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References
D. V. Bailey and C. Paar. Efficient arithmetic in finite field extensions with application in elliptic curve cryptography. Journal of Cryptology, 2000.
P. Barrett. Implementing the Rivest Shamir and Adleman public-key encryption algorithm on a standard digital signal processor. In A. M. Odlyzko, editor, Advances in Cryptology–-CRYPTO 86, Proceedings, Lecture Notes in Computer Science, vol. 263, pp. 311–323. Springer, Berlin, Germany, 1986.
E. Berlekamp. Algebraic Coding Theory. McGraw-Hill, New York, NY, 1968.
R. Blahut. Theory and Practice of Error Control Codes. Addison-Wesley, Reading, MA, 1983.
A. Bosselaers, R. Govaerts, and J. Vandewalle. Comparison of three modular reduction functions. In Crypto ’93, Lecture Notes in Computer Science, vol. 773, pp. 175–186, 1994.
M. Brown, D. Hankerson, J. López, and A. Menezes. Software implementation of the NIST elliptic curves over prime fields. Topics in Cryptology – CT-RSA 2001, Lecture Notes in Computer Science, vol. 2020, pp. 250–265, Springer, Berlin, Germany, 2001
J. F. Dhem. Efficient modular reduction algorithm in \(\mathcal{F}_q[x]\) and its application to “left to right” modular multiplication in \(\mathcal{F}_2[x]\). In C. D. Walter, editor, Cryptographic Hardware and Embedded Systems – CHES 2003, Lecture Notes in Computer Science, vol. 2779, pp. 203–213. Springer, Berlin, Germany, 2003.
W. Diffie and M. E. Hellman. New directions in cryptography. IEEE Transactions on Information Theory, 22:644–654, November 1976.
IEEE P1363. Standard specifications for public-key cryptography.
D. E. Knuth. The Art of Computer Programming, Volume 2, Seminumerical Algorithms. Addison-Wesley, Reading, MA, Third edition, 1998.
N. Koblitz. Elliptic curve cryptosystems. Mathematics of Computation, 48(177):203–209, January 1987.
Ç. K. Koç and T. Acar. Montgomery multiplication in GF\((2^k)\). Designs, Codes and Cryptography, 14(1):57–69, April 1998.
Ç. K. Koç, T. Acar, and B. S. Kaliski Jr. Analyzing and comparing Montgomery multiplication algorithms. IEEE Micro, 16(3):26–33, June 1996.
R. J. McEliece. Finite Fields for Computer Scientists and Engineers. Kluwer Academic Publishers, Boston, MA, Second edition, 1989.
A. Menezes, P. Van Oorschot, and S. Vanstone. Handbook of Applied Cryptography. CRC Press, Boca Raton, FL, 1997.
A. J. Menezes, I. F. Blake, X. Gao, R. C. Mullen, S. A. Vanstone, and T. Yaghoobian. Applications of Finite Fields. Kluwer Academic Publishers, Boston, MA, 1993.
V. Miller. Uses of elliptic curves in cryptography. In H. C. Williams, editor, Advances in Cryptology–-CRYPTO 85, Proceedings, Lecture Notes in Computer Science, No. 218, pp. 417–426. Springer, Berlin, Germany, 1985.
P. L. Montgomery. Modular multiplication without trial division. Mathematics of Computation, 44(170):519–521, April 1985.
W. W. Peterson and E. J. Weldon Jr. Error-Correcting Codes. MIT Press, Cambridge, MA, 1972.
J. Solinas. Generalized Mersenne numbers. Technical Report CORR 99-39, Dept. of C&O, University of Waterloo, 1999.
S. B. Wicker and V. K. Bhargava, editors. Reed-Solomon Codes and Their Applications. IEEE Press, New York, NY, 1994.
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Erdem, S.S., Yanik, T., Koç, Ç.K. (2009). Fast Finite Field Multiplication. In: Koç, Ç.K. (eds) Cryptographic Engineering. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-71817-0_5
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