Abstract
GCD algorithm is a well known algorithm for computing modular division and inversion which is widely used in Elliptic Curve Cryptography (ECC). Also division is the most time-consuming operation in Elliptic and Hyperelliptic Curve Cryptography. The conventional radix-2 GCD algorithm, is performed modular division over GF(2m) in approximately 2m iterations (or clock cycles). These algorithms consist of at least four comparisons at each iteration. In this paper the conventional algorithm is extended to radix-4. To increase the efficiency of algorithm the number of comparisons is reduced. So the algorithm enables very fast computation of division over GF(2m). The proposed algorithm described in such a way that its hardware realization is straightforward. The implemented results show reducing the division time to m clock cycles. Also the proposed architecture is compared with other reported dividers and it has been shown that the proposed architecture only occupies %14 more LUT (over GF(2163)) while the computation time is decreased to half.
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