Elliptic curve public-key cryptosystems - An introduction

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1528, Issue , 1998, Pages 131-141

  De Win, Erik ^a   Preneel, Bart ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

PUBLIC KEY CRYPTOGRAPHY; SECURITY OF DATA; SECURITY SYSTEMS;

DISCRETE LOGARITHMS; ELLIPTIC CURVE; PUBLIC KEY CRYPTOSYSTEMS; PUBLIC KEYS;

GEOMETRY;

EID: 24744434189     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-49248-8_5     Document Type: Conference Paper

References (25)

1. ANSI X9.62-199x: Public-Key Cryptography for the Financial Services Industry: The Elliptic Curve Digital Signature Algorithm (ECDSA), November 11, 1997.
2. A. Atkin and F. Morain, "Elliptic curves and primality proving," Mathematics of Computation, Vol. 61 (1993), pp. 29-68.
3. D. Bailey and C. Paar, "Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms," Advances in Cryptology, Proc. Crypto'98, LNCS 1462, H. Krawczyk, Ed., Springer-Verlag, 1998, pp. 472-485.
4. n)," Advances in Cryptology, Proc. Asiacrypt'96, LNCS 1163, K. Kim and T. Matsumoto, Eds., Springer-Verlag, 1996, pp. 65-76.
5. E. De Win, S. Mister, B. Preneel and M. Wiener, "On the performance of signature schemes based on elliptic curves," Proceedings of the ANTS III conference, LNCS 1423, J. Buhler, Ed., Springer-Verlag, 1998, pp. 252-266.
6. D.M. Gordon, "A survey of fast exponentiation methods," Journal of Algorithms, Vol. 27, pp. 129-146, 1998.
7. J. Guajardo and C. Paar, "Efficient algorithms for elliptic curve cryptosystems," Advances in Cryptology, Proc. Crypto'97, LNCS 1294, B. Kaliski, Ed., Springer-Verlag, 1997, pp. 342-356.
8. G. Harper, A. Menezes and S. Vanstone, "Public-key cryptosystems with very small key length," Advances in Cryptology, Proc. Eurocrypt'92, LNCS 658, R.A. Ruep-pel, Ed., Springer-Verlag, 1993, pp. 163-173.
9. IEEE P1363: Editorial Contribution to Standard for Public-Key Cryptography, July 27, 1998.
10. nd Edition, Addison-Wesley, Reading, Mass., 1981.
11. ISO/IEC 9796-2, "Information technology - Security techniques - Digital signature schemes giving message recovery, Part 2: Mechanisms using a hash-function," 1997.
12. N. Koblitz, "Elliptic curve cryptosystems," Mathematics of Computation, Vol. 48, no. 177 (1987), pp. 203-209.
13. H.W. Lenstra Jr., "Factoring integers with elliptic curves," Annals of Mathematics, Vol. 126 (1987), pp. 649-673.
14. A. Menezes, Elliptic Curve Public-Key Cryptosystems, Kluwer Academic Publishers, 1993.
15. A. Menezes, T. Okamoto and S. Vanstone, "Reducing elliptic curve logarithms to logarithms in a finite field," IEEE Transactions on Information Theory, Vol. 39 (1993), pp. 1639-1646.
16. A. Menezes, P. van Oorschot and S. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997.
17. V.S. Miller, "Use of elliptic curves in cryptography," Advances in Cryptology Proc. Crypto'85, LNCS 218, H.C. Williams, Ed., Springer-Verlag, 1985, pp. 417-426.
18. A. Miyaji, T. Ono and H. Cohen, "Efficient elliptic curve exponentiation," Proceedings of ICICS'97, LNCS 1334, Y. Han, T. Okamoto and S. Qing, Eds., Springer-Verlag, 1997, pp. 282-290.
19. n)," Discrete Applied Mathematics, Vol. 22 (1988/1989), pp. 149-161.
20. http://grouper.ieee.org/groups/1363/.
21. T. Satoh and K. Araki, "Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves," Commentarii Math. Univ. St. Pauli, Vol. 47 (1998), pp. 81-92.
22. N. Smart, "The discrete logarithm problem on elliptic curves of trace one," preprint, 1998.
23. R. Schroeppel, H. Orman, S. O'Malley and O. Spatscheck, "Fast key exchange with elliptic curve systems," Advances in Cryptology, Proc. Crypto'95, LNCS 963, D. Coppersmith, Ed., Springer-Verlag, 1995, pp. 43-56.
24. M. Wiener, "Performance comparison of public-key cryptosystems," Crypto Bytes, Vol. 4., No. 1, Summer 1998, pp. 1-5.
25. http://www.x9.org/.