A New Multiplication Algorithm and VLSI Architecture Over $GF(2^m)$ Using Gaussian Normal Basis
Soonhak Kwon, Hiecheol Kim, Chun-Pyo Hong, Chang‐Hoon Kim · 2006
Multiplications in finite fields are one of the most important arithmetic operations for implementations of elliptic curve cryptographic systems. In this paper, we propose a new multiplication algorithm and VLSI architecture over using Gaussian normal basis. The proposed algorithm is designed by using a symmetric property of normal elements multiplication and transforming coefficients of normal elements. The proposed multiplication algorithm is applicable to all the five recommended fields for elliptic curve cryptosystems by NIST and IEEE 1363, where {163, 233, 283, 409, 571}. A new VLSI architecture based on the proposed multiplication algorithm is faster or requires less hardware resources compared with previously proposed normal basis multipliers over . In addition, we gives an easy method finding a basic multiplication matrix of normal elements.