Using Automatic Generation of Relaxation Constraints to Improve the Preimage Attack on 39-step MD4

TL;DR

This paper presents an improved SAT-based preimage attack on the MD4-39 hash function by automatically generating relaxation constraints using black-box optimization, leading to more effective attack strategies.

Contribution

It introduces an automatic method for generating relaxation constraints via black-box optimization, enhancing SAT-based preimage attacks on MD4-39.

Findings

New relaxation constraints improve attack success

Automated constraint generation outperforms manual methods

Significant reduction in attack complexity

Abstract

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.