Design of low complexity GF(2m) multiplier based on Karatsuba algorithm

The multiplication is the basic arithmetic operation of others over the finite field GF(2m) which have widespread applications. In this paper, we analyze the complexity of the classic multiplier mixed Karatsuba multiplier for 2-term polynomials in the finite field GF(2m). By using a method to transform the multiplication operands, we can obtain the complexity of Karatsuba multiplier with any iteration step for any given length m and the constraint when the iteration should be stopped. The results show that this method has a low space complexity and is especially suitable for elliptic curve cryptography (ECC) in which m is suggested to be prime.

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