Speeding Up the Search Algorithm for the Best Differential and Best Linear Trails

Abstract

For judging the resistance of a block cipher to differential cryptanalysis or linear cryptanalysis it is necessary to establish an upper bound on the probability of the best differential or the bias of the best linear approximation. However, getting a tight upper bound is not a trivial problem. We attempt it by searching for the best differential and the best linear trails, which is a challenging task in itself. Based on some previous works, new strategies are proposed to speed up the search algorithm, which are called starting from the narrowest point, concretizing and grouping search patterns, and trialling in minimal changes order strategies. The efficiency of the resulting improved algorithms allows us to state that the probability (bias) of the best 4-round differential (linear) trail in NOEKEON is $$2^{-51}$$ ( $$2^{-25}$$ ) and the probability (bias) of the best 10-round (11-round) differential (linear) trail is at most $$2^{-131}$$ ( $$2^{-71}$$ ). For SPONGENT, the best differential trails for certain number of rounds in the permutation functions with width $$b\in \{88, 136, 176, 240\}$$ are found. That allows us to update some results presented by its designers.