High-Speed Implementation of ECC Scalar Multiplication in GF(p) for Generic Montgomery Curves

Abstract

Elliptic curve-based cryptography (ECC) has become the automatic choice for public key cryptography due to its lightweightness compared to Rivest–Shamir–Adleman (RSA). The most important operation in ECC is elliptic curve scalar multiplication, and its efficient implementation has gathered significant attention in the research community. Fast implementation of ECC scalar multiplication is often desired for speed-critical applications such as runtime authentication in automated cars, web server certification, and so on. Such fast architectures are achieved by implementing ECC scalar multiplication in fields with pseudo-Mersenne prime or Solinas prime. In this paper, we aim to implement a fast implementation of ECC scalar multiplication for any generic Montgomery curve in Galois Field in p [GF(p)] without having the constraint of using any specialized modulus. We will show that the proposed ECC scalar multiplication architecture is as fast as scalar multiplication in special curves like Curve25519, albeit with little area overhead. The proposed architecture can be modified to support ECC scalar multiplication in both Montgomery and short Weierstrass curves.