Efficient Linear Array for Multiplication in GF(2m) Using a Normal Basis for Elliptic Curve Cryptography

We present a new sequential normal basis multiplier over GF(2 m ). The gate complexity of our multiplier is significantly reduced from that of Agnew et al. and is comparable to that of Reyhani-Masoleh and Hasan, which is the lowest complexity normal basis multiplier of the same kinds. On the other hand, the critical path delay of our multiplier is same to that of Agnew et al. Therefore it is supposed to have a shorter or the same critical path delay to that of Reyhani-Masoleh and Hasan. Moreover our method of using a Gaussian normal basis makes it easy to find a basic multiplication table of normal elements. So one can easily construct a circuit array for large finite fields, GF(2 m ) where m = 163, 233, 283, 409, 571, i.e. the five recommended fields by NIST for elliptic curve cryptography.