Faster ECC over

In this paper, we show efficient elliptic curve cryptography implementations over advanced ARMv8 processor. We improve the previous binary field multiplication over the processor with finely aligned multiplication and incomplete reduction techniques by taking advantages of advanced 64-bit polynomial multiplication (PMULL). This approach shows performance enhancements by a factor of 1.34 times than previous implementation of binary field multiplication. For the point addition and doubling, the special types of multiplication, squaring and addition operations are combined together and optimized, where one reduction operation is optimized in each case. The scalar multiplication is implemented in constant-time window method, which is secure against timing attacks. Finally the proposed implementations achieved 759,630/331,944 clock cycles for random/fixed scalar multiplications for B-571 curve over ARMv8, respectively.