Short memory scalar multiplication on Koblitz curves

Lecture Notes in Computer Science

Volumn 3659, Issue , 2005, Pages 91-105

  Okeya, Katsuyuki ^a   Takagi, Tsuyoshi ^b   Vuillaume, Camille ^a  

^a HITACHI LTD   (Japan)

^b FUTURE UNIVERSITY HAKODATE   (Japan)

Author keywords

Change of basis; Elliptic curve cryptosystems; Koblitz curves; NAF; Normal basis; Polynomial basis; Scalar multiplication; Smartcard

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER HARDWARE; COMPUTER SOFTWARE; CRYPTOGRAPHY; EMBEDDED SYSTEMS; POLYNOMIALS; SMART CARDS;

CHANGE-OF-BASIS; ELLIPTIC CURVE CRYPTOSYSTEMS; KOBLITZ CURVES; NAF; NORMAL BASIS; POLYNOMIAL BASIS; SCALAR MULTIPLICATION;

STORAGE ALLOCATION (COMPUTER);

EID: 27244460246     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11545262_7     Document Type: Conference Paper

References (18)

1. Avanzi, R. M., Ciet, M., Sica, F.: Faster scalar multiplication on Koblitz curves combining point halving with the Frobenius endomorphism. In Proc. of PKC'04, LNCS 2947, pp.28-40, 2004.
2. Brickell, E. F., Gordon, D. M., McCurley, K. S., Wilson, D. B.: Fast exponentiation with precomputation: algorithms and lower bounds. In Proc. of Eurocrypt'92, LNCS 658, pp.200-209, 1993.
3. Chevallier-Mames, B., Ciet, M., Joye, M.: Low-cost solutions for preventing simple side-channel analysis: side-channel atomicity. In IEEE Trans. Computers 53(6), pp. 760-768, 2004.
4. Coron, J.-S., M'Raïhi, D., Tymen, C.: Fast generation of pairs (k, [k]P) for Koblitz elliptic curves. In Proc. of SAC'01, LNCS 2259, pp. 151-164, 2001.
5. Dahab, R., Hankerson, D., Hu, F., Long, M., López, J., Menezes, A.: Software multiplication using normal bases. Technical report CACR 2004-12, University of Waterloo, 2004.
6. Hankerson, D., López, J., Menezes, A.: Software implementation of elliptic curve cryptography over binary fields. In Proc. of CHES'00, LNCS 1965, pp. 1-24, 2001.
7. IEEE P1363A. Standard specifications for public-key cryptography, annex A, number-theoretic background, 2000.
8. Joye, M., Tymen, C.: Compact encoding of non-adjacent forms with applications to elliptic curve cryptography. In Proc. of PKC'01, LNCS 1992, pp. 353-364, 2001.
9. Joye, M., Tymen, C.: Protections against differential analysis for elliptic curve cryptography: An algebraic approach. In Proc. of CHES'01, LNCS 2162, pp. 377-390, 2001.
10. Kaliski, B.S., Yin, Y.L.: Storage-efficient finite field basis conversion. In Proc. of SAC'98, LNCS 1556, pp. 81-93, 1999.
11. Koblitz, N.: Elliptic curve cryptosystems. In Mathematics of Computation, 48(177), pp. 203-209, 1987.
12. Koblitz, N.: CM-curves with good cryptographic properties. In Proc. of Crypto'91, LNCS 576, pp. 279-287, 1992.
13. Miller, V. S.: Use of elliptic curves in cryptography. In Proc. of Crypto'85, LNCS 218, pp. 417-426, 1986.
14. Massey, J., Omura, J. K.: Computational method and apparatus for finite field arithmetic. US Patent 4587627, 1986.
15. Möller, B.: Improved techniques for fast exponentiation. In Proc. of ICISC'02, LNCS 2587, pp 298-312, 2003.
16. Park, D. J., Sim, S. G., Lee, P. J.: Fast scalar multiplication method using change-of-basis matrix to prevent power analysis attacks on Koblitz curves. In Proc. of WISA 2003, LNCS 2908, pp. 474-488, 2003.
17. Solinas, J. A.: An improved algorithm for arithmetic on a family of elliptic curves. In Proc. of Crypto'97, LNCS 1294, pp. 357-371, 1997.
18. Solinas, J. A.: Efficient arithmetic on Koblitz curves. In Designs, Codes, and Cryptography, 19(2-3), pp. 195-249, 2000.