An analysis of exponentiation based on formal languages

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

Volumn 1592, Issue , 1999, Pages 375-388

  O’connor, Luke ^a  

^a IBM RESEARCH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL LINGUISTICS; FORMAL LANGUAGES; SLIDING MODE CONTROL;

EXPONENTIATION ALGORITHMS; EXPONENTIATIONS; N-BIT EXPONENTS; SIGNED DIGITS; SIGNED-DIGIT REPRESENTATION; SLIDING WINDOW; SLIDING WINDOW METHODS; WEIGHT DISTRIBUTIONS;

CRYPTOGRAPHY;

EID: 84957671552     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48910-X_26     Document Type: Conference Paper

References (24)

1. See the Maple homepage at http://www.maplesoft.com.
2. S. Arno and F. Wheeler. Signed digit representations of minimal hamming weight. IEEE Transactions on Computers, 42(8):1007-1010, 1993.
3. E. A. Bender and S. G. Williamson. Foundations of Applied Combinatorics. Addison-Wesley Publishing Company, 1991.
4. J. Bos and M. Coster. Addition chain heuristics. Advances in Cryptology, CRYPTO 89, Lecture Notes in Computer Science, vol. 218, G. Brassard ed., Springer-Verlag, pages 400-407, 1990.
5. N. Chomsky and P. Schutzenberger. The algebraic theory of context-free languages. In P Bra_ort and North Holland Hirchberg, D., editors, Computer programming and formal languages, pages 118-161, 1963.
6. W. Di_e and M. Hellman. New directions in cryptography. IEEE Transactions on Information Theory, 22(6):472-492, 1976.
7. T. ElGamal. A public key cryptosystem and signature system based on discrete logarithms. IEEE Transactions on Information Theory, 31(4):473-481, 1985.
8. D. Gollman, Y. Han, and C. Mitchell. Redundant integer representations and fast exponentiation. Designs, Codes and Cryptography, 7:135-151, 1996.
9. R. L. Graham, D. E. Knuth, and O. Patshnik. Concrete Mathematics, A Foundation for Computer Science, First Edition. Addison Wesley, 1989.
10. J. Hopcroft and J. Ullman. An Introduction to Automata, Languages and Computation. Reading, MA: Addison Wesley, 1979.
11. L. Hui and K.-Y. Lam. Fast square-and-multiply exponentiation for RSA. Electronics Letters, 30(17):1396-1397, 1994.
12. J. Jedwab and C. Mitchell. Minimum weight modified signed-digit representations and fast exponentiation. Electronics Letters, 25:1171-1172, 1989.
13. C. K. Kǫc. High-radix and bit encoding techniques for modular exponentiation. International Journal of Computer Mathematics, 40:139-156, 1991.
14. C. K. Kǫc. Analysis of sliding window techniques for exponentiation. Computer and Mathematics with Applications, 30(10):17-24, 1995.
15. D. E. Knuth. The Art of Computer Programming: Volume 2, Seminumerical Algorithms. Addsion Wesley, 1981.
16. N. Koblitz. CM curves with good cryptographic properties. Advances in Cryptology, CRYPTO 91, Lecture Notes in Computer Science, vol. 576, J. Feigenbaum ed., Springer-Verlag, pages 279-287, 1992.
17. K. Koyama and T. Tsuruoka. Speeding up elliptic curve cryptosystems using a signed binary window method. In Advances in Cryptology, CRYPTO 92, Lecture Notes in Computer Science, vol. 740, E. F. Brickell ed., Springer-Verlag, pages 345-357, 1992.
18. A. Menezes, P. van Oorschot, and S. Vanstone. Handbook of Applied Cryptography. CRC press, 1996.
19. F. Morain and J. Olivos. Speeding up the computations on an ellipticcurve using addition-subtraction chains. Theoretical Informatics and Applications, 24(6):531- 544, 1990.
20. G. Reitwiesener. Binary arithmetic. In F. L. Alt, editor, Advances in Computers, pages 232-308, 1960.
21. R. L. Rivest, A. Shamir, and L. Adleman. A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM, 21(2):120-126, 1978.
22. R Sedgewick and P. Flajolet. An introduction to the analysis of algorithms. Addison-Wesley Publishing Company, 1996.
23. J. A. Solinas. An improved algorithm for arithmetic on a family of elliptic curves. Advances in Cryptology, CRYPTO 97, B. S. Kaliski ed., Springer-Verlag, pages 357-371, 1997., Lecture Notes in Computer Science, vol. 1294
24. Y. Yacobi. Exponentiating faster with addition chains. Advances in Cryptology, EUROCRYPT 90, Lecture Notes in Computer Science, vol. 473, I. B. DamgåRD ed., Springer-Verlag, pages 222-229, 1991.