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http://dx.doi.org/10.13089/JKIISC.2008.18.1.41

Systolic Architecture for Digit Level Modular Multiplication/Squaring over GF($2^m$)  

Lee, Jin-Ho (School of Computer Engineering, Kyungil University)
Kim, Hyun-Sung (School of Computer Engineering, Kyungil University)
Abstract
This paper presents a new digit level LSB-first multiplier for computing a modular multiplication and a modular squaring simultaneously over finite field GF($2^m$). To derive $L{\times}L$ digit level architecture when digit size is set to L, the previous algorithm is used and index transformation and merging the cell of the architecture are proposed. The proposed architecture can be utilized for the basic architecture for the crypto-processor and it is well suited to VLSI implementation because of its simplicity, regularity, and concurrency.
Keywords
Public-key cryptosystem; Finite fields; Digit-level architecture; Modular multiplier;
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1 A. M. Odlyzko, "Discrete logarithms in finite fields and their cryptographic significance", Proc. Eurocrypt84, pp. 224-314, 1984
2 C. C. Wang, T. K. Truong, H. M. Shao, L. J. Deutsch, J. K. Omura, and I. S. Reed, "VLSI architectures for computing multiplications and inverses in GF($2^{m}$)", IEEE Trans. Computer, vol. C-34, pp. 709-717, 1985   DOI   ScienceOn
3 C. L. Wang and J. L. Lin, "Systolic array implementation of multipliers for finite fields GF($2^{m}$)", IEEE Trans. Circuits Systems, vol. 38, pp. 796-800, 1991   DOI   ScienceOn
4 I. S. Hsu. T. K. Truong, L.J. Deutsch, and I. S. Reed, "A comparison of VLSI architecture of finite field multipliers using dual, normal, standard bases", IEEE Trans. Computer, vol. 37, pp. 735-739, 1988   DOI   ScienceOn
5 C. S. Yeh, I. S. Reed, and T. K. Truong, "Systolic multipliers for finite fields GF($2^{m}$)", IEEE Trans. Computer, vol. C-33, pp. 357-360, 1984   DOI   ScienceOn
6 W. Diffie and M. Hellman,"New directions in cryptography", IEEE Trans. on Info. Theory, vol. 22, pp. 644-654, 1976   DOI
7 D. E. R. Denning, Cryptography and data security, Reading, MA: Addison-Wesley, 1983
8 S. Y. Kung, VLSI array processors, Englewood Cliffs, NJ:Prentice-Hall, 1988
9 J. H. Guo and C. L. Wang, "Digit-serial systolic multiplier for finite fields GF($2^{m}$)", IEE Proc. Comp. Digit. Tech., vol. 145, no. 2, pp. 143-148, 1998   DOI   ScienceOn
10 W. W. Peterson and E. J. Weldon, Error-correcting codes, Cambridge, MA: MIT Press, 1972
11 김기원, 이건직, 유기영, "GF($2^{m}$)상에서 2-디지트 시리얼 시스톨릭 곱셈기 설계 및 분석", 한국정보과학회 가을 학술발표논문집, 27(2), pp. 605-607, 2000
12 S. Y. Kung, VLSI array processors, Englewood Cliffs, NJ:Prentice-Hall, 1988
13 A.J. Menezes, Applications of finite fields, Boston, MA: Kluwer Academic Publishers, 1993
14 유기영, 김정준, "유한필드 GF($2^{m}$)상의 시스톨릭 곱셈/제곱기", 정보과학회논문지, 28(5), pp. 289-300, 2001
15 H. S. Kim and K. Y. Yoo, "Area efficient exponentiation using modular multiplier/squarer in GF($2^{m}$)", Lecture notes in computer science, vol. 2108, pp. 262-267, 2001   DOI
16 P. A. Scott, S.E. Tavares, and L.E. Peppard, "A fast VLSI multiplier for GF($2^{m}$)", IEEE Jour. of Selected Areas in Comm., vol. 4. pp. 62-66, 1986   DOI
17 E. R. Berlekamp, Algebraic coding theory, New York: McGraw-Hill, 1968
18 R. Lidl, H. Niederreiter, and P. M. Cohn, Finite fields(Encyclopedia of mathematics and its applications), Cambridge University Press, 1997
19 I. S. Reed and T. K. Truong,"The use of finite fields to compute convolutions", IEEE Trans. Inform. Theory, vol. IT-21, pp. 208-213, 1975