Hardware implementation of a novel inversion algorithm

Computation of multiplicative inverses in finite fields GF (p) and GF (2ⁿ) is the most time consuming operation in elliptic curve cryptography especially when affine coordinates are used. Since the existing algorithms based on extended Euclidean algorithm do not permit a fast software implementation, projective coordinates, which eliminate almost all of the inversion operations from the curve arithmetic, are preferred. In this paper, a hardware implementation of inversion algorithms for both binary extension and prime fields is presented. The algorithms are varying slightly from the Montgomery inverse algorithm. A hardware structure, using multiword format is implemented on chip, which allows scalability with a broader precision range