Jacobi quartic curves revisited

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

Volumn 5594 LNCS, Issue , 2009, Pages 452-468

  Hisil, Huseyin ^a   Wong, Kenneth Koon Ho ^a   Carter, Gary ^a   Dawson, Ed ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Efficient elliptic curve arithmetic; Jacobi model of elliptic curves; Point multiplication

Indexed keywords

EFFICIENT ELLIPTIC CURVE ARITHMETIC; ELLIPTIC CURVE; JACOBI MODEL OF ELLIPTIC CURVES; NEW RESULTS; POINT DOUBLINGS; POINT MULTIPLICATION; PRECOMPUTE; PRIME NUMBER; SCALAR MULTIPLICATION; SINGLE POINT; WINDOWING TECHNIQUES;

JACOBIAN MATRICES;

GEOMETRY;

EID: 70350663101     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02620-1_31     Document Type: Conference Paper

References (25)

1. Avanzi, R.M.: A note on the signed sliding window integer recoding and its left-to-right analogue. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 130-143. Springer, Heidelberg (2004)
2. Billet, O., Joye, M.: The Jacobi model of an elliptic curve and side-channel analysis. In: Fossorier, M.P.C., Høholdt, T., Poli, A. (eds.) AAECC 2003. LNCS, vol. 2643, pp. 34-42. Springer, Heidelberg (2003)
3. Bernstein, D.J., Lange, T.: Analysis and optimization of elliptic-curve single-scalar multiplication. In: Finite Fields and Applications Fq8. Contemporary Mathematics, American Mathematical Society, vol. 461, pp. 1-18 (2008)
4. Bernstein, D.J., Lange, T.: eBACS: ECRYPT benchmarking of cryptographic systems (2008), http://bench.cr.yp.to
5. Bernstein, D.J., Lange, T.: Explicit-formulas database, http://www.hyperelliptic.org/EFD
6. 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)
7. Bernstein, D.J., Birkner, P., Joye, M., Lange, T., Peters, C.: Twisted Edwards curves. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 389-405. Springer, Heidelberg (2008)
8. Chudnovsky, D.V., Chudnovsky, G.V.: Sequences of numbers generated by addition in formal groups and new primality and factorization tests. Advances in Applied Mathematics 7(4), 385-434 (1986)
9. Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation using mixed coordinates. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 51-65. Springer, Heidelberg (1998)
10. Cohen, H., Frey, G. (eds.): Handbook of Elliptic and Hyperelliptic Curve Cryptography. CRC Press, Boca Raton (2005)
11. Duquesne, S.: Improving the arithmetic of elliptic curves in the Jacobi model. Information Processing Letters 104(3), 101-105 (2007)
12. Eisenträger, K., Lauter, K., Montgomery, P.L.: Fast elliptic curve arithmetic and improved Weil pairing evaluation. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 343-354. Springer, Heidelberg (2003)
13. 4, http://home.sandiego.edu/~langton/ eell.pdf
14. Galbraith, S.D., Lin, X., Scott, M.: Endomorphisms for faster elliptic curve cryptography on a large class of curves. In: EUROCRYPT 2009. LNCS, vol. 5479, pp. 518-535. Springer, Heidelberg (2009)
15. Gaudry, P., Thomé, E.: The mpFq library and implementing curve-based key exchanges. In: SPEED 2007, pp. 49-64 (2007), http://www.loria.fr/~gaudry/publis/mpfq.pdf
16. Hankerson, D., Menezes, A.J., Vanstone, S.A.: Guide to Elliptic Curve Cryptography. Springer, New York (2003)
17. Hisil, H., Carter, G., Dawson, E.: New formulae for efficient elliptic curve arithmetic. In: Srinathan, K., Rangan, C.P., Yung, M. (eds.) INDOCRYPT 2007. LNCS, vol. 4859, pp. 138-151. Springer, Heidelberg (2007)
18. Hisil, H., Wong, K.K., Carter, G., Dawson, E.: Faster group operations on elliptic curves. In: Australasian Information Security Conference (AISC 2009), Wellington, New Zealand (January 2009);
19. Conferences in Research and Practice in Information Technology (CRPIT), vol. 98, pp. 7-19 (2009)
20. Hisil, H., Wong, K.K., Carter, G., Dawson, E.: Twisted Edwards curves revisited. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 326-343. Springer, Heidelberg (2008)
21. Jacobi, C.G.J.: Fundamenta nova theoriae functionum ellipticarum. Sumtibus Fratrum Borntræger (1829)
22. Longa, P., Gebotys, C.: Novel precomputation schemes for elliptic curve cryptosystems. In: ACNS 2009. LNCS. Springer, Heidelberg (to appear, 2009)
23. Möller, B.: Improved techniques for fast exponentiation. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 298-312. Springer, Heidelberg (2003)
24. Monagan, M., Pearce, R.: Rational simplification modulo a polynomial ideal. In: ISSAC 2006, pp. 239-245. ACM, New York (2006)
25. Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis. Cambridge University Press, Cambridge (1927)