On the Complexity of the Herding Attack and Some Related Attacks on Hash Functions

In this paper, we analyze the complexity of the construction of the $2^k$-diamond structure proposed by Kelsey and Kohno. 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 {\it message complexity} (i.e., the number of hash computations required to build the required structure). We also analyze the {\it 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: \begin{enumerate} \item The message complexity for the construction of a diamond structure is $\sqrt{k}$ times more than the amount previously stated in literature. \item The time complexity is $n$ times the message complexity, where $n$ is the size of hash value. \end{enumerate} Due to the above two results, the herding attack~\cite{KK06} and the second preimage attack~\cite{ABFHKSZ08} on iterated hash functions have increased complexity. We also show that the message complexity of herding and second preimage attacks on ``hash twice\u27\u27 is $n$ times the complexity claimed by~\cite{ABDK09}, by giving a more detailed analysis of the attack

On hash functions using checksums

We analyse the security of iterated hash functions that compute an input dependent checksum which is processed as part of the hash computation. We show that a large class of such schemes, including those using non-linear or even one-way checksum functions, is not secure against the second preimage attack of Kelsey and Schneier, the herding attack of Kelsey and Kohno and the multicollision attack of Joux. Our attacks also apply to a large class of cascaded hash functions. Our second preimage attacks on the cascaded hash functions improve the results of Joux presented at Crypto’04. We also apply our attacks to the MD2 and GOST hash functions. Our second preimage attacks on the MD2 and GOST hash functions improve the previous best known short-cut second preimage attacks on these hash functions by factors of at least 226 and 254, respectively. Our herding and multicollision attacks on the hash functions based on generic checksum functions (e.g., one-way) are a special case of the attacks on the cascaded iterated hash functions previously analysed by Dunkelman and Preneel and are not better than their attacks. On hash functions with easily invertible checksums, our multicollision and herding attacks (if the hash value is short as in MD2) are more efficient than those of Dunkelman and Preneel

Generic attacks on iterated hash functions

Includes bibliographical references (leaves 126-132).We survery the existing generic attacks on hash functions based on the Merkle­Damgard construction: that is, attacks in which the compression function is treated as a black box

Generic Attacks on Hash Functions

The subject of this thesis is a security property of hash functions, called chosen-target forced-prefix preimage (CTFP) resistance and the generic attack on this property, called the herding attack. The study of CTFP resistance started when Kelsey-Kohno introduced a new data structure, called a diamond structure, in order to show the strength of a CTFP resistance property of a hash function. In this thesis, we concentrate on the complexity of the diamond structure and its application in the herding attack. We review the analysis done by Kelsey and Kohno and point out a subtle flaw in their analysis. We propose a correction of their analysis and based on our revised analysis, calculate the message complexity and the computational complexity of the generic attacks that are based on the diamond structure. As an application of the diamond structure on generic attacks, we propose a multiple herding attack on a special generalization of iterated hash functions, proposed by Nandi-Stinson

New Second Preimage Attacks on Dithered Hash Functions with Low Memory Complexity

Dithered hash functions were proposed by Rivest as a method to mitigate second preimage attacks on Merkle-Damgard hash functions. Despite that, second preimage attacks against dithered hash functions were proposed by Andreeva et al. One issue with these second preimage attacks is their huge memory requirement in the precomputation and the online phases. In this paper, we present new second preimage attacks on the dithered Merkle-Damgard construction. These attacks consume significantly less memory in the online phase (with a negligible increase in the online time complexity) than previous attacks. For example, in the case of MD5 with the Keranen sequence, we reduce the memory complexity from about 2^51 blocks to about 2^26.7 blocks (about 545 MB). We also present an essentially memoryless variant of Andreeva et al. attack. In case of MD5-Keranen or SHA1-Keranen, the offline and online memory complexity is 2^15.2 message blocks (about 188–235 KB), at the expense of increasing the offline time complexity

Quantum Attacks on Hash Constructions with Low Quantum Random Access Memory

At ASIACRYPT 2022, Benedikt, Fischlin, and Huppert proposed the quantum herding attacks on iterative hash functions for the first time. Their attack needs exponential quantum random access memory (qRAM), more precisely {$2^{0.43n}$} quantum accessible classical memory (QRACM). As the existence of large qRAM is questionable, Benedikt et al. leave an open question on building low-qRAM quantum herding attacks. In this paper, we answer this open question by building a quantum herding attack, where the time complexity is slightly increased from Benedikt et al.\u27s $2^{0.43n}$ to ours $2^{0.46n}$, but {it does not need qRAM anymore (abbreviated as no-qRAM)}. Besides, we also introduce various low-qRAM {or no-qRAM} quantum attacks on hash concatenation combiner, hash XOR combiner, Hash-Twice, and Zipper hash functions

Evaluating the Security of Merkle-Damgård Hash Functions and Combiners in Quantum Settings

In this work, we evaluate the security of Merkle-Damgård (MD) hash functions and their combiners (XOR and concatenation combiners) in quantum settings. Two main quantum scenarios are considered, including the scenario where a substantial amount of cheap quantum random access memory (qRAM) is available and where qRAM is limited and expensive to access. We present generic quantum attacks on the MD hash functions and hash combiners, and carefully analyze the complexities under both quantum scenarios. The considered securities are fundamental requirements for hash functions, including the resistance against collision and (second-)preimage. The results are consistent with the conclusions in the classical setting, that is, the considered resistances of the MD hash functions and their combiners are far less than ideal, despite the significant differences in the expected security bounds between the classical and quantum settings. Particularly, the generic attacks can be improved significantly using quantum computers under both scenarios. These results serve as an indication that classical hash constructions require careful security re-evaluation before being deployed to the post-quantum cryptography schemes

07021 Abstracts Collection -- Symmetric Cryptography

From .. to .., the Dagstuhl Seminar 07021 ``Symmetric Cryptography\u27\u27 automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available