Efficient Arithmetic for Some Finite Fields
نویسنده
چکیده
We propose a class of finite fields where the reduction costs one addition. Their size is in the range of interest for ECC. We extend the idea of OEFs to Optimal Extension Rings, that is Z/(2 ± 1) where 2 ± 1 = ap with p a big prime and a a small cofactor. In 29 cases a = 3, in other 11 cases a = 17. We propose several classes of finite fields where the reduction costs at most five additions, at least one. We propose a class of fields that optimizes inversion by Fermat Little Theorem.
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