MD4 is Not One-Way

MD4 is a hash function introduced by Rivest in 1990. It is still used in some contexts, and the most commonly used hash function (MD5, SHA-1, SHA-2) are based on the design principles of MD4. MD4 has been extensively studied and very efficient collision attacks are known, but it is still believed to be a one-way function. In this paper we show a partial pseudo-preimage attack on the compression function of MD4, using some ideas from previous cryptanalysis of MD4. We can choose 64 bits of the output for the cost of 2 compression function computations (the remaining bits are randomly chosen by the preimage algorithm). This gives a preimage attack on the compression function of MD4 with complexity 2, and we extend it to an attack on the full MD4 with complexity 2. As far as we know this is the first preimage attack on a member of the MD4 family.