Advanced Algebraic Attack on Trivium

Abstract

This paper presents an algebraic attack against Trivium that breaks 625 rounds using only $4096$ bits of output in an overall time complexity of $2^{42.2}$ Trivium computations. While other attacks can do better in terms of rounds ($799$), this is a practical attack with a very low data usage (down from $2^{40}$ output bits) and low computation time (down from $2^{62}$). From another angle, our attack can be seen as a proof of concept: how far can algebraic attacks can be pushed when several known techniques are combined into one implementation? All attacks have been fully implemented and tested; our figures are therefore not the result of any potentially error-prone extrapolation, but results of practical experiments