Abstract
In this work, we present a new structure for multiplication in finite fields. This structure is based on a digit-level LFSR (Linear Feedback Shift Register) multiplier, in which the area of the digit-multipliers is reduced using the Karatsuba method. We compare our results with the other works of the literature for F <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">397</inf> . Furthermore, we propose new formulas for multiplication in F <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">36.97</inf> . These new formulas reduce the number of F <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">397</inf> -multiplications from 18 to 15. The finite fields F <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">397</inf> and F <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">36.97</inf> are important fields for pairing based cryptography.
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