A Scalable Finite Field Multiplier

The hardware ‑ software codesign of cryptosistems, is the best solution to reach a reasonable yield in systems with resources limitation. In the last years, the cryptosistems based on elliptic curves (CEE) have acquired an increasing importance, managing at present to form a part of the industrial standards. In the underlying finite field of an CEE squaring and field multiplication is the next computational costly operations other than field inversion. This paper presents an algorithm for multiplication in binary fields GF(2^m) using a polynomial basis representation and with interleaving reduction. The finite field multiplier operates over a variety of binary fields and it is scalable.