Algebraic Attacks on the Encryption Scheme HADESMiMC

Abstract

HADESMiMC is a recent symmetric cryptographic algorithm working with elements in a finite field. It is proposed as a candidate cipher for secure data transfers using Multiparty Computation (MPC). MPC is particularly useful when multiple parties want to do shared computations without having to reveal their data to each other. As HADESMiMC is a fairly new algorithm, the work regarding cryptanalysis is very limited. The goal of this thesis is to perform algebraic attacks on polynomial systems modelled from HADESMiMC by computing a Gröbner basis using the F4 algorithm. In the analysis, the optimal guessed variables for best overall performance for solving the modelled polynomial systems are identified. This leads to lower time complexity heavily dependent on the highest computational degree in the F4 algorithm. Further, the different degree estimates are evaluated, and an alternative polynomial modelling leading to significant speedups and memory reductions is discovered.