Double-Base number system for multi-scalar multiplications

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

Volumn 5479 LNCS, Issue , 2009, Pages 502-517

  Doche, Christophe ^a   Kohel, David R ^b   Sica, Francesco ^c  

^a MACQUARIE UNIVERSITY   (Australia)

^b AIX MARSEILLE UNIVERSITY   (France)

^c MOUNT ALLISON UNIVERSITY   (Canada)

Author keywords

Double Base Number System; Elliptic curve cryptography; Koblitz curves.; scalar multiplication

Indexed keywords

AVERAGE NUMBERS; BASE SYSTEMS; CO-ORDINATE SYSTEM; DOUBLE- BASE NUMBER SYSTEM; DOUBLINGS; ELLIPTIC CURVE CRYPTOGRAPHY; HIGH REDUNDANCY; JOINT SPARSE FORM; KOBLITZ CURVES.; MULTI-SCALAR MULTIPLICATIONS; SCALAR MULTIPLICATION; SPEED-UP;

CRYPTOGRAPHY;

GRAPH THEORY;

EID: 67650697249     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-01001-9_29     Document Type: Conference Paper

References (21)

1. Adikari, J., Dimitrov, V., Imbert, L.: Hybrid Binary-Ternary Joint Sparse Form and its Application in Elliptic Curve Cryptography, http://eprint.iacr. org/2008/
2. Avanzi, R.M., Cohen, H., Doche, C., Frey, G., Nguyen, K., Lange, T., Vercauteren, F.: Handbook of Elliptic and Hyperelliptic Curve Cryptography. Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton (2005)
3. Avanzi, R.M., Dimitrov, V.S., Doche, C., Sica, F.: Extending scalar multiplication using double bases. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol.4284, pp. 130-144. Springer, Heidelberg (2006)
4. Avanzi, R.M., Sica, F.: Scalar multiplication on koblitz curves using double bases. In: Nguyên, P.Q. (ed.) VIETCRYPT 2006. LNCS, vol.4341, pp. 131-146. Springer, Heidelberg (2006)
5. Bernstein, D.J., Lange, T.: Faster addition and doubling on elliptic curves. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol.4833, pp. 29-50. Springer, Heidelberg (2007)
6. Bernstein, D.J., Birkner, P., Lange, T., Peters, C.: Optimizing double-base ellipticcurve single-scalar multiplication. In: Srinathan, K., Rangan, C.P., Yung, M. (eds.) INDOCRYPT 2007. LNCS, vol.4859, pp. 167-182. Springer, Heidelberg (2007)
7. Bernstein, D.J., Lange, T.: Explicit-formulas database, http://www.hyperelliptic.org/EFD/
8. Ciet, M., Joye, M., Lauter, K., Montgomery, P.L.: Trading Inversions for Multiplications in Elliptic Curve Cryptography. Des. Codes Cryptogr. 39(2), 189-206 (2006)
9. Ciet, M., Lange, T., Sica, F., Quisquater, J.-J.: Improved algorithms for efficient arithmetic on elliptic curves using fast endomorphisms. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol.2656, pp. 388-400. Springer, Heidelberg (2003)
10. N-1. IEEE Trans. on Circuits and Systems 42(7), 377-380 (1995)
11. Dimitrov, V.S., Imbert, L., Mishra, P.K.: Efficient and secure elliptic curve point multiplication using double-base chains. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol.3788, pp. 59-78. Springer, Heidelberg (2005) (Pubitemid 43763469)
12. Dimitrov, V.S., Järvinen, K.U., Jacobson Jr., M.J., Chan, W.F., Huang, Z.: FPGA implementation of point multiplication on koblitz curves using kleinian integers. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol.4249, pp. 445-459. Springer, Heidelberg (2006) (Pubitemid 44700075)
13. Dimitrov, V.S., Jullien, G.A., Miller, W.C.: An Algorithm for Modular Exponentiation. Information Processing Letters 66(3), 155-159 (1998) (Pubitemid 128401899)
14. Doche, C., Habsieger, L.: A tree-based approach for computing double-base chains. In: Mu, Y., Susilo, W., Seberry, J. (eds.) ACISP 2008. LNCS, vol.5107, pp. 433- 446. Springer, Heidelberg (2008)
15. Doche, C., Kohel, D.R., Sica, F.: Double-Base Number System for Multi-Scalar Multiplications, http://eprint.iacr.org/2008/
16. Hankerson, D., Menezes, A.J., Vanstone, S.A.: Guide to Elliptic Curve Cryptography. Springer, Heidelberg (2003)
17. Okeya, K., Takagi, T., Vuillaume, C.: Short memory scalar multiplication on koblitz curves. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol.3659, pp. 91-105. Springer, Heidelberg (2005) (Pubitemid 41520699)
18. Park, D.J., Sim, S.G., Lee, P.J.: Fast scalar multiplication method using change-ofbasis matrix to prevent power analysis attacks on koblitz curves. In: Chae, K.-J., Yung, M. (eds.) WISA 2003. LNCS, vol.2908, pp. 474-488. Springer, Heidelberg (2004) (Pubitemid 39743432)
19. Solinas, J.A.: Low-weight binary representations for pairs of integers. Combinatorics and Optimization Research Report CORR 2001-41, University of Waterloo (2001)
20. Straus, E.G.: Addition chains of vectors (problem 5125). Amer. Math. Monthly 70, 806-808 (1964)
21. Washington, L.C.: Elliptic Curves. Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton (2003); number theory and Cryptography