Paper 2021/1400

Three Input Exclusive-OR Gate Support For Boyar-Peralta's Algorithm (Extended Version)

Anubhab Baksi, Vishnu Asutosh Dasu, Banashri Karmakar, Anupam Chattopadhyay, and Takanori Isobe

Abstract

The linear layer, which is basically a binary non-singular matrix, is an integral part of cipher construction in a lot of private key ciphers. As a result, optimising the linear layer for device implementation has been an important research direction for about two decades. The Boyar-Peralta's algorithm (SEA'10) is one such common algorithm, which offers significant improvement compared to the straightforward implementation. This algorithm only returns implementation with XOR2 gates, and is deterministic. Over the last couple of years, some improvements over this algorithm has been proposed, so as to make support for XOR3 gates as well as make it randomised. In this work, we take an already existing improvement (Tan and Peyrin, TCHES'20) that allows randomised execution and extend it to support three input XOR gates. This complements the other work done in this direction (Banik et al., IWSEC'19) that also supports XOR3 gates with randomised execution. Further, noting from another work (Maximov, Eprint'19), we include one additional tie-breaker condition in the original Boyar-Peralta's algorithm. Our work thus collates and extends the state-of-the-art, at the same time offers a simpler interface. We show several results that improve from the lastly best-known results.