Fast exponentiation algorithms based on batch-processing and precomputation

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E80-A, Issue 1, 1997, Pages 34-39

  Tsuruoka, Yukio ^a   Koyama, Kenji ^a  

^a Nippon Telegraph and Telephone Corporation   (Japan)

Author keywords

Addition chains

Indexed keywords

ALGEBRA; ALGORITHMS; BATCH DATA PROCESSING; VECTORS;

ELLIPTIC CURVES; EXPONENTIATION METHOD; VECTOR ADDITION CHAINS;

CRYPTOGRAPHY;

EID: 0030712808     PISSN: 09168508     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. T. ElGamal, "A public key cryptosystem and signature. scheme based on discrete logarithms," IEEE Trans. Inf. Theory, vol.IT-31, no.4, pp.469-472, 1985.
2. L. Harn and Y. Xu, "Design of generalized ElGamal type digital signature schemes based on discrete logarithm," Electron. Lett., vol.30, no.24, 1994.
3. P.L. Montgomery, "Modular multiplication without trial division," Math, of Computation, vol.44, pp.519-521, 1985.
4. V. Miller, "Use of elliptic curves in cryptography," Proc. of CRYPTO'85 (LNCS-218), pp.417-426, 1985.
5. N. Koblitz, "Elliptic curve cryptosystems," Math, of Computation, vol.48, pp.203-209, 1987.
6. p," IEICE Trans. Fundamentals, vol.E77-A, no.4, pp.630-635, 1994.
7. J. Chao, K. Tanada, and S. Tsujii, "Design of elliptic curves with controllable lower boundary of extension degree for reduction attacks," Advances in Cryptology -CRYPTO'94, pp.50-55, 1994.
8. R.L. Rivest, A. Shamir, and L. Adleman, "A method for obtaining digital signatures and public-key cryptosystems," Commun. ACM, vol.21, no.2, pp.120-126, 1978.
9. D.E. Knuth, "Seminumerical algorithm (arithmetic)," The Art of Computer Programming, vol.2, Addison Wesley, 1969.
10. J. Bos and M. Coster, "Addition chain heuristics," Proc. of CRYPTO'89, 1989.
11. E.F. Brickeil, D.M. Gordon, K.S. McCurley, and D.B. Wilson, "Fast exponentiation with precomputation," Proc. of EUROCRYPT'92, 1992.
12. P. Rooij, "Efficient exponentiation using precomputation and vector addition chains," Proc. of EUROCRYPT'94, pp.403-415, 1994.
13. C.H. Lim and P.J. Lee, "More flexible exponentiation with precomputation," Proc CRYPTO'94, pp.95-107, 1994.
14. F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition subtraction chains," Theoretical Informatics and Applications, vol.24, no.6, pp.531-544, 1990.
15. K. Koyama and Y. Tsuruoka, "A Signed Binary Window Method for Fast Computing over Elliptic Curves," IEICE Trans. Fundamentals, vol.E76-A, no.1, pp.55-62, 1993.
16. S. Goldwasser and J. Killian, "Almost all primes can be quickly certified," Proc. 18th STOC. Berkeley, pp.316-329, 1986.
17. H.W. Lenstra Jr., "Factoring integers with elliptic curves," Ann. of Math. 126, pp.649-673, 1987.
18. Straus, Amer. Math. M, vol.71, pp.807-808, 1964.
19. J. Olivos, "On Vectorial Addition Chains," Journal of Algorithms, 2, pp. 13-21, 1981.
20. A.C. Yao, "On the evaluation of powers," SIAM J. Computing, vol.5, no.1, 1976.
21. Y. Tsuruoka, "A fast algorithm on addition sequences," Proc. of Korea-Japan Joint Workshop on Information Security and Cryptology '93, 1993.