Preimage Attack Research Articles

New multivariate hash function quadratic polynomials multiplying linear polynomials

In this study the authors propose a new multivariate hash function with HAsh Iterative FrAmework framework which we call the hash function quadratic polynomials multiplying linear polynomials (QML). The new hash function is made of cubic polynomials which are the products of quadratic polynomials and linear polynomials. The authors design the quadratic-polynomial part of the compression function based on the centre map of the multivariate public key cryptosystem Matsumoto-Imai cryptosystem (MI). The hash function QML can keep the three cryptography properties and be immune to the pre-image attack, second pre-image attack, collision attack, differential attack and algebraic attack. The required memory storage is about 50% of the one which is built of the cubic polynomials and their coefficients are random. On the avalanche effect, by experiments the authors get the result that about one half of the output bits are different when one input bit is changed randomly. The one-round diffusion of the hash function QML is twice of that of Blake. Also the authors simplify the matrixes of the new hash function, analyse the rationality and show the comparable data. Finally, the authors give the advice to the parameters of the new hash function and summarise the paper.

Second order collision for the 42-step reduced DHA-256 hash function

At the Cryptographic Hash Workshop hosted by NIST in 2005, Lee et al. proposed the DHA-256 (Double Hash Algorithm-256) hash function. The design of DHA-256 builds upon the design of SHA-256, but introduces additional strengthening features such as optimizing the message expansion and step function against local collision attacks. Previously, DHA-256 was analyzed by J. Zhong and X. Lai, who presented a preimage attack on 35 steps of the compression function with complexity 2239.6. In addition, the IAIK Krypto Group provided evidence that there exists a 9-step local collision for the DHA-256 compression function with probability higher than previously predicted. In this paper, we analyze DHA-256 in the context of higher order differential attacks. In particular, we provide a practical distinguisher for 42 out of 64 steps and give an example of a colliding quartet to validate our results.

A SAT-based preimage analysis of reduced Keccak hash functions

In this paper, we present a preimage attack on reduced versions of Keccak hash functions. We use our recently developed toolkit CryptLogVer for generating the conjunctive normal form, CNF, which is passed to the SAT solver PrecoSAT. We found preimages for some reduced versions of the function and showed that full Keccak function has a comfortable security margin against this kind of attack.

Preimage and pseudo-collision attacks on step-reduced SM3 hash function

SM3 [12] is the Chinese cryptographic hash standard which was announced in 2010 and designed by Wang et al. It is based on the Merkle–Damgård design and its compression function can be seen as a block cipher used in Davies–Meyer mode. It uses message block of length 512 bits and outputs hash value of length 256 bits.This letter studies the security of SM3 hash function against preimage attack and pseudo-collision attack by using the weakness of diffusion process and linear message expansion. We propose preimage attacks on 29-step and 30-step SM3, and pseudo-preimage attacks on 31-step and 32-step SM3 out of 64 steps. The complexities of these attacks are 2245 29-step operations, 2251.1 30-step operations, 2245 31-step operations and 2251.1 32-step operations, respectively. These (pseudo-)preimage attacks are all from the 1-st step of the reduced SM3. Furthermore, these (pseudo-)preimage attacks can be converted into pseudo-collision attacks on SM3 reduced to 29 steps, 30 steps, 31 steps and 32 steps with complexities of 2122, 2125.1, 2122 and 2125.1 respectively. As far as we know, the previously best known preimage attacks on SM3 cover 28 steps (from the 1-st step) and 30 steps (from the 7-th step).

Using carry-truncated addition to analyze add-rotate-xor hash algorithms

We introduce a truncated addition operation on pairs of N-bit binary numbers that interpolates between ordinary addition mod and bitwise addition in . We use truncated addition to analyze hash functions that are built from the bit operations add, rotate, and xor, such as Blake, Skein, and Cubehash. Any ARX algorithm can be approximated by replacing ordinary addition with truncated addition, and we define a metric on such algorithms which we call the sensitivity. This metric measures the smallest approximation agreeing with the full algorithm a statistically useful portion of the time (we use ). Because truncated addition greatly reduces the complexity of the non-linear operation in ARX algorithms, the approximated algorithms are more susceptible to both collision and pre-image attacks, and we outline a potential collision attack explicitly. We particularize some of these observations to the Skein hash function.

Differential Fault Analysis on the MD5 Compression Function

The MD5, proposed by R. Riverst in 1992, is a widely used hash function with Merkle-Damgard structure. In the literature, many studies have been devoted to classical cryptanalysis on the MD5, such as the collision attack, the preimage attack etc. In this paper, we propose a new differential fault analysis on the MD5 compression function in the word-oriented random fault model. The simulating experimental results show that 144 random faults on average are required to obtain the current input message block. Our method not only increases the efficiency of fault injection, but also decreases the number of fault hash values. It provides a new reference for the security analysis of the same structure of the hash compression functions.

Meet-in-the-Middle Preimage Attacks on AES Hashing Modes and an Application to Whirlpool

We study the security of AES in the open-key setting by showing an analysis on hash function modes instantiating AES including Davies-Meyer, Matyas-Meyer-Oseas, and Miyaguchi-Preneel modes. In particular, we propose preimage attacks on these constructions, while most of previous work focused their attention on collision attacks or distinguishers using non-ideal differential properties. This research is based on the motivation that we should evaluate classical and important security notions for hash functions and avoid complicated attack models that seem to have little relevance in practice. We apply a recently developed meet-in-the-middle preimage approach. As a result, we obtain a preimage attack on 7 rounds of Davies-Meyer AES and a second preimage attack on 7 rounds of Matyas-Meyer-Oseas and Miyaguchi-Preneel AES. Considering that the previous best collision attack only can work up to 6 rounds, the number of attacked rounds reaches the best in terms of the classical security notions. In our attacks, the key is regarded as a known constant, and the attacks thus can work for any key length in common.

Meet-in-the-Middle (Second) Preimage Attacks on Two Double- Branch Hash Functions RIPEMD and RIPEMD-128

Even though meet-in-the-middle preimage attack framework has been successfully applied to attack most of narrow-pipe hash functions, it seems difficult to apply this framework to attack double-branch hash functions. Only few results have been published on this research. This paper proposes a refined strategy of applying meet-in-the-middle attack framework to double-branch hash functions. The main novelty is a new local-collision approach named one-message-word local collision. We have applied our strategy to two double-branch hash functions RIPEMD and RIPEMD-128, and obtain the following results.• On RIPEMD. We find a pseudo-preimage attack on 47-step compression function, where the full version has 48 steps, with a complexity of 2119. It can be converted to a second preimage attack on 47-step hash function with a complexity of 2124.5. Moreover, we also improve previous preimage attacks on (intermediate) 35-step RIPEMD, and reduce the complexity from 2113 to 296.• On RIPEMD-128. We find a pseudo-preimage on (intermediate) 36-step compression function, where the full version has 64 steps, with a complexity of 2123. It canl be converted to a preimage attack on (intermediate) 36-step hash function with a complexity of 2126.5.Both RIPEMD and RIPEMD-128 produce 128-bit digests. Therefore our attacks are faster than the brute-force attack, which means that our attacks break the theoretical security bound of the above step-reduced variants of those two hash functions in the sense of (second) preimage resistance. The maximum number of the attacked steps on both those two hash functions is 35 among previous works based to our best knowledge. Therefore we have successfully increased the number of the attacked steps. We stress that our attacks does not break the security of full-version RIPEMD and RIPEMD-128. But the security mergin of RIPEMD becomes very narrow. On the other hand, RIPEMD-128 still has enough security margin.

Preimage Attacks against PKC98-Hash and HAS-V

We propose preimage attacks against PKC98-Hash and HAS-V. PKC98-Hash is a 160-bit hash function proposed at PKC 1998, and HAS-V, a hash function proposed at SAC 2000, can produce hash values of 128+32k (k=0,1,...,6) bits. These hash functions adopt the Merkle-Damgard and Davies-Meyer constructions. One unique characteristic of these hash functions is that their step functions are not injective with a fixed message. We utilize this property to mount preimage attacks against these hash functions. Note that these attacks can work for an arbitrary number of steps. The best proposed attacks generate preimages of PKC98-Hash and HAS-V-320 in 264 and 2256 compression function computations with negligible memory, respectively. This is the first preimage attack against the full PKC98-Hash function.

Meet-in-the-Middle Preimage Attacks on Hash Modes of Generalized Feistel and Misty Schemes with SP Round Function

We assume that the domain extender is the Merkle-Damgård (MD) scheme and he message is padded by a ‘1’, and minimum number of ‘0’s, followed by a fixed size length information so that the length of padded message is multiple of block length. Under this assumption, we analyze securities of the hash mode when the compression function follows the Davies-Meyer (DM) scheme and the underlying block cipher is one of the plain Feistel or Misty scheme or the generalized Feistel or Misty schemes with Substitution-Permutation (SP) round function. We do this work based on Meet-in-the-Middle (MitM) preimage attack techniques, and develop several useful initial structures.

Preimage and Second-Preimage Attacks on PGV Hashing Modes of Round-Reduced ARIA, Camellia, and Serpent

Preimage and Second-Preimage Attacks on PGV Hashing Modes of Round-Reduced ARIA, Camellia, and Serpent

TTradeoff tables for compression functions: how to invert hash values radeoff Tables for Compression Functions: How to Invert Hash Values

Hash functions are one of the ubiquitous cryptographic functions used widely for various applications such as digital signatures, data integrity, authentication protocols, MAC algorithms, RNGs, etc. Hash functions are supposed to be one-way, i.e., preimage resistant. One interesting property of hash functions is that they process arbitrary-length messages into fixed-length outputs. In general, this can be achieved mostly by applying compression functions onto the message blocks of fixed length, recursively. The length of the message is incorporated as padding in the last block prior to the hash, a procedure called the Merkle-Damgard strengthening. In this paper, we introduce a new way to find preimages on a hash function by using a rainbow table of its compression function even if the hash function utilizes the Merkle-Damgard (MD) strengthening as a padding procedure. To overcome the MD strengthening, we identify the column functions as representatives of certain set of preimages, unlike conventional usage of rainbow tables or Hellman tables to invert one-way functions. As a different approach, we use the position of the given value in the table to invert it. The workload of finding a preimage of a given arbitrary digest value is 2^{2n/3} steps by using 2^{2n/3} memory, where n is both the digest size and the length of the chaining value. We give some extensions of the preimage attack on certain improved variants of MD constructions such as using output functions, incorporating the length of message blocks or using random salt values. Moreover, we introduce the notion of ``near-preimage'' and mount an attack to find near-preimages. We generalize the attack when the digest size is not equal to the length of chaining value. We have verified the results experimentally, in which we could find a preimage in one minute for the 40-bit hash function, whereas the exhaustive search took roughly one week on a standard PC.

Improved preimage attack on 3-pass HAVAL

HAVAL is a hash function proposed by Zheng et al. in 1992, including 3-, 4- and 5-pass versions. We improve pseudo-preimage and preimage attacks on 3-pass HAVAL at the complexity of 2172 and 2209.6, respectively, as compared to the previous best known results: 2192 and 2225 by Sasaki et al. in 2008. We extend the skip interval for partial-patching and apply the initial structure technique to find the better message chunks, and combine the indirect-partial-matching, partial-fixing and multi-neutral-word partial-fixing techniques to improve the attacks based on the meet-in-the-middle method. These are the best pseudo-preimage and preimage attacks on 3-pass HAVAL.

Improved preimage attack on one-block MD4

MD4 is a hash function designed by Rivest in 1990. The design philosophy of many important hash functions, such as MD5, SHA-1 and SHA-2, originated from that of MD4. We propose an improved preimage attack on one-block MD4 with the time complexity 295 MD4 compression function operations, as compared to the 210711The time complexity should be 2105.77 according to our analysis, as shown in appendix:MD4-In-SAC08. The detailed computation procedure about how to get the time complexity 2107 was not presented in Sasaki and Aoki, 2008. complexity of the previous attack by Aoki et al. (SAC 2008). The attack is based on previous methods, but introduces new techniques. We also use the same techniques to improve the pseudo-preimage and preimage attacks on Extended MD4 with 225.2 and 212.6 improvement factor, as compared to previous attacks by Sasaki et al. (ACISP 2009).

On the complexity of the herding attack and some related attacks on hash functions

In this article, we analyze the complexity of the construction of the 2 k -diamond structure proposed by Kelsey and Kohno (LNCS, Vol 4004, pp 183–200, 2006). We point out a flaw in their analysis and show that their construction may not produce the desired diamond structure. We then give a more rigorous and detailed complexity analysis of the construction of a diamond structure. For this, we appeal to random graph theory (in particular, to the theory of random intersection graphs), which allows us to determine sharp necessary and sufficient conditions for the message complexity (i.e., the number of hash computations required to build the required structure). We also analyze the computational complexity for constructing a diamond structure, which has not been previously studied in the literature. Finally, we study the impact of our analysis on herding and other attacks that use the diamond structure as a subroutine. Precisely, our results shows the following: Due to the above two results, the herding attack (Kelsey and Kohno, LNCS, Vol 4004, pp 183–200, 2006) and the second preimage attack (Andreeva et al., LNCS, Vol 4965, pp 270–288, 2008) on iterated hash functions have increased complexity. We also show that the message complexity of herding and second preimage attacks on “hash twice” is n times the complexity claimed by Andreeva et al. (LNCS, Vol 5867, pp 393–414, 2009), by giving a more detailed analysis of the attack.

Preimage Attack on 23-Step Tiger

This paper evaluates the preimage resistance of the Tiger hash function. To our best knowledge, the maximum number of the attacked steps is 17 among previous preimage attacks on Tiger, where the full version has 24 steps. Our attack will extend the number of the attacked steps to 23. The main contribution is a pseudo-preimage attack on the compression function up to 23 steps with a complexity of 2181 following the meet-in-the-middle approach. This attack can be converted to a preimage attack on 23-step Tiger hash function with a complexity of 2187.5. The memory requirement of our attack is 222 words. A Tiger digest has 192bits. Therefore, our attacks are faster than the exhaustive search.

On the Full MAC Security of a Double-Piped Mode of Operation

We revisit the double-pipe construction introduced by Lucks at Asiacrypt 2005. Lucks originally studied the construction for iterated hash functions and showed that the approach is effective in improving security against various types of collision and (second-)preimage attacks. Instead, in this paper we apply the construction to the secret-key setting, where the underlying FIL (fixed-input-length) compression function is equipped with a dedicated key input. We make some adjustments to Lucks' original design so that now the new mode works with a single key and operates as a domain extension of MACs (message authentication codes). Though more than twice as slow as the Merkle-Damgard construction, the double-piped mode enjoys security strengthened beyond the birthday bound. More specifically, when iterating an FIL-MAC whose output size is n-bit, the new double-piped mode yields an AIL-(arbitrary-input-length-)MAC with security up to O(2n) query complexity. This bound contrasts sharply with the birthday bound of O(2n/2), which was the best MAC security accomplished by earlier constructions.

Free-starting preimage attacks on BLAKE-32

As one of SHA-3 candidate algorithms for the second round competition BLAKE adopts local wide-pipe technology and improved MD iteration structure.Its core is the core of Chacha cipher algorithm and its security has not been proved.By analyzing the structure and the characteristics of message permutation three rounds free-starting preimage attack could be applied to BLAKE by using splice-and-subsection technology.The result shows that the designing deficiency of message permutation affects the security of BLAKE algorithm.

TWISTERπ – a framework for secure and fast hash functions

In this paper we present TWISTER π, a framework for hash functions. It is an improved version of TWISTER, a candidate of the NIST SHA-3 hash function competition. TWISTER π is built upon the ideas of wide pipe and sponge functions. The core of this framework is a – very easy to analyse – Twister-Round providing both extremely fast diffusion as well as collision-freeness for one internal Twister-Round. The total security level is claimed to be not below 2 n/2 for collision attacks and 2 n for (2nd) pre-image attacks. TWISTER π instantiations are secure against all known generic attacks. We also propose two instances TWISTER π-n for hash output sizes n = 256 and n = 512. These instantiations are highly optimised for 64-bit architectures and run very fast in hardware and software, e.g TWISTER π-256 is faster than SHA2-256 on 64-bit platforms and TWISTER π-512 is faster than SHA2-512 on 32-bit platforms. Furthermore, TWISTER π scales very well on low-end platforms.

EPC: A Provably Secure Permutation Based Compression Function

The security of permutation-based hash functions in the ideal permutation model has been studied when the input-length of compression function is larger than the input-length of the permutation function. In this paper, we consider permutation based compression functions that have input lengths shorter than that of the permutation. Under this assumption, we propose a permutation based compression function and prove its security with respect to collision and (second) preimage attacks in the ideal permutation model. The proposed compression function can be seen as a generalization of the compression function of MD6 hash function.