## Cryptology ePrint Archive: Report 2021/1016

Quantum collision finding for homomorphic hash functions

Juan Carlos Garcia-Escartin and Vicent Gimeno and Julio José Moyano-Fernández

Abstract: Hash functions are a basic cryptographic primitive. Certain hash functions try to prove security against collision and preimage attacks by reductions to known hard problems. These hash functions usually have some additional properties that allow for that reduction. Hash functions which are additive or multiplicative are vulnerable to a quantum attack using the hidden subgroup problem algorithm for quantum computers. Using a quantum oracle to the hash, we can reconstruct the kernel of the hash function, which is enough to find collisions and second preimages. When the hash functions are additive with respect to the group operation in an Abelian group, there is always an efficient implementation of this attack. We present concrete attack examples to provable hash functions, including a preimage attack to $\oplus$-linear hash functions and for certain multiplicative homomorphic hash schemes.

Category / Keywords: foundations / hash functions; quantum attacks; collisions; hidden subgroup problem

Date: received 2 Aug 2021, last revised 9 Aug 2021

Contact author: juagar at tel uva es

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