Using Automatic Generation of Relaxation Constraints to Improve the Preimage Attack on 39-step MD4
This work addresses a specific cryptographic security problem for hash function analysis, representing an incremental improvement over prior attacks.
The authors tackled the problem of finding preimages for the MD4-39 hash function by introducing relaxation constraints to simplify equations, which were then solved using SAT solvers. They developed an automatic method to generate these constraints, resulting in a preimage attack that significantly outperforms existing competition.
In this paper we construct preimage attack on the truncated variant of the MD4 hash function. Specifically, we study the MD4-39 function defined by the first 39 steps of the MD4 algorithm. We suggest a new attack on MD4-39, which develops the ideas proposed by H. Dobbertin in 1998. Namely, the special relaxation constraints are introduced in order to simplify the equations corresponding to the problem of finding a preimage for an arbitrary MD4-39 hash value. The equations supplemented with the relaxation constraints are then reduced to the Boolean Satisfiability Problem (SAT) and solved using the state-of-the-art SAT solvers. We show that the effectiveness of a set of relaxation constraints can be evaluated using the black-box function of a special kind. Thus, we suggest automatic method of relaxation constraints generation by applying the black-box optimization to this function. The proposed method made it possible to find new relaxation constraints that contribute to a SAT-based preimage attack on MD4-39 which significantly outperforms the competition.