An area-time efficient point-multiplication architecture for ECC over GF(2m) using polynomial basis

Abstract

The modern age has seen an enormous progress in communications. Millions of devices communicate over the web transmitting confidential information which sometimes is of national importance. Securing these devices has become prime concern in this evolutionary digital world. Elliptic curve cryptography has grabbed quite attention for securing these devices primely because of its small-key size with relatively same-level of security when compared to other cryptosystems. The high performance of ECC relies on the finite-field arithmetic operations. Point-multiplication is the most resource consuming and time critical ECC operation. Many architectures and algorithms are presented in the literature to address the area complexity and time complexity of point-multiplication. In this paper, a point-multiplication architecture for generic irreducible polynomials is proposed based on the modified Montgomery-ladder algorithm. In addition, the FF-inversion operation of point multiplication is realized by employing modified Itoh–Tsujii algorithm to achieve reduction in the computation time. The hardware complexity and delay of the proposed point multiplication architecture are estimated, and a comparison with the corresponding point multiplication architectures available in the literature is presented. It is observed that the proposed architecture achieves area-time efficiency of around 17%–86% and 42%–98%, respectively, over GF(2163) and GF(2233) when compared to the architectures available in the literature.