PARA'04 State-of-the-Art
in Scientific Computing
June 20-23, 2004 (Home page)
Updated: February 5, 2004

New Architecture for Inversion and Division over GF(2^m)

Kyeoung Ju Ha
Daegu Hanny University
290,Yugok-dong, Gyeongsan-si
Gyeongsanbuk-do, Korea
email: kjha@dhu.ac.kr

In this paper, we propose the new architecture for inversion and division over GF(2^m).

In finite field, the division can be computed using the multiplication and the inversion of the multiplication since A(x)/B(x) is equal to A(x)B(x)-1.

The inversion of the multiplication is a special case of the exponentiation since B(x)-1 is equal to B(x)2m-2 in finite field. Accordingly, we propose the architecture for the inversion first, and then propose the architecture for the division.

To do this, we show the algorithm how to get the inversion of the multiplication using AB² operation. And then give a architecture for the inversion using exponeniation operation. Finally we give the architecture for the division.

The proposed architecture is much more efficient in terms of the space and time than that of the systolic array and can be utilized more efficiently in crypto systems.

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