Advanced Algebraic Attack on Trivium

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 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 output bits) and low computation time (down from 2). 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.