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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 10 > No. 5


Accelerating Finite Field Inversion in GF(3m) for Elliptic Curve Cryptography

PP: 1645-1655
Walid Mahmoud, Huapeng Wu,
Ternary extension fields GF(3m) have been used in cryptographic applications based on bilinear-mappings in elliptic curve cryptography. In this paper, we focus on accelerating inversion in GF(3m) which is an indispensable operation in such applications. We propose a fast execution-time inversion algorithm which decomposes (m−1) of GF(3m) into several factors and a remainder and restricts the remainder to belong to the shortest addition chain of a suitable factor. Thus, unlike other algorithms that not decompose (m−1) and search for large near-optimal addition chains for (m−1) to compute the inverse, our algorithm relies on much smaller and known chains for the suitable factors. In decomposing (m−1) with the use of small and known chains for the suitable factors, as far as we know, our proposal is the fastest polynomial-time inversion algorithm in comparison with its counterparts.

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