Collision Resistance from Multi-collision Resistance

IF 2.2 3区计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Journal of Cryptology Pub Date : 2024-03-06 DOI:10.1007/s00145-024-09495-5

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Abstract

Collision-resistant hash functions ( \(\textsf{CRH}\) ) are a fundamental and ubiquitous cryptographic primitive. Several recent works have studied a relaxation of \(\textsf{CRH}\) called t-way multi-collision-resistant hash functions ( \(t\text {-}\textsf{MCRH}\) ). These are families of functions for which it is computationally hard to find a t-way collision, even though such collisions are abundant (and even \((t-1)\) -way collisions may be easy to find). The case of \(t=2\) corresponds to standard \(\textsf{CRH}\) , but it is natural to study t- \(\textsf{MCRH}\) for larger values of t. Multi-collision resistance seems to be a qualitatively weaker property than standard collision resistance. Nevertheless, in this work we show a non-blackbox transformation of any moderately shrinking t- \(\textsf{MCRH}\) , for \(t \in \{3,4\}\) , into an (infinitely often secure) \(\textsf{CRH}\) . This transformation is non-constructive—we can prove the existence of a \(\textsf{CRH}\) but cannot explicitly point out a construction. Our result partially extends to larger values of t. In particular, we show that for suitable values of \(t>t'\) , we can transform a t- \(\textsf{MCRH}\) into a \(t'\) - \(\textsf{MCRH}\) , at the cost of reducing the shrinkage of the resulting hash function family and settling for infinitely often security. This result utilizes the list-decodability properties of Reed–Solomon codes.

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从多重防撞功能到防撞功能

摘要抗碰撞哈希函数（Collision-resistant hash functions）是一种基本的、无处不在的密码原语。最近的一些著作研究了 \(\textsf{CRH}\) 的一种松弛，称为 t-way 多重抗碰撞哈希函数（ \(t\text {-}\textsf{MCRH}\) ）。这些函数族在计算上很难找到 t 路碰撞，尽管这种碰撞非常多（甚至 \((t-1)\)-向碰撞也很容易找到）。t=2）的情况对应于标准的（textsf{CRH}），但对于更大的t值，研究t-（textsf{MCRH}）是很自然的。尽管如此，在这项工作中，我们展示了对于 \(t \in \{3,4\}\)，任何适度收缩的 t- \(\textsf{MCRH}\)的非黑箱变换，并将其转化为（无限次安全的） \(\textsf{CRH}\)。这种转换是非构造性的--我们可以证明一个\(\textsf{CRH}\)的存在，但不能明确指出一个构造。我们的结果部分扩展到了更大的 t 值。特别是，我们证明了对于合适的 \(t>t'\)值，我们可以将一个 t- \(\textsf{MCRH}\)转换成一个 \(t'\) - \(\textsf{MCRH}\)，代价是减少由此产生的哈希函数族的收缩率，并满足无限频繁的安全性。这一结果利用了里德-所罗门码的列表可解码特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Cryptology 工程技术-工程：电子与电气

CiteScore

7.10

自引率

3.30%

发文量

审稿时长

18 months

期刊介绍： The Journal of Cryptology is a forum for original results in all areas of modern information security. Both cryptography and cryptanalysis are covered, including information theoretic and complexity theoretic perspectives as well as implementation, application, and standards issues. Coverage includes such topics as public key and conventional algorithms and their implementations, cryptanalytic attacks, pseudo-random sequences, computational number theory, cryptographic protocols, untraceability, privacy, authentication, key management and quantum cryptography. In addition to full-length technical, survey, and historical articles, the journal publishes short notes.

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