Searching cubes for testing Boolean functions and its application to Trivium

In this paper, we describe a sub-maximal degree monomial test and propose a heuristic algorithm for searching favourable cubes, for testing Boolean functions formed by stream ciphers. We apply them to Trivium, and mount a distinguisher on Trivium reduced to 839 rounds with 2
³⁷
complexity, which is so far the best distinguisher on reduced Trivium.