Extending scalar multiplication using double bases

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

Volumn 4284 LNCS, Issue , 2006, Pages 130-144

  Avanzi, Roberto ^a   Dimitrov, Vassil ^b   Doche, Christophe ^c   Sica, Francesco ^d  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b UNIVERSITY OF CALGARY   (Canada)

^c MACQUARIE UNIVERSITY   (Australia)

^d MOUNT ALLISON UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ELLIPTIC CURVE; KOBLITZ CURVES; OPTIMAL CONSTANT; OPTIMAL PARAMETER; RECODING; SCALAR MULTIPLICATION; SMALL MEMORY FOOTPRINT; SPEED-UPS; STANDARD METHOD; STORAGE REQUIREMENTS; SUPERSINGULAR CURVES;

CRYPTOGRAPHY; GENE EXPRESSION; NETWORK SECURITY;

CURVE FITTING;

EID: 77649268304     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11935230_9     Document Type: Conference Paper

References (25)

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, Lecture Notes in Computer Science 2947, pp. 28-40. Springer, 2004.
2. R. Avanzi, C. Heuberger, and H. Prodinger. On Redundant τ-adic Expansions and Non-Adjacent Digit Sets. To appear in Proceedings of SAC 2006 (Workshop on Selected Areas in Cryptography), Lecture Notes in Computer Science. Springer.
3. 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, Lecture Notes in Computer Science 3897, pp. 332-344. Springer, 2006.
4. R. Avanzi and F. Sica. Scalar Multiplication on Koblitz Curves using Double Bases. To appear in Proceedings of Vietcrypt 2006, Lecture Notes in Computer Science. Springer, 2006.
5. P. Barreto, H. Y. Kim, B. Lynn, and M. Scott. Efficient algorithms for pairingbased cryptosystems. In Advances in Cryptology - CRYPTO 2002, Lecture Notes in Computer Science 2442, pp. 354-369. Springer, 2002.
6. M. Ciet and F. Sica. An Analysis of Double Base Number Systems and a Sublinear Scalar Multiplication Algorithm. In Progress in Cryptology - Proceedings of Mycrypt 2005, Lecture Notes in Computer Science 3715, pp. 171-182. Springer, 2005.
7. J.-S. Coron, D. M'Ra?̈hi, and C. Tymen. Fast generation of pairs (k, [k]P) for Koblitz elliptic curves. In Proceedings of SAC 2001, Lecture Notes in Computer Science 2259, pp. 151-164. Springer, 2001.
8. 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, Lecture Notes in Computer Science 3788, pp. 59-78. Springer, 2005.
9. V. S. Dimitrov, L. Imbert, and P. K. Mishra. Fast elliptic curve point multiplication using double-base chains. Cryptology ePrint Archive, Report 2005/069, 2005. Available from http://eprint.iacr.org/.
10. 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.
11. V. S. Dimitrov, G. A. Jullien, and W. C. Miller. An algorithm for modular exponentiation. Information Processing Letters, 66(3):155-159, 1998.
12. C. Doche and T. Lange. Arithmetic of Elliptic Curves, in Handbook of Elliptic and Hyperelliptic Curve Cryptography, H. Cohen and G. Frey Eds. CRC Press, Inc., 2005.
13. C. Doche and T. Lange. Arithmetic of Special Curves, in Handbook of Elliptic and Hyperelliptic Curve Cryptography, H. Cohen and G. Frey Eds. CRC Press, Inc., 2005.
14. K. Fong, D. Hankerson, J. López, and A. J. Menezes. Field Inversion and Point Halving Revisited. IEEE Trans. Comp., 53(8), pp. 1047-1059, August 2004.
15. R. P. Gallant, J. L. Lambert, and S. A. Vanstone. Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms. In Advances in Cryptology - CRYPTO 2001, Lecture Notes in Computer Science 2139, pp. 190-200. Springer, 2001.
16. E. W. Knudsen. Elliptic Scalar Multiplication Using Point Halving. In Advances in Cryptography - ASIACRYPT 1999, Lecture Notes in Computer Science 1716, pp. 135-149. Springer, 1999.
17. N. Koblitz. CM-curves with good cryptographic properties. In Advances in Cryptology - CRYPTO 1991, Lecture Notes in Computer Science 576, pp. 279-287, Berlin, 1991. Springer.
18. A. J. Menezes. Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers, 1993.
19. K. Okeya, T. Takagi, and C. Vuillaume. Short Memory Scalar Multiplication on Koblitz Curves. In Proceedings of CHES 2005, Lecture Notes in Computer Science 3659, pp. 91-105. Springer, 2005.
20. D. J. Park, S. G. Sim, and P. J. Lee. Fast scalar multiplication method using changeof-basis matrix to prevent power analysis attacks on Koblitz curves. In Proceedings of WISA 2003, Lecture Notes in Computer Science 2908, pp. 474-488. Springer, 2003.
21. G.W. Reitwiesner. Binary arithmetic. Advances in Computers, 1, pp. 231-308, 1960.
22. R. Schroeppel. Elliptic curve point ambiguity resolution apparatus and method. International Application Number PCT/US00/31014, filed 9 November 2000.
23. R. Schroeppel. Elliptic curves: Twice as fast!, 2000. Presentation at the Crypto 2000 Rump Session.
24. J. A. Solinas. An Improved Algorithm for Arithmetic on a Family of Elliptic Curves. In Advances in Cryptology - CRYPTO 1997, Lecture Notes in Computer Science 1294, pp. 357-371. Springer, 1997.
25. J. A. Solinas. Efficient arithmetic on Koblitz curves. Designs, Codes and Cryptography, 19, pp. 195-249, 2000.