Fast inversion algorithm in GF(2m) suitable for implementation with a polynomial multiply instruction on GF(2)


The authors propose a quick inversion algorithm in Galois field GF(2m). In this algorithm, the operations required in many contiguous iterations of a previously reported algorithm based on the extended Euclid's algorithm are represented as a matrix. These operations are performed at once through the matrix by means that of a polynomial multiply instruction on GF(2). When the word size of a processor is 32 or 64 and m is larger than 233 for National Institute of Standards and Technology (NIST)-suggested irreducible polynomials, the proposed algorithm computes inversion with less polynomial multiply directions on GF(a pair of) and exclusive-OR instructions needed by previously reported inversion algorithms on a mean.

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