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 $2^{55.1}$

Comparison of hash function algorithms against attacks: a review

Hash functions are considered key components of nearly all cryptographic protocols, as well as of many security applications such as message authentication codes, data integrity, password storage, and random number generation. Many hash function algorithms have been proposed in order to ensure authentication and integrity of the data, including MD5, SHA-1, SHA-2, SHA-3 and RIPEMD. This paper involves an overview of these standard algorithms, and also provides a focus on their limitations against common attacks. These study shows that these standard hash function algorithms suffer collision attacks and time inefficiency. Other types of hash functions are also highlighted in comparison with the standard hash function algorithm in performing the resistance against common attacks. It shows that these algorithms are still weak to resist against collision attacks

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

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 double-branch 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

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

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

2-Dimension Sums: Distinguishers Beyond Three Rounds of RIPEMD-128 and RIPEMD-160

This paper presents differential-based distinguishers against ISO standard hash functions RIPEMD-128 and RIPEMD-160. The compression functions of RIPEMD-128/-160 adopt the double-branch structure, which updates a chaining variable by computing two functions and merging their outputs. Due to the double size of the internal state and difficulties of controlling two functions simultaneously, only few results were published before. In this paper, second-order differential paths are constructed on reduced RIPEMD-128 and -160. This leads to a practical 4-sum attack on 47 steps (out of 64 steps) of RIPEMD-128 and 40 steps (out of 80 steps) of RIPEMD-160. We then extend the distinguished property from the 4-sum to other properties, which we call \emph{a 2-dimension sum} and \emph{a partial 2-dimension sum}. As a result, the practical partial 2-dimension sum is generated on 48 steps of RIPEMD-128 and 42 steps of RIPEMD-160, with a complexity of $2^{35}$ and $2^{36}$, respectively. Theoretically, $2$-dimension sums are generated faster than the exhaustive search up to 52 steps of RIPEMD-128 and 51 steps of RIPEMD-160, with a complexity of $2^{101}$ and $2^{158}$, respectively. The practical attacks are implemented, and examples of generated (partial) 2-dimension sums are presented

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

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