Fast software implementation of binary elliptic curve cryptography

This paper presents an efficient and side-channel-protected software implementation of scalar multiplication for the standard National Institute of Standards and Technology (NIST) and Standards for Efficient Cryptography Group binary elliptic curves. The enhanced performance is achieved by leveraging Intel’s AVX architecture and utilizing the pclmulqdq processor instruction. The fast carry-less multiplication is further used to speed up the reduction on the Haswell platform. For the five NIST curves over $$GF(2^m)$$GF(^2m) with $$m$$m$$\in $$∈$$\{163,233,283,409,571\}$${163,233,283,409,571}, the resulting scalar multiplication implementation is about 5–12 times faster than that of OpenSSL-1.0.1e, enhancing the ECDHE and ECDSA algorithms significantly.