TinyECCK16: An efficient field multiplication algorithm on 16-bit environment and its application to Tmote Sky sensor motes

Recently, the result of TinyECCK (Tiny Elliptic Curve Cryptosystem with Koblitz curve) shows that both field multiplication and reduction over GF(2 ^m) are related to a heavy amount of duplicated memory accesses and that reducing the number of these duplications noticeably improves the performance of elliptic curve operations such as scalar multiplications, signing and verification. However, in case that the underlying word size is extended from 8-bit to 16-bit or 32-bit, the efficiency of the techniques proposed in TinyECCK is decreased because the number of memory accesses to load or store an element in GF(2^m) is significantly reduced. Therefore, in this paper, we propose a technique which makes left-to-right (ltr) comb method which is widely used as an efficient multiplication algorithm over GF(2m) suitable for extended word sizes and present TinyECCK16 (Tiny Elliptic Curve Cryptosystem with Koblitz curve on 16-bit word) which is implemented with the proposed multiplication algorithm on 16-bit Tmote Sky mote. The proposed algorithm is faster than typical ltr comb method by 15.06% and the 16-bit version of the algorithm proposed in TinyECCK by 5.12% over GF(2¹⁶³).