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An Efficient Bit-serial Systolic Multiplier over GF($2^m$)  

Lee Won-Ho (위덕대학교 컴퓨터멀티미디어공학부)
Yoo Kee-Young (경북대학교 컴퓨터공학과)
Publication Information
Journal of KIISE:Computer Systems and Theory / v.33, no.1_2, 2006 , pp. 62-68 More about this Journal
Abstract
The important arithmetic operations over finite fields include multiplication and exponentiation. An exponentiation operation can be implemented using a series of squaring and multiplication operations over GF($2^m$) using the binary method. Hence, it is important to develop a fast algorithm and efficient hardware for multiplication. This paper presents an efficient bit-serial systolic array for MSB-first multiplication in GF($2^m$) based on the polynomial representation. As compared to the related multipliers, the proposed systolic multiplier gains advantages in terms of input-pin and area-time complexity. Furthermore, it has regularity, modularity, and unidirectional data flow, and thus is well suited to VLSI implementation.
Keywords
Cryptography; Finite Fields; Multiplication; Exponentiation;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 N. Y. Kim, H. S. Kim, and K. Y. Yoo, 'Computation of $AB^2$ multiplication in GF($2^m$) using low-complexity systolic architecture,' lEE Proc. Circuits, Devices & Systems, vol.150, No.2, pp.119-123, 2003   DOI   ScienceOn
2 이원호, 유기영 '공간 효율적인 비트-시리얼 제곱/곱셈기 및 $AB^2$-곱셈기', 정보과학회 논문지: 시스템 및 이론, 제31권, 제1\cdot2호, pp.1-9, 2004   과학기술학회마을
3 S. Y. Kung, VLSI Array Processors, PrenticeHall, Englewood Cliffs, NJ, 1988
4 K. Y. Yoo 'A Systolic Array Design Methodology for Sequential Loop Algorithms,' Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY, 1992
5 D. D. Gajski, Principles of Digital Design, Prentice Hall, Upper Saddle River, NJ, 1997
6 C. L. Wang, 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
7 M. C. Mekhallalati and A. S. Ashur, 'Novel Structures for Serial Multiplication over the Finite Field GF($2^m$),', Workshop on VLSI Signal Processing, Vol.IX, pp.65-74, 1996
8 S. K. Jain, L. Song, K. K. Parhi, 'Efficient Semisystolic Architectures for Finite-Field Arithmetic,' IEEE Trans. on VLSI Systems, Vol.6. pp.101-113, 1998   DOI   ScienceOn
9 C. S. Yeh, I. S. Reed, T. K. Truong, 'Systolic multipliers for finite fields GF($2^m$),' IEEE Trans. Computer, Vol.C-33, pp.357-360, 1984   DOI   ScienceOn
10 C. L. Wang and J. H. Guo, 'New Systolic Array for C + $AB^2$, 'Inversion and Division in GF($2^m$),', IEEE Trans. Computer, vol.49, pp.1120-1125, 2000   DOI   ScienceOn
11 S. Bandyopadhyay, A. Sengupta, 'Algorithms for multiplication in Galois field for implementing using systolic arrays,' Proc. Inst. Elect. Eng., Vol.35, pp.336-339, 1988
12 P. A. Scott, S. E. Tavares, L. E. Peppard, 'A fast VLSI multiplier for GF($2^m$),' IEEE J. Selected Areas in Communication, Vol.4, pp.62-66, 1986   DOI