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.
Mahmoud, Walid and Wu, Huapeng
"Speeding Up Finite Field Inversion for Cryptographic Applications,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 28.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss5/28