On Software Implementation of Arithmetic Operations on Prime Fields using AVX2

AVX2 is the newest instruction set on Intel Haswell processor that provides simultaneous execution of operations over vectors of data. This work presents the advances on the applicability of AVX2 on the development of prime field arithmetic, which is a building block for the construction of Elliptic Curve Cryptosystems. Having as a goal the efficient and secure implementation of prime field arithmetic, we show some advantages that vector instructions offer compared against 64-bit implementations. In order to validate the results of our research, we present a benchmark obtained on a Haswell processor.