Montgomery Multiplication in Gf2
نویسندگان
چکیده
We show that the multiplication operation c = a br ,1 in the eld GF2 k can be implemented signiicantly faster in software than the standard multiplication, where r is a special xed element of the eld. This operation is the nite eld analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level algorithms for computing the product, perform a thorough performance analysis, and compare the algorithm to the standard multiplication algorithm in GF2 k. The Montgomery multiplication can be used to obtain fast software implementations of the discrete exponentiation operation, and is particularly suitable for cryptographic applications where k is large.
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