Toward Efficient Multiplication Algorithms over Finite Fields in Lagrange Representation

Ming Long Qi; Luo Zhong; Qing Ping Guo

doi:10.4028/www.scientific.net/AMM.20-23.323

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 20-23Toward Efficient Multiplication Algorithms over...

Toward Efficient Multiplication Algorithms over Finite Fields in Lagrange Representation

Abstract:

In this paper, we present a representative theory for finite fields called the Lagrange Representation recently initialized by Bajard et al. Our contribution is of introducing a new method for computing the leading coefficient of an arbitrary field polynomial, and establishing a field modular multiplication algorithm. Some concrete examples are given in order to emphasize illustration of the method.

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Periodical:

Applied Mechanics and Materials (Volumes 20-23)

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323-327

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.20-23.323

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Online since:

January 2010

Authors:

Ming Long Qi, Luo Zhong, Qing Ping Guo

Keywords:

Field Multiplication Algorithm, Finite Field, Lagrange Representation

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References

[1] N. Koblitz: Elliptic curve cryptosystems, Mathematics of Computation Vol. 48(1987), p.203.

DOI: 10.1090/s0025-5718-1987-0866109-5

Google Scholar

[2] V. Miller, Use of elliptic curves in cryptography, in: Advances in Cryptology, edited by Springer-Verlag, volume 218 of LNCS, proceeding's of CRYPTO'85 (1986), pp.417-426.

DOI: 10.1007/3-540-39799-x_31

Google Scholar

[3] E. Berlekamp : Bit-serial Reed-Solomon encoder, IEEE Transactions on Inf. Th. IT-28(1982).

Google Scholar

[4] W. Diffie and M. Hellman: New directions in cryptography, in: IEEE Transactions on Information Theory Vol. 24(1976), pp.644-654.

DOI: 10.1109/tit.1976.1055638

Google Scholar

[5] J.L. Massey and J.K. Omura: Computational Method and Apparatus for Finite Field Arithmetic, U.S. Patent 4, 587, 627. (1986).

Google Scholar

[6] J.C. Bajard and C. Nègre: Arithmetic Operations in Finite Fields of Medium Prime Characteristic Using the Lagrange Representation, IEEE Transaction on Computers Vol. 55-9 (2006), p.1167.

DOI: 10.1109/tc.2006.136

Google Scholar

[7] J.C. Bajard, L. Imbert, C. Nègre and T. Plantard: Efficient multiplication in ( ) k GF p for elliptic curve cryptography, in: ARITH'16: IEEE Symposium on Computer Arithmetic (June 2003), pp.181-187.

DOI: 10.1109/arith.2003.1207677

Google Scholar

[8] J.C. Bajard, L. Imbert and T. Plantard: Modular number systems: Beyond the Mersenne family, in: SAC'04: 11th International Workshop on Selected Areas in Cryptography (August 2004), pp.159-169.

DOI: 10.1007/978-3-540-30564-4_11

Google Scholar

[9] P.L. Montgomery: Modular Multiplication without Trial Division, Math. Computation Vol. 44-170(1985), pp.519-521.

DOI: 10.1090/s0025-5718-1985-0777282-x

Google Scholar

[10] C.K. Koc and T. Acar: Montgomery Multiplication in (2 ) k GF , Designs, Codes, and Cryptography Vol. 14-1(1998), pp.57-69.

Google Scholar