Montgomery Multiplication in GF(2k)

Designs, Codes, and Cryptography

Volumn 14, Issue 1, 1998, Pages 57-69

  Koç, Çetin K ^a   Acar, Tolga ^a  

^a Oregon State University   (United States)

Author keywords

Cryptography; Finite fields; Multiplication

Indexed keywords

EID: 0002842804     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008208521515     Document Type: Article

References (17)

1. G. B. Agnew, R. C. Mullin, I. Onyszchuk, and S. A. Vanstone. An implementation for a fast public-key cryptosystem. Journal of Cryptology, Vol. 3, No. 2 (1996) pp. 63-79.
2. 2155. IEEE Journal on Selected Areas in Communications, Vol. 11, No. 5 (1993) pp. 804-813.
3. W. Diffie and M. E. Hellman. New directions in cryptography. IEEE Transactions on Information Theory, Vol. 22 (1976) pp. 644-654.
4. S. R. Dussé and B. S. Kaliski Jr. A cryptographic library for the Motorola DSP56000. In I. B. Damgård, editor, Advances in Cryptology - EUROCRYPT 90, Lecture Notes in Computer Science, No. 473, Springer-Verlag, New York (1990) pp. 230-244.
5. G. Harper, A. Menezes, and S. Vanstone. Public-key cryptosystems with very small key lengths. In R.A. Rueppel, editor, Advances in Cryptology - EUROCRYPT 92, Lecture Notes in Computer Science, No. 658, Springer-Verlag, New York (1992) pp. 163-173.
6. D. E. Knuth. The Art of Computer Programming: Seminumerical Algorithms, volume 2. Addison-Wesley, Reading, MA, Second edition (1981).
7. N. Koblitz. A Course in Number Theory and Cryptography. New York, NY: Springer-Verlag, New York, NY, Second edition (1994).
8. k). In Proceedings, 9th Symposium on Computer Arithmetic, Asilomar, California, July 6-9, 1997 pp. 225-231.
9. R. Lidl and H. Niederreiter. Introduction to Finite Fields and Their Applications. Cambridge University Press, Cambridge, UK (1994).
10. R. J. McEliece. Finite Fields for Computer Scientists and Engineers. Kluwer Academic Publishers, Boston, MA (1987).
11. A. J. Menezes, editor. Applications of Finite Fields. Kluwer Academic Publishers, Boston, MA (1993).
12. A. J. Menezes. Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers, Boston, MA (1993).
13. P. L. Montgomery. Modular multiplication without trial division. Mathematics of Computation, Vol. 44, No. 170 (1985) pp. 519-521.
14. n). Discrete Applied Mathematics, Vol. 22 (1988) pp. 149-161.
15. J. Omura and J. Massey. Computational method and apparatus for finite field arithmetic. U.S. Patent Number 4,587,627, May 1986.
16. R. Schroeppel, S. O'Malley, H. Orman, and O. Spatscheck. Fast key exchange with elliptic curve systems. In D. Coppersmith, editor, Advances in Cryptology - CRYPTO 95, Lecture Notes in Computer Science, No. 973, pages 43-56, Springer-Verlag, New York, NY (1995) pp. 43-56.
17. n). In Advances in Cryptology - ASIACRYPT 96, Lecture Notes in Computer Science, No. 1163, Springer-Verlag, New York (1996) pp. 65-76.