Improved techniques for fast exponentiation

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

Volumn 2587, Issue , 2003, Pages 298-312

  Möller, Bodo ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 35248820671     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-36552-4_21     Document Type: Article

References (19)

1. AMERICAN NATIONAL STANDARDS INSTITUTE (ANSI). Public key cryptography for the financial services industry: The elliptic curve digital signature algorithm (ECDSA). ANSI X9.62, 1998.
2. BOSMA, W. Signed bits and fast exponentiation. Department of Mathematics, University of Nijmegen, Report No. 9935, 1999.
3. COHEN, H., ONO, T., AND MIYAJI, A. Efficient elliptic curve exponentiation using mixed coordinates. In Advances in Cryptology - ASIACRYPT '98 (1998), K. Ohta and D. Pei, Eds., vol. 1514 of Lecture Notes in Computer Science, pp. 51-65.
4. GORDON, D. M. A survey of fast exponentiation methods. Journal of Algorithms 27 (1998), 129-146.
5. JOYE, M., AND TYMEN, C. Compact encoding of non-adjacent forms with applications to elliptic curve cryptography. In Public Key Cryptography - PKC 2001 (2001), K. Kim, Ed., vol. 1992 of Lecture Notes in Computer Science, pp. 353-364.
6. KNUTH, D. E. The Art of Computer Programming - Vol. 2: Seminumerical Algorithms (3rd ed.). Addison-Wesley, 1998.
7. LEE, P.-J., AND LIM, C.-H. Method for exponentiation in a public-key cryptosystem. United States Patent 5,999,627, 1999.
8. LIM, C. H., AND LEE, P. J. More flexible exponentiation with precomputation. In Advances in Cryptology - CRYPTO '94 (1994), Y. G. Desmedt, Ed., vol. 839 of Lecture Notes in Computer Science, pp. 95-107.
9. MIYAJI, A., ONO, T., AND COHEN, H. Efficient elliptic curve exponentiation. In International Conference on Information and Communications Security - ICICS '97 (1997), Y. Han, T. Okamoto, and S. Qing, Eds., vol. 1334 of Lecture Notes in Computer Science, pp. 282-290.
10. MÖLLER, B. Algorithms for multi-exponentiation. In Selected Areas in Cryptography - SAC 2001 (2001), S. Vaudenay and A. M. Youssef, Eds., vol. 2259 of Lecture Notes in Computer Science, pp. 165-180.
11. NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY (NIST). Digital Signature Standard (DSS). FIPS PUB 186-2, 2000.
12. PIPPENGER, N. On the evaluation of powers and related problems (preliminary version). In 17th Annual Symposium on Foundations of Computer Science (1976), IEEE Computer Society, pp. 258-263.
13. REITWIESNER, G. W. Binary arithmetic. Advances in Computers 1 (1960), 231-308.
14. SAKAI, Y., AND SAKURAI, K. Algorithms for efficient simultaneous elliptic scalar multiplication with reduced joint Hamming weight representation of scalars. In Information Security - ISC 2002 (2002), A. H. Chan and V. Gligor, Eds., vol. 2433 of Lecture Notes in Computer Science, pp. 484-499.
15. SCHROEPPEL, R., ORMAN, H., O'MALLEY, S., AND SPATSCHECK, O. Fast key exchange with elliptic curve systems. In Advances in Cryptology - CRYPTO '95 (1995), D. Coppersmith, Ed., vol. 963 of Lecture Notes in Computer Science, pp. 43-56.
16. SOLINAS, J. A. An improved algorithm for arithmetic on a family of elliptic curves. In Advances in Cryptology - CRYPTO '97 (1997), B. S. Kaliski, Jr., Ed., vol. 1294 of Lecture Notes in Computer Science, pp. 357-371.
17. SOLINAS, J. A. Efficient arithmetic on Koblitz curves. Designs, Codes and Cryptography 19 (2000), 195-249.
18. THURBER, E. G. On addition chains l(mn) ≤ l(n) - 6 and lower bounds for c(r). Duke Mathematical Journal 40 (1973), 907-913.
19. YAO, A. C.-C. On the evaluation of powers. SIAM Journal on Computing 5 (1976), 100-103.