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Area Efficient Bit-serial Squarer/Multiplier and AB$^2$-Multiplier  

이원호 (경북대학교 컴퓨터공학과)
유기영 (경북대학교 컴퓨터공학과)
Publication Information
Journal of KIISE:Computer Systems and Theory / v.31, no.1_2, 2004 , pp. 1-9 More about this Journal
Abstract
The important arithmetic operations over finite fields include exponentiation, division, and inversion. An exponentiation operation can be implemented using a series of squaring and multiplication operations using a binary method, while division and inversion can be performed by the iterative application of an AB$^2$ operation. Hence, it is important to develop a fast algorithm and efficient hardware for this operations. In this paper presents new bit-serial architectures for the simultaneous computation of multiplication and squaring operations, and the computation of an $AB^2$ operation over $GF(2^m)$ generated by an irreducible AOP of degree m. The proposed architectures offer a significant improvement in reducing the hardware complexity compared with previous architectures, and can also be used as a kernel circuit for exponentiation, division, and inversion architectures. Furthermore, since the Proposed architectures include regularity and modularity, they can be easily designed on VLSI hardware and used in IC cards.
Keywords
Cryptography; Finite Fields; Irreducible AOP; Exponentiation; Multiplication; Division;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 W. W. Peterson and E. J. Weldom, Error-Correcting Codes. Cambridge, MA: MIT Press, 1972
2 D. E. R. Denning, Cryptography and Data security. Reading MA: Addison-Wesley, 1983
3 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, Mar. 1975   DOI
4 D. E. Knuth, The art of computer programming, Vol. 2: seminumerical algorithms. Addison-Wesley, Reading, Mass., 2nd edition, 1981
5 C. L. Wang, and J. L. Lin, 'Systolic array implementation of multipliers for finite field $GF(2^m)$,' IEEE Trans. Circuits System, vol. 38, pp. 796-800, July, 1991   DOI   ScienceOn
6 J. H. Guo and C. L. Wang, 'Digit-serial systolic multiplier for finite fields $GF(2^m)$,' IEE Proc. Compu, Digit. Tech, vol. 145, pp.l43~148, 1998   DOI   ScienceOn
7 E. D. Mastrovito, 'VLSI architecture for computations in Galois fields,' Ph. D. dissertation, Dept. Elec. Eng., Linkoping Univ., Linkoping, Sweeden, 1991
8 S. W. Wei, 'A systolic power-sum for $GF(2^m)$,' IEEE Trans. Computer, vol. 43, pp.226~229, Feb. 1994   DOI   ScienceOn
9 C. L. Wang and J. L. Lin, 'A systolic architecture for inverses and divisions in $GF(2^m)$,' IEEE Trans. Computer, vol. 42, pp.1141-1146, Sep. 1993   DOI   ScienceOn
10 S. T. J. Fenn, M. G. Parker, M. Benaissa, and D. Taylor, '$GF(2^m)$ multiplication and division over the dual basis,' IEEE Trans. Computer, vol. 45, pp.319-327, Mar. 1996   DOI   ScienceOn
11 S. T. J. Fenn, M. G. Parker, M. Benaissa, and D. Taylor, 'Bit-serial multiplication in $GF(2^m)$ using irreducible all-one polynomials,' IEE Proc. Compu., Digit. Tech, vol. 144, pp.391-393, 1997   DOI   ScienceOn
12 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. VLSI Technology, Systems, and Applications, pp.113-117, 1997
13 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.H20~1125, Oct., 2000   DOI   ScienceOn
14 T. Itoh, and S. Tsujii, 'Structure of parallel multipliers for a class of fields $GF(2^m)$,' Info. Trans., pp.21-40, 1989   DOI
15 M. A. Hasan, M. Z. Wang, and V. K. Bhargava, 'A modified Massey-Omura parallel multipliers for a class of finite fields,' IEEE Trans. Computer, C-42, pp.1278-1280, 1993   DOI   ScienceOn
16 C. K. Koc and B. Sunar, 'Low-complexity bit-parallel canonical and normal basis multipliers for a class of finite fields,' IEEE Trans. Computer, vol. C-47, pp.353-356, Mar. 1998