Scalar multiplication on Koblitz curves using double bases

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

Volumn 4341 LNCS, Issue , 2006, Pages 131-146

  Avanzi, Roberto ^a   Sica, Francesco ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b MOUNT ALLISON UNIVERSITY   (Canada)

Author keywords

Double base number systems; Elliptic curves; Koblitz curves; Scalar multiplication; Sublinear algorithms

Indexed keywords

CRYPTOGRAPHY; GEOMETRY; NUMBERING SYSTEMS;

DOUBLE BASE NUMBER SYSTEM; ELLIPTIC CURVE; KOBLITZ CURVES; SCALAR MULTIPLICATION; SUBLINEAR ALGORITHM;

CURVE FITTING;

EID: 84887303740     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11958239_9     Document Type: Conference Paper

References (21)

1. R. Avanzi, M. Ciet, and F. Sica. Faster Scalar Multiplication on Koblitz Curves combining Point Halving with the Frobenius Endomorphism. In Proceedings of PKC 2004, Volume 2947 of Lecture Notes in Computer Science, pages 28-40. Springer, 2004.
2. R. Avanzi, V. S. Dimitrov, C. Doche, and F. Sica. Extending Scalar Multiplication using Double Bases. In Proceedings of Asiacrypt 2006, Lecture Notes in Computer Science. Springer, 2006.
3. R. Avanzi, C. Heuberger, and H. Prodinger. On Redundant τ-adic Expansions and Non-Adjacent Digit Sets. In Proceedings of SAC 2006 (Workshop on Selected Areas in Cryptography), Lecture Notes in Computer Science. Springer.
4. R. Avanzi, C. Heuberger, and H. Prodinger. Minimality of the Hamming Weight of the τ-NAF for Koblitz Curves and Improved Combination with Point Halving. In Proceedings of SAC 2005, Volume 3897 of Lecture Notes in Computer Science, pages 332-344. Springer, 2006.
5. M. Ciet and F. Sica. An Analysis of Double Base Number Systems and a Sublinear Scalar Multiplication Algorithm. In E. Dawson and S. Vaudenay, editors, Progress in Cryptology - Proceedings of Mycrypt 2005, Volume 3715 of Lecture Notes in Computer Science, pages 171-182. Springer, 2005.
6. V. S. Dimitrov, L. Imbert, and P. K. Mishra. Efficient and secure elliptic curve point multiplication using double-base chains. In Advances in Cryptology - ASIACRYPT 2005, Volume 3788 of Lecture Notes in Computer Science, pages 59-78. Springer, 2005.
7. V. S. Dimitrov, K. Jarvinen, M. J. Jacobson Jr, W. F. Chan, and Z. Huang. FPGA Implementation of Point Multiplication on Koblitz Curves Using Kleinian Integers. In Proceedings of CHES 2006, Lecture Notes in Computer Science. Springer, 2006.
8. V. S. Dimitrov, G. A. Jullien, and W. C. Miller. An algorithm for modular exponentiation. Information Processing Letters, 66(3):155-159, 1998.
9. R. P. Gallant, J. L. Lambert, and S. A. Vanstone. Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms. In J. Kilian, editor, Advances in Cryptology - Proceedings of CRYPTO 2001, Volume 2139 of Lecture Notes in Computer Science, pages 190-200. Springer, 2001.
10. G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers. Oxford University Press, fifth edition, 1979.
11. E. W. Knudsen. Elliptic Scalar Multiplication Using Point Halving. In K.-Y. Lam, E. Okamoto, and C. Xing, editors, Advances in Cryptography - Proceedings of ASIACRYPT 1999, Volume 1716 of Lecture Notes in Computer Science, pages 135-149. Springer, 1999.
12. N. Koblitz. Elliptic Curve Cryptosystems. Mathematics of Computation, 48(177):203-209, 1987.
13. N. Koblitz. CM-curves with good cryptographic properties. In Joan Feigenbaum, editor, Advances in Cryptology - Proceedings of CRYPTO 1991, Volume 576 of Lecture Notes in Computer Science, pages 279-287, Berlin, 1991. Springer.
14. V.S. Miller. Use of Elliptic Curves in Cryptography. In H.C. Williams, editor, Advances in Cryptology - Proceedings of CRYPTO 1985, Volume 218 of Lecture Notes in Computer Science, pages 417-426. Springer, 1986.
15. J.A. Muir and D.R. Stinson. New Minimal Weight Representations for Left-to-Right Window Methods. In Topics in cryptology - CT-RSA 2005, Volume 3376 of Lecture Notes in Comput. Sci., pages 366-383. Springer-Verlag, Berlin, 2005.
16. K. Okeya, T. Takagi, and C. Vuillaume. Short Memory Scalar Multiplication on Koblitz Curves. In Proceedings of CHES 2005, Volume 3659 of Lecture Notes in Computer Science, pages 91-105. Springer, 2005.
17. G.W. Reitwiesner. Binary arithmetic. Advances in Computers, 1:231-308, 1960.
18. R. Schroeppel. Elliptic curves: Twice as fast!, 2000. Presentation at the Crypto 2000 Rump Session.
19. J. A. Solinas. An Improved Algorithm for Arithmetic on a Family of Elliptic Curves. In Burton S. Kaliski Jr., editor, Advances in Cryptology - Proceedings of CRYPTO 1997, Volume 1294 of Lecture Notes in Computer Science, pages 357-371. Springer, 1997.
20. J. A. Solinas. Efficient arithmetic on Koblitz curves. Designs, Codes and Cryptography, 19:195-249, 2000.
21. A.C. Yao. On the evaluation of powers. SIAM Journal on Computing, 5:100-103, 1976.