Fast Implementation for Modular Inversion and Scalar Multiplication in the Elliptic Curve Cryptography

Modular inversion and Scalar multiplication are the kernel for computations in the GF(p) used by many public-key cryptosystem in data security systems. Various algorithms have been used for both software and hardware implementation of GF (p) inversion, but its application is limited because of the constraint of its speed. In this paper, a fast GF(p) inversion algorithm is proposed which can be used in both software and hardware realizations and is particularly suitable for VLSI implementations. Also an efficient algorithm for scalar multiplication in ECC is discussed and the corresponding comparative results are given. The results of numerical tests and performance comparisons manifests that the proposed algorithms can remarkably improve the computational efficiency. Hence, it has practical significance for the implementation of ECC and is expected to be applied to data security.