On the performance of signature schemes based on elliptic curves

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

Volumn 1423, Issue , 1998, Pages 252-266

  De Win, Erik ^a   Mister, Serge ^b   Preneel, Bart ^a   Wiener, Michael ^c  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b QUEEN S UNIVERSITY   (Canada)

^c Entrust Technologies   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

C++ (PROGRAMMING LANGUAGE); GEOMETRY; NUMBER THEORY;

ASSEMBLY LANGUAGE; DESIGN DECISIONS; EXPONENTIATION ALGORITHMS; SIGNATURE ALGORITHMS; SIGNATURE SCHEME; SIGNED BINARIES; SOFTWARE IMPLEMENTATION; STANDARD BASIS;

CRYPTOGRAPHY;

EID: 84947730530     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0054867     Document Type: Conference Paper

References (28)

1. ANSI X9.62-199x: Public Key Cryptography for the Financial Services Industry: The Elliptic Curve Digital Signature Algorithm (ECDSA), June 11, 1997.
2. A. Atkin and F. Morain, "Elliptic curves and primality proving," Mathematics of Computation, Vol. 61 (1993), pp. 29-68.
3. P. Barrett, "Implementing the Rivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor," Advances in Cryptology, Proc. Crypto’86, LNCS 263, A. Odlyzko, Ed., Springer-Verlag, 1987, pp. 311-323.
4. E. Brickell, D. Gordon, K. McCurley and D. Wilson, "Fast exponentiation with precomputation," Advances in Cryptology, Proc. Eurocrypt’92, LNCS 658, R.A. Rueppel, Ed., Springer-Verlag, 1993, pp. 200-207.
5. E. De Win, A. Bosselaers, S. Vandenberghe, P. De Gersem and J. Vandewalle, "A fast software implementation for arithmetic operations in GF(2")," Advances in Cryptology, Proc. Asiacrypt’96, LNCS 1163, K. Kim and T. Matsumoto, Eds., Springer-Verlag, 1996, pp. 65-76.
6. D. Gordon, "A survey of fast exponentiation methods," draft, 1996.
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. Rueppel, Ed., Springer-Verlag, 1993, pp. 163-173.
9. IEEE P1363: Editorial Contribution to Standard for Public Key Cryptography, August 18, 1997.
10. B. Kaliski Jr., "The Montgomery inverse and its applications," IEEE Transactions on Computers, Vol. 44, no. 8 (1995), pp. 1064-1065.
11. nd Edition, Addison-Wesley, Reading, Mass., 1981.
12. N. Koblitz, "Elliptic curve cryptosystems," Mathematics of Computation, Vol. 48, no. 177 (1987), pp. 203-209.
13. N. Koblitz, "CM-curves with good cryptographic properties," Advances in Cryptology, Proc. Crypto’91, LNCS 576, J. Feigenbaum, Ed., Springer-Verlag, 1997, pp. 279-287.
14. C. Koç, "Analysis of sliding window techniques for exponentiation," Computers Math. Applic., Vol. 30, no. 10 (1995), pp. 17-24.
15. K. Koyama and Y. Tsuruoka, "Speeding up elliptic cryptosystems by using a signed binary window method," Advances in Cryptology, Proc. Crypto '92, LNCS 740, E. Brickell, Ed., Springer-Verlag, 1993, pp. 345-357.
16. H.W. Lenstra Jr., "Factoring integers with elliptic curves," Annals of Mathematics, Vol. 126 (1987), pp. 649-673.
17. A. Menezes, Elliptic curve public key cryptosystems, Kluwer Academic Publishers, 1993.
18. 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.
19. A. Menezes, P. van Oorschot and S. Vanstone, Handbook of applied cryptography, CRC Press, 1997.
20. 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.
21. 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.
22. P. Montgomery, "Modular multiplication without trial division," Mathematics of Computation, Vol. 44 (1985), pp. 519-521.
23. F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Informatique Théorique et Applications, Vol. 24, pp. 531-543, 1990.
24. n)," Discrete Applied Mathematics, Vol. 22 (1988/1989), pp. 149-161.
25. G. Reitwiesner, "Binary arithmetic," Advances in Computers, Vol. 1 (1960), pp. 231-308
26. 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.
27. N. Smart, "Elliptic Curve Discrete Logarithms," message to newsgroup sci.math.research.no.3430BAB8.4878@hplb.hpl.hp.com, Sept. 30 1997.
28. J. Solinas, "An improved algorithm for arithmetic on a family of elliptic curves," Advances in Cryptology, Proc. Crypto’97, LNCS 1294, B-Kaliski, Ed., Springer-Verlag, 1997, pp. 357-371.