Collision Attack for the Hash Function Extended MD4

Extended MD4 is a hash function proposed by Rivest in 1990 with a 256-bit hash value. The compression function consists of two different and independent parallel lines called Left Line and Right Line, and each line has 48 steps. The initial values of Left Line and Right Line are denoted by IV0 and IV1 respectively. Dobbertin proposed a collision attack for the compression function of Extended MD4 with a complexity of about 240 under the condition that the value for IV0 = IV1 is prescribed. In this paper, we gave a collision attack on the full Extended MD4 with a complexity of about 237. Firstly, we propose a collision differential path for both lines by choosing a proper message difference, and deduce a set of sufficient conditions that ensure the differential path hold. Then by using some precise message modification techniques to improve the success probability of the attack, we find two-block collisions of Extended MD4 with less than 237 computations. This work provides a new reference to the collision analysis of other hash functions such as RIPEMD-160 etc. which consist of two lines.

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