Fast simultaneous scalar multiplication on elliptic curve with montgomery form

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

Volumn 2259, Issue , 2001, Pages 255-267

  Akishita, Toru ^a  

^a SONY CORPORATION   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY;

ELLIPTIC CURVE; MONTGOMERY; SCALAR MULTIPLICATION; SIGNATURE VERIFICATION;

CRYPTOGRAPHY;

EID: 84949195082     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45537-x_20     Document Type: Conference Paper

References (19)

1. ANSI X9.62-1998, Public Key Cryptography for the Financial Services Industry: The Elliptic Curve Digital Signature Algorithm (ECDSA), Working Draft, September 1998.
2. D. V. Bailey and C. Paar, “Optimal Extension Fieldfor Fast Arithmetic in Public Key Algorithms”, Advances in Cryptography-CRYPTO’98, LNCS 1462, pp. 472-485, 1998.
3. M. Brown, D. Hankerson, J. Lopez, andA. Menezes, “Software Implementation of the NIST Elliptic Curves Over Prime Fields”, Topics in Cryptology – CT-RSA 2001, LNCS 2020, pp. 250-265, 2001.
4. H. Cohen, A. Miyaji, and T. Ono, “Efficient Elliptic Curve Exponentiation Using MixedCo ordinates”, Advances in Cryptography-ASIACRYPT’98, LNCS 1514, pp. 51-65, 1998.
5. T. El Gamal, “A Public Key Cryptosystem anda Signature Scheme Basedon Discrete Logarithms”, IEEE Transaction on Information Theory, Vol. 31, pp. 469-472, 1985.
6. GNU MP Library GMP, version 3.1.1, October 2000. http://www.swox.com/gmp/
7. D. Hankerson, J. Lopéz, andA. Menezes, “Software Implementation of Elliptic Curve Cryptography over Binary Fields”, Cryptographic Hardware and Embedded Systems-CHES 2000, LNCS 1965, pp. 3-24, 2000.
8. IEEE P1363, Standard Specifications for Public Key Cryptography, Draft Version 13, November 1999. http://grouper.ieee.org/groups/1363/
9. T. Kobayashi, H. Morita, K. Kobayashi, andF. Hoshino, “Fast Elliptic Curve Algorithm Combining Frobenius Map and Table Reference to Adapt to Higher Characteristic”, Advances in Cryptography-EUROCRYPT’99, LNCS 1592, pp. 176-189, 1999.
10. N. Koblitz, “Elliptic Curve Cryptosystems”, Mathematics of Computation, vol. 48, pp. 203-209, 1987.
11. P. C. Kocher, “Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, andOther Systems”, Advances in Cryptology – CRYPTO’96, LNCS 1109, pp. 104-113, 1996.
12. C. H. Lim and H. S. Hwang, “Fast Implementation of Elliptic Arithmetic in GF(pn)”, Public Key Cryptography-PKC 2000, LNCS 1751, pp. 405-421, 2000.
13. J. Lopéz and R. Dahab, “Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)”, Selected Areas in Cryptology-SAC’98, LNCS 1556, pp. 201-212, 1999.
14. J. Lopéz and R. Dahab, “Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation”, Cryptographic Hardware and Embedded Systems-CHES’99, LNCS 1717, pp. 316-327, 1999.
15. V. Miller, “Uses of Elliptic Curves in Cryptography”, Advances in Cryptography-CRYPTO’85, LNCS 218, pp. 417-426, 1986.
16. P. L. Montgomery, “Speeding the PollardandElliptic Curve Methods of Factorization”, Mathematics of Computation, vol. 48, pp. 243-264, 1987.
17. K. Okeya, H. Kurumatani, and K. Sakurai, “Elliptic Curves with the Montgomery-Form andTheir Cryptographic Applications”, Public Key Cryptography-PKC 2000, LNCS 1751, pp. 238-257, 2000.
18. K. Okeya and K. Sakurai, “Efficient Elliptic Curve Cryptosystems from a Scalar Multiplication Algorithm with Recovery of the y-coordinate on a Montgomery-Form Elliptic Curve”, Preproceedings of Cryptographic Hardware and Embedded Systems-CHES 2001, pp. 129-144, 2001.
19. E. D. Win, S. Mister, B. Preneel, and M. Wiener, “On the Performance of Signature Schemes Basedon Elliptic Curves”, Algorithm Number Theory-ANTS III, LNCS 1423, pp. 252-266, 1998.