inferences and so simplifications in order to reduce the computational complexity of the SAT solving. This is mainly realized thanks to the use as a preprocessor of learning and pruning techniques from the community. Third, thanks to a probabilistic reasoning applied on the formulas, we present a weakness based on the use of round constants to detect probabilistic relations as implications or equivalences between certain vari- ables. Finally, we present a practical framework to exploit these weaknesses through the inversions of reduced-step versions of MD4, MD5, SHA-0 and SHA-1 and open some prospects

Preimages for SHA-1

This research explores the problem of finding a preimage — an input that, when passed through a particular function, will result in a pre-specified output — for the compression function of the SHA-1 cryptographic hash. This problem is much more difficult than the problem of finding a collision for a hash function, and preimage attacks for very few popular hash functions are known. The research begins by introducing the field and giving an overview of the existing work in the area. A thorough analysis of the compression function is made, resulting in alternative formulations for both parts of the function, and both statistical and theoretical tools to determine the difficulty of the SHA-1 preimage problem. Different representations (And- Inverter Graph, Binary Decision Diagram, Conjunctive Normal Form, Constraint Satisfaction form, and Disjunctive Normal Form) and associated tools to manipulate and/or analyse these representations are then applied and explored, and results are collected and interpreted. In conclusion, the SHA-1 preimage problem remains unsolved and insoluble for the foreseeable future. The primary issue is one of efficient representation; despite a promising theoretical difficulty, both the diffusion characteristics and the depth of the tree stand in the way of efficient search. Despite this, the research served to confirm and quantify the difficulty of the problem both theoretically, using Schaefer's Theorem, and practically, in the context of different representations