## Cryptology ePrint Archive: Report 2005/281

Herding Hash Functions and the Nostradamus Attack

Abstract: In this paper, we develop a new attack on Damg{\aa}rd-Merkle hash functions, called the \emph{herding attack}, in which an attacker who can find many collisions on the hash function by brute force can first provide the hash of a message, and later herd'' any given starting part of a message to that hash value by the choice of an appropriate suffix. We introduce a new property which hash functions should have--Chosen Target Forced Prefix (CTFP) preimage resistance--and show the distinction between Damg{\aa}rd-Merkle construction hashes and random oracles with respect to this property. We describe a number of ways that violation of this property can be used in arguably practical attacks on real-world applications of hash functions. An important lesson from these results is that hash functions susceptible to collision-finding attacks, especially brute-force collision-finding attacks, cannot in general be used to prove knowledge of a secret value