Problems on Gaussian Normal Basis Multiplication for Elliptic Curve Cryptosystem

摘要

Several standards such as IEEE Standard 1363-2000 and FIPS 186-2 employ Gaussian normal basis (GNB). Gaussian normal basis is a special class of normal basis. Gaussian normal basis can solve the problem that multiplication in normal basis is an very difficult and complicated operation. Two equations have been proposed in the literature to transfer GNB to polynomial basis for easy multiplication. However, we find that GNB is not correctly transformed to polynomial basis for some m values over GF(2~m). We will show the problems and expect some feedback about this problem from other researchers.