New point addition formulae for ECC applications

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

Volumn 4547 LNCS, Issue , 2007, Pages 189-201

  Meloni, Nicolas ^a,b  

^a UNIVERSITÉ DE MONTPELLIER   (France)

^b CNRS   (France)

Author keywords

Addition chains; Elliptic curve; Exponentiation; Fibonacci; Scalar multiplication

Indexed keywords

ALGORITHMS; NUMBER THEORY; NUMERICAL METHODS; PROBLEM SOLVING;

ADDITION CHAINS; EXPONENTIATION; FIBONACCI; SCALAR MULTIPLICATION;

CURVE FITTING;

EID: 38149033703     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-73074-3_15     Document Type: Conference Paper

References (14)

1. Brier, E., Joye, M.: Weierstraß elliptic curves and side-channel attacks. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 335-345. Springer, Heidelberg (2002)
2. Capocelli, R.M.: A generalization of fibonacci trees. In: Third In. Conf. on Fibonacci Numbers and their Applications (1988)
3. Cohen, H., Frey, G. (eds.): Handbook of Elliptic and Hyperelliptic Cryptography. Chapman & Hall, Sydney, Australia (2006)
4. Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation using mixed coordinates. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, Springer, Heidelberg (1998)
5. Doche, C., Imbert, L.: Extended double-base number system with applications to elliptic curve cryptography. In: Barua, R., Lange, T. (eds.) INDOCRYPT 2006. LNCS, vol. 4329, pp. 335-348. Springer, Heidelberg (2006)
6. Hankerson, D., Menezes, A., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer, Heidelberg (2004)
7. Knudsen, E.W.: Elliptic scalar multiplication using point halving. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 135-149. Springer, Heidelberg (1999)
8. Knuth, D., Yao, A.: Analysis of the subtractive algorithm for greater common divisors. Proc. Nat. Acad. Sci. USA 72(12), 4720-4722 (1975)
9. Koblitz, N.: Elliptic curve cryptosystems. Mathematics of Computation 48, 203-209 (1987)
10. Lopez, J., Dahab, R.: Fast multiplication on elliptic curves over GF (2 m) without precomputation. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 316-327. Springer, Heidelberg (1999)
11. Miller, V.S.: Uses of elliptic curves in cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417-428. Springer, Heidelberg (1986)
12. m-n) via Lucas chains (1983), Available at ftp.cwi.nl:/pub/pmontgom/Lucas.ps.gz
13. Montgomery, P.: Speeding the pollard and elliptic curve methods of factorization. Mathematics of Computation 48, 243-264 (1987)
14. Solinas, J.A.: Improved algorithms for arithmetic on anomalous binary curves. Technical report, University of Waterloo (1999), http://www.cacr.math. uwaterloo.ca/techreports/1999/corr99-46.pdf