Security of Cyclic Double Block Length Hash Functions

Abstract. We provide the first proof of security for Abreast-DM, one of the oldest and most wellknown constructions for turning a block cipher with n-bit block length and 2n-bit key length into a 2n-bit cryptographic hash function. In particular, we prove that when Abreast-DM is instantiated with AES-256, i.e. a block cipher with 128-bit block length and 256-bit key length, any adversary that asks less than 2124.42 queries cannot find a collision with success probability greater than 1/2. Surprisingly, this about 15 years old construction is one of the few constructions that have the desirable feature of a near-optimal collision resistance guarantee. We generalize our techniques used in the proof of Abreast-DM to a huge class of double block length (DBL) hash functions that we will call cyclic. Using this generalized theorem we are able to derive several DBL constructions that lead to compression functions that even have a higher security guarantee and are more efficient than Abreast...

• Type: Conference
• Year: 2009
• Where: IMA
• Authors: Ewan Fleischmann, Michael Gorski, Stefan Lucks
• Keywords: Block Cipher, Block Length, Cryptography, IMA 2009, Key Length