Collisions and Semi-Free-Start Collisions for Round-Reduced RIPEMD-160

In this paper, we propose an improved cryptanalysis of the double-branch hash function RIPEMD-160 standardized by ISO/IEC. Firstly, we show how to theoretically calculate the step differential probability of RIPEMD-160, which was stated as an open problem by Mendel $et$ $al.$ at ASIACRYPT 2013. Secondly, based on the method proposed by Mendel $et$ $al.$ to automatically find a differential path of RIPEMD-160, we construct a 30-step differential path where the left branch is sparse and the right branch is controlled as sparse as possible. To ensure the message modification techniques can be applied to RIPEMD-160, some extra bit conditions should be pre-deduced and well controlled. These extra bit conditions are used to ensure that the modular difference can be correctly propagated. This way, we can find a collision of 30-step RIPEMD-160 with complexity $2^{70}$. This is the first collision attack on round-reduced RIPEMD-160. Moreover, by a different choice of the message words to merge two branches and adding some conditions to the starting point, the semi-free-start collision attack on the first 36-step RIPEMD-160 from ASIACRYPT 2013 can be improved. However, the previous way to pre-compute the equation $T^{\lll S_0}\boxplus C_0=(T\boxplus C_1)^{\lll S_1}$ costs too much. To overcome this obstacle, we are inspired by Daum\u27s $et~al$. work on MD5 and describe a method to reduce the time complexity and memory complexity to pre-compute that equation. Combining all these techniques, the time complexity of the semi-free-start collision attack on the first 36-step RIPEMD-160 can be reduced by a factor of $2^{15.3}$ to $2^{55.1}$

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

MOIM: a novel design of cryptographic hash function

A hash function usually has two main components: a compression function or permutation function and mode of operation. In this paper, we propose a new concrete novel design of a permutation based hash functions called MOIM. MOIM is based on concatenating two parallel fast wide pipe constructions as a mode of operation designed by Nandi and Paul, and presented at Indocrypt 2010 where the size of the internal state is significantly larger than the size of the output. And the permutations functions used in MOIM are inspired from the SHA-3 finalist Grøstl hash function which is originally inspired from Rijndael design (AES). As a consequence there is a very strong confusion and diffusion in MOIM. Also, we show that MOIM resists all the generic attacks and Joux attack in two defense security levels

Analysis and Design Security Primitives Based on Chaotic Systems for eCommerce

Security is considered the most important requirement for the success of electronic commerce, which is built based on the security of hash functions, encryption algorithms and pseudorandom number generators. Chaotic systems and security algorithms have similar properties including sensitivity to any change or changes in the initial parameters, unpredictability, deterministic nature and random-like behaviour. Several security algorithms based on chaotic systems have been proposed; unfortunately some of them were found to be insecure and/or slow. In view of this, designing new secure and fast security algorithms based on chaotic systems which guarantee integrity, authentication and confidentiality is essential for electronic commerce development. In this thesis, we comprehensively explore the analysis and design of security primitives based on chaotic systems for electronic commerce: hash functions, encryption algorithms and pseudorandom number generators. Novel hash functions, encryption algorithms and pseudorandom number generators based on chaotic systems for electronic commerce are proposed. The securities of the proposed algorithms are analyzed based on some well-know statistical tests in this filed. In addition, a new one-dimensional triangle-chaotic map (TCM) with perfect chaotic behaviour is presented. We have compared the proposed chaos-based hash functions, block cipher and pseudorandom number generator with well-know algorithms. The comparison results show that the proposed algorithms are better than some other existing algorithms. Several analyses and computer simulations are performed on the proposed algorithms to verify their characteristics, confirming that these proposed algorithms satisfy the characteristics and conditions of security algorithms. The proposed algorithms in this thesis are high-potential for adoption in e-commerce applications and protocols

Analysis of RIPEMD-160: New Collision Attacks and Finding Characteristics with MILP

The hash function RIPEMD-160 is an ISO/IEC standard and is being used to generate the bitcoin address together with SHA-256. Despite the fact that many hash functions in the MD-SHA hash family have been broken, RIPEMD-160 remains secure and the best collision attack could only reach up to 34 out of 80 rounds, which was published at CRYPTO 2019. In this paper, we propose a new collision attack on RIPEMD-160 that can reach up to 36 rounds with time complexity $2^{64.5}$. This new attack is facilitated by a new strategy to choose the message differences and new techniques to simultaneously handle the differential conditions on both branches. Moreover, different from all the previous work on RIPEMD-160, we utilize a MILP-based method to search for differential characteristics, where we construct a model to accurately describe the signed difference transitions through its round function. As far as we know, this is the first model targeting the signed difference transitions for the MD-SHA hash family. Indeed, we are more motivated to design this model by the fact that many automatic tools to search for such differential characteristics are not publicly available and implementing them from scratch is too time-consuming and difficult. Hence, we expect that this can be an alternative easy tool for future research, which only requires to write down some simple linear inequalities

Automating Collision Attacks on RIPEMD-160

As an ISO/IEC standard, the hash function RIPEMD-160 has been used to generate the Bitcoin address with SHA-256. However, due to the complex doublebranch structure of RIPEMD-160, the best collision attack only reaches 36 out of 80 steps of RIPEMD-160, and the best semi-free-start (SFS) collision attack only reaches 40 steps. To improve the 36-step collision attack proposed at EUROCRYPT 2023, we explored the possibility of using different message differences to increase the number of attacked steps, and we finally identified one choice allowing a 40-step collision attack. To find the corresponding 40-step differential characteristic, we re-implement the MILP-based method to search for signed differential characteristics with SAT/SMT. As a result, we can find a colliding message pair for 40-step RIPEMD-160 in practical time, which significantly improves the best collision attack on RIPEMD-160. For the best SFS collision attack published at ToSC 2019, we observe that the bottleneck is the probability of the right-branch differential characteristics as they are fully uncontrolled in the message modification. To address this issue, we utilize our SAT/SMT-based tool to search for high-probability differential characteristics for the right branch. Consequently, we can mount successful SFS collision attacks on 41, 42 and 43 steps of RIPEMD-160, thus significantly improving the SFS collision attacks. In addition, we also searched for a 44-step differential characteristic, but the differential probability is too low to allow a meaningful SFS collision attack

Practical free-start collision attacks on 76-step SHA-1

In this paper we analyze the security of the compression function of SHA-1 against collision attacks, or equivalently free-start collisions on the hash function. While a lot of work has been dedicated to the analysis of SHA-1 in the past decade, this is the first time that free-start collisions have been considered for this function. We exploit the additional freedom provided by this model by using a new start-from-the-middle approach in combination with improvements on the cryptanalysis tools that have been developed for SHA-1 in the recent years. This results in particular in better differential paths than the ones used for hash function collisions so far. Overall, our attack requires about $2^{50}$ evaluations of the compression function in order to compute a one-block free-start collision for a 76-step reduced version, which is so far the highest number of steps reached for a collision on the SHA-1 compression function. We have developed an efficient GPU framework for the highly branching code typical of a cryptanalytic collision attack and used it in an optimized implementation of our attack on recent GTX 970 GPUs. We report that a single cheap US\$ 350 GTX 970 is sufficient to find the collision in less than 5 days. This showcases how recent mainstream GPUs seem to be a good platform for expensive and even highly-branching cryptanalysis computations. Finally, our work should be taken as a reminder that cryptanalysis on SHA-1 continues to improve. This is yet another proof that the industry should quickly move away from using this function