Improved Key Recovery Attacks on Reduced-Round Salsa20 and ChaCha

Salsa20 is a stream cipher designed by Bernstein in 2005 and Salsa20/12 has been selected into the final portfolio of the eSTREAM Project. ChaCha is a variant of Salsa20 with faster diffusion for similar performance. The previous best results on Salsa20 and ChaCha proposed by Aumasson et al. exploits the differential properties combined with the probabilistic neutral bits (PNB). In this paper, we extend their approach by considering a new type of distinguishers, named (column and row) chaining distinguishers. Besides, we exhibit new high probability second-order differential trails not covered by the previous methods, generalize the notion of PNB to probabilistic neutral vectors (PNV) and show that the set of PNV is no smaller than that of PNB. Based on these findings, we present improved key recovery attacks on reduced-round Salsa20 and ChaCha. Both time and data complexities of our attacks are smaller than those of the best former results.