## Cryptology ePrint Archive: Report 2019/459

From Collisions to Chosen-Prefix Collisions - Application to Full SHA-1

Gaëtan Leurent and Thomas Peyrin

Abstract: A chosen-prefix collision attack is a stronger variant of a collision attack, where an arbitrary pair of challenge prefixes are turned into a collision. Chosen-prefix collisions are usually significantly harder to produce than (identical-prefix) collisions, but the practical impact of such an attack is much larger. While many cryptographic constructions rely on collision-resistance for their security proofs, collision attacks are hard to turn into a break of concrete protocols, because the adversary has limited control over the colliding messages. On the other hand, chosen-prefix collisions have been shown to break certificates (by creating a rogue CA) and many internet protocols (TLS, SSH, IPsec).

In this article, we propose new techniques to turn collision attacks into chosen-prefix collision attacks. Our strategy is composed of two phases: first, a birthday search that aims at taking the random chaining variable difference (due to the chosen-prefix model) to a set of pre-defined target differences. Then, using a multi-block approach, carefully analysing the clustering effect, we map this new chaining variable difference to a colliding pair of states using techniques developed for collision attacks.

We apply those techniques to MD5 and SHA1, and obtain improved attacks. In particular, we have a chosen-prefix collision attack against SHA1 with complexity between $2^{66.9}$ and $2^{69.4}$ (depending on assumptions about the cost of finding near-collision blocks), while the best-known attack has complexity $2^{77.1}$. This is within a small factor of the complexity of the classical collision attack on SHA1 (estimated as $2^{64.7}$). This represents yet another warning that industries and users have to move away from using SHA1 as soon as possible.

Category / Keywords: secret-key cryptography / hash function, cryptanalysis, chosen-prefix collision, SHA1, MD5

Original Publication (with minor differences): IACR-EUROCRYPT-2019

Date: received 6 May 2019, last revised 22 May 2019

Contact author: gaetan leurent at inria fr,thomas peyrin@ntu edu sg

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2019/459

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