An Implementation of Elliptic Curve Cryptosystems Over F2155

IEEE Journal on Selected Areas in Communications

Volumn 11, Issue 5, 1993, Pages 804-813

  Agnew, G B ^a   Mullin, R C ^a   Vanstone, S A ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CODES (SYMBOLS); DATA COMMUNICATION SYSTEMS;

DISCRETE LOGARITHM PROBLEM; MULTIPLICATIVE GROUP; PUBLIC KEY CRYPTOGRAPHY;

CRYPTOGRAPHY;

EID: 0027614379     PISSN: 07338716     EISSN: None     Source Type: Journal    
DOI: 10.1109/49.223883     Document Type: Article

References (21)

1. G. Agnew, R. Mullin, I. Onyszchuk, and S. Vanstone, “An implementation for a fast public key cryptosystem,” J. Cryptol., vol. 3, pp. 63–79, 1991.
2. W. Diffie and M. Hellman, “New directions in cryptography,” IEEE Trans. Inform. Theory, vol. IT-22, pp. 644–654, 1976.
3. T. ElGamal, “A public key cryptosystem and a signature scheme based on discrete logarithms,” IEEE Trans. Inform. Theory, vol. IT-31, pp. 469–472, 1985.
4. S. Gao and H. Lenstra, “Optimal normal bases,” preprint, 1992.
5. N. Koblitz, “Constructing elliptic curve cryptosystems in characteristic 2,” in Advances in Cryptology: Proceedings of Crypto’ 90, Lecture Notes in Computer Science, vol. 537. New York: Springer-Verlag, 1991, pp. 156–167.
6. K. McCurley, “The discrete logarithm problem,” in Cryptol. Computat. Number Theory, Proc. Symp. Appl. Math., vol. 42, pp. 49–74, 1990.
7. A. Menezes, T. Okamoto, and S. Vanstone, “Reducing elliptic curve logarithms to logarithms in a finite field,” in Proc. 22nd Annu. ACM Symp. Theory Computing, 1991, pp. 80–89.
8. A. Menezes and S. Vanstone, “Isomorphism classes of elliptic curves over finite fields of characteristic 2,” Utilitas Mathematica, vol. 38, pp. 135–154, 1990.
9. A. Menezes and S. Vanstone, “Elliptic curve cryptosystems and their implementation,” submitted to J. Cryptol., 1991.
10. A. Menezes, S. Vanstone, and R. Zuccherato, “Counting points on elliptic curves over F 2 m”, to appear in Math. Computat., 1992.
11. V. Miller, “Uses of elliptic curves in cryptography,” in Advances in Cryptology: Proceedings of Crypto ’85, Lecture Notes in Computer Science,” vol. 218. New York: Springer-Verlag, 1986, pp. 417–426.
12. V. Miller, “Short programs for functions on curves,” unpublished manuscript, 1986.
13. P. Montgomery, “Speeding the Pollard and elliptic curve methods of factorization,” Math. Computat., vol. 48, pp. 243–264, 1987.
14. R. Mullin, “Optimal normal bases,” in Designs, Codes and Groups (Proceedings of the Marshall Hall Conference). New York: Wiley, (to appear).
15. R. Mullin, I. Onyszchuk, S. Vanstone, and R. Wilson, “Optimal normal bases in GF(pn),” Discrete Appl. Math., vol. 22, pp. 149-161,1988/89.
16. National Institute of Standards and Technology, Digital Signature Standard, FIPS Publ. XX, 1991.
17. J. Pollard, “Monte Carlo methods for index computation (mode p),” Math. vol. 32, 918–924, 1978.
18. C. Schnorr, “Efficient signature generation by smart cards,” J. Cryptol., vol. 4, pp. 1612–1674, 1991.
19. R. Schoof, “Elliptic curves over finite fields and the computation of square roots mod p,” Math. Computat., vol. 44, pp. 483–494, 1985.
20. R. Schoof, “Nonsingular plane cubic curves over finite fields,” J. Combinatorial Theory, vol. A46, pp. 183–211, 1987.
21. J. Silverman, The Arithmetic of Elliptic Curves. New York: Springer-Verlag, 1986.