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This contribution introduces a class of Galois field used to achieve fast finite field arithmetic which we call an Optimal Extension Field (OEF). This approach is well suited for implementation of public-key cryptosystems based on elliptic and hyperelliptic curves. Whereas previous reported optimizations focus on finite fields of the form GF(p) and GF(2m), an OEF...
We propose a novel area/time efficient elliptic curve cryptography (ECC) processor architecture which performs all finite field arithmetic operations in the discrete Fourier domain. The proposed architecture utilizes a class of optimal extension fields (OEF)GF(qm) where the field characteristic is a Mersenne prime q = 2n − 1 and m = n. The main advantage of our architecture is that it achieves...
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