Cryptanalysis of Double-Block-Length Hash Mode MJH

A double-block-length (DBL) hash mode of block ciphers, MJH has been proved to be collision-resistant in the ideal cipher model upto 22n/3−log n queries. In this paper we provide first cryptanalytic results for MJH. We show that a collision attack on MJH has the time complexity below the birthday bound. When block ciphers with 128-bit blocks are used, it has time complexity around 2, which is to be compared to the birthday attack having complexity 2. We also give a preimage attack on MJH. It has the time complexity of 2 with n-bit block ciphers, which is to be compared to the brute force attack having complexity 2.