Collisions in fast generation of ideal classes and points on hyperelliptic and elliptic curves

Applicable Algebra in Engineering, Communications and Computing

Volumn 15, Issue 5, 2005, Pages 329-337

  Lange, Tanja ^a   Shparlinski, Igor ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b MACQUARIE UNIVERSITY   (Australia)

Author keywords

Collisions; Discrete Logarithm; Hyperelliptic Curves; Koblitz Curves; Public Key Cryptography

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; LINEAR EQUATIONS; POLYNOMIALS; PUBLIC KEY CRYPTOGRAPHY; SET THEORY; THEOREM PROVING;

COLLISIONS; DISCRETE LOGARITHM; HYPERELLIPTIC CURVES; KOBLITZ CURVES;

RANDOM PROCESSES;

EID: 13644269957     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00200-004-0161-9     Document Type: Article

References (15)

1. Behlen, P.: Algebraic geometry and coding theory, PhD thesis, Eindhoven University of Technology, 2001
2. Bosma, W.: Signed bits and fast exponentiation. J. Théorie des Nombres Bordeaux 13, 27-41 (2001)
3. Doumen, J.: Some applications of coding theory in cryptography, PhD thesis, Eindhoven University of Technology, 2003
4. Everest, G., van der Poorten, A.J., Shparlinski, I.E., Ward, T.B.: Recurrence sequences. Amer. Math. Soc. 2003
5. Galbraith, S.D., McKee, J.: The probability that the number of points on an elliptic curve over a finite field is prime. J. London Math. Soc. 62, 671-684 (2000)
6. Günther, C., Lange, T., Stein, A.: Speeding up the arithmetic on Koblitz curves of genus two. Proc. SAC'00, Lect. Notes in Comp. Sci. Springer-Verlag, Berlin, 2012, 106-117 (2001)
7. Koblitz, N.: CM curves with good cryptographic properties. Proc. Crypto'91, Lect. Notes in Comp. Sci. Springer-Verlag, Berlin, 576, 279-287 (1992)
8. Koblitz, N.: Almost primality of group orders of elliptic curves defined over small finite fields. Experiment. Math. 10, 553-558 (2001)
9. Lange, T.: Efficient arithmetic on hyperelliptic curves. PhD thesis, Universität Ges-amthochschule Essen, 2001
10. Lange, T.: Koblitz Curve Cryptosystems. To appear in Finite Fields and Their Applications, online 24 August 2004
11. Müller, V.: Fast multiplication on elliptic curves over small fields of characteristic two. J. Cryptol. 11, 219-234 (1998)
12. Mumford, D.: Tata lectures on Theta II. Birkhäuser, 1984
13. Pohlig, S., Hellman, M.: An improved algorithm for computing logarithms over GF(p) and its cryptographic significance. IEEE Transactions on Information Theory IT-24, 106-110 (1978)
14. Smart, N.P.: Elliptic curve cryptosystems over small fields of odd characteristic. J. Cryptol. 12, 141-151 (1999)
15. Solinas, J.: Efficient arithmetic on Koblitz curves. Designs, Codes and Cryptography 19, 195-249 (2000)