Applied Mathematics & Information Sciences

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Finite field inversion is considered a very time-consuming operation in scalar multiplication required in elliptic curve cryptosystems. A fast inversion algorithm in binary extension fields using normal basis representation is proposed. It is based on Fermat’s theorem. Compared to existing similar methods, it is shown that for a given extension degree m of the concerned field the proposed algorithm requires as few as or fewer multiplications than any other similar algorithm in the literature.