A New Multiplication Algorithm and VLSI Architecture Over GF(2m) Using Gaussian Normal Basis 


Vol. 31,  No. 12, pp. 1297-1308, Dec.  2006


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  Abstract

Multiplications in finite fields are one of the most important arithmetic operations for implementations of elliptic curve cryptographic systems. In this paper, we propose a new multiplication algorithm and VLSI architecture over GF(2m) using Gaussian normal basis. The proposed algorithm is designed by using a symmetric property of normal elements multiplication and transforming coefficients of normal elements. The proposed multiplication algorithm is applicable to all the five recommended fields GF(2m) for elliptic curve cryptosystems by NIST and IEEE 1363, where m∈{163, 233, 283, 409, 571}. A new VLSI architecture based on the proposed multiplication algorithm is faster or requires less hardware resources compared with previously proposed normal basis multipliers over GF(2m). In addition, we gives an easy method finding a basic multiplication matrix of normal elements.

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  Cite this article

[IEEE Style]

S. Kwon, C. H. Kim, H. Kim, C. P. Hong, "A New Multiplication Algorithm and VLSI Architecture Over GF(2m) Using Gaussian Normal Basis," The Journal of Korean Institute of Communications and Information Sciences, vol. 31, no. 12, pp. 1297-1308, 2006. DOI: .

[ACM Style]

Soonhak Kwon, Chang Hoon Kim, Hiecheol Kim, and Chun Pyo Hong. 2006. A New Multiplication Algorithm and VLSI Architecture Over GF(2m) Using Gaussian Normal Basis. The Journal of Korean Institute of Communications and Information Sciences, 31, 12, (2006), 1297-1308. DOI: .

[KICS Style]

Soonhak Kwon, Chang Hoon Kim, Hiecheol Kim, Chun Pyo Hong, "A New Multiplication Algorithm and VLSI Architecture Over GF(2m) Using Gaussian Normal Basis," The Journal of Korean Institute of Communications and Information Sciences, vol. 31, no. 12, pp. 1297-1308, 12. 2006.

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pISSN : 1226 - 4717
eISSN : 2287 - 3880