International Association
for Cryptologic Research

This paper presents an efficient and side channel protected software implementation of point multiplication for the standard NIST and SECG binary elliptic curves. The enhanced performance is achieved by improving the L\\`{o}pez-Dahab/Montgomery method at the algorithmic level, and by leveraging Intel\'s AVX architecture and the pclmulqdq processor instruction at the coding level.

The fast carry-less multiplication is further used to speed up the reduction on the newest Haswell platforms.

For the five NIST curves over $GF(2^m)$ with $m$ $\\in$ $\\{163,233,283,409,571\\}$, the resulting point multiplication implementation is about 6 to 12 times faster than that of OpenSSL-1.0.1e, enhancing the ECDHE and ECDSA algorithms significantly.