Improved generalizations of the Karatsuba algorithm in GF(2n)

Abstract

The process of multiplications in Finite Fields required huge resources. If those implemented in the Elliptic Curve Cryptography (ECC), the need of resources would be inflated because those processes were enough to dominated in every ECC level. There were many researches to found methods that could reduce the number of multiplications. One method that was well-known and developed was Karatsuba ofman algorithm, where the development of this research were General Karatsuba Multiplier, Efficient Multiplier in GF((2n)4) Generalizations of Karatsuba Algorithm, 5-6-7 Term Karatsuba-Like Formulae, and improved modulo functions. From those researches is made a better algorithm than Generalizations of Karatsuba Algorithm and it is expected to leads to generalize the form n-Term Karatsuba-Like Formulae.