[KSCI] Korea Science Citation Index Service

Efficient systolic VLSI architecture for division in $GF(2^m)$

Kim, Ju-Young (School of Information, Communication and Electronics Engineering, The Catholic University of Korea)
Park, Tae-Geun (School of Information, Communication and Electronics Engineering, The Catholic University of Korea)

Publication Information

Journal of the Institute of Electronics Engineers of Korea SD / v.44, no.3, 2007 , pp. 35-42 More about this Journal

Abstract

The finite-field division can be applied to the elliptic curve cryptosystems. However, an efficient algorithm and the hardware design are required since the finite-field division takes much time to compute. In this paper, we propose a radix-4 systolic divider on $GF(2^m)$ with comparative area and performance. The algorithm of the proposed divide, is mathematically developed and new counter structure is proposed to map on low-cost systolic cells, so that the proposed systolic architecture is suitable for YLSI design. Compared to the bit-parallel, bit-serial and digit-serial dividers, the proposed divider has relatively effective high performance and low cost. We design and synthesis $GF(2^{193})$ finite-field divider using Dongbuanam $0.18{\mu}m$ standard cell library and the maximum clock frequency is 400MHz.

Keywords

finite field divider; systolic; radix-4; VLSI;

Citations & Related Records

Reference

1	J. H. Guo and C. L. Wang, 'Hardware-efficient systolic architecture for inversion and division in GF( $2^{m}$ ),' IEE Proc. Comput. Digit. Tech., vol. 145, No. 4, pp.272-178, July 1998 DOI ScienceOn
2	W. H. Lee, K. J. Lee and K. Y. Yoo, 'New Digit-Serial Systolic Arrays for Power-Sum and Division Operatin in GF( $2^{m}$ ),' ICCSA 2004, LNCS 3045, pp.638-647, 2004
3	S. W. Wei, 'VLSI architectures for computing exponentiations, multiplicative inverses, and divisions in GF $2^{m}$ ,' IEEE Trans. Circuits and Systems, vol.44, pp.847-855, 1997
4	J. H. Guo and C. L. Wang, 'Bit-Serial Systolic Array Implementation of Euclid's Algorithm for Inversion and Division in GF( $2^{m}$ ),' Proc. 1997 Int. Symp. on VLSI Technology, Systems, and Applications, pp. 113-117, Taipei, Taiwan, June 1997
5	IEEE P1363, Standard Specifications for Public key Cryptography, 2000
6	J. H. Guo and C. L. Wang, 'Novel digit-serial systolic array implementation of Euclid's algorithm for division in GF( $2^{m}$ ),,' Proc. 1998 IEEE int. symp. on Circuits and Systems, vol. 2, pp.478-481, 1998
7	이찬호, 이정호, 'ECC 연산을 위한 가변 연산 구 조를 갖는 정규기저 곱셈기와 역원기,' 대한전자공학회논문지 제 40권 SD편 제 12호, 2003

KSCI

Efficient systolic VLSI architecture for division in 상에서의 나눗셈연산을 위한 효율적인 시스톨릭 VLSI 구조

Efficient systolic VLSI architecture for division in $GF(2^m)$