Performance Analysis of Reversible Finite Field Arithmetic Architectures Over GF(p) and GF(2m) in Elliptic Curve Cryptography

Elliptic curve cryptosystems (ECC) are becoming more and more popular and are included in many standards, as they offer high security strength when compared with other conventional public-key cryptosystems, for the same key length. But the security strength of hardware implementations of ECC is challenged by side channel attacks (SCA) such as power analysis. Reversible logic circuits ideally consume zero energy, which serves as the motivation to implement cryptographic algorithms against power analysis attacks. This paper proposes two new hardware architectures for performing montgomery multiplication in GF(p) and GF(2m), as they are the power consuming operations in ECC. The two architectures are optimized to reduce the hardware cost and they are then implemented in reversible logic with reduced number of quantum cost. In this work, the reversible logic synthesis is performed with Toffoli family of reversible gates. The performance metrics of all the multipliers are analyzed and properly tabulated. Scalar multiplication on elliptic curve points, which is the core operation used in every elliptic curve cryptosystem, has been implemented in reversible logic by using the proposed reversible montgomery multipliers.