On the use of weber polynomials in elliptic curve cryptography

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

Volumn 3093, Issue , 2004, Pages 335-349

  Konstantinou, Elisavet ^a,b   Stamatiou, Yannis C ^a,c,d   Zaroliagis, Christos ^a,b  

^a University of Patras and Computer Technology Institute   (Greece)

^b UNIVERSITY OF PATRAS   (Greece)

^c UNIVERSITY OF THE AEGEAN   (Greece)

^d ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL EFFICIENCY; CRYPTOGRAPHY; GEOMETRY; MATHEMATICAL TRANSFORMATIONS; PUBLIC KEY CRYPTOGRAPHY; SMART CARDS;

COMPLEX MULTIPLICATION; COMPUTATIONAL DEMANDS; CRYPTOGRAPHIC APPLICATIONS; ELLIPTIC CURVE CRYPTOGRAPHY; HILBERT POLYNOMIAL; PUBLIC-KEY INFRASTRUCTURE; RESOURCE-LIMITED DEVICES; SECURITY PROPERTIES;

POLYNOMIALS;

EID: 35048865761     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-25980-0_28     Document Type: Article

References (23)

1. A.O.L. Atkin and F. Morain, Elliptic curves and primality proving, Mathematics of Computation 61, pp. 29-67, 1993.
2. H. Baier and J. Buchmann, Efficient construction of cryptographically strong elliptic curves, in Progress in Cryptology - INDOCRYPT 2000, Lecture Notes in Computer Science Vol. 1977, Springer-Verlag, pp. 191-202, 2000.
3. H. Baier, Efficient Algorithms for Generating Elliptic Curves over Finite Fields Suitable for Use in Cryptography, PhD Thesis, Dept. of Computer Science, Technical Univ. of Darmstadt, May 2002.
4. I. Blake, G. Seroussi, and N. Smart, Elliptic curves in cryptography, London Mathematical Society Lecture Note Series 265, Cambridge University Press, 1999.
5. A. Enge and F. Morain, Comparing invariants for class fields of imaginary quadratic fields, in Algorithmic Number Theory - ANTS-V, Lecture Notes in Computer Science Vol. 2369, Springer-Verlag, pp. 252-266, 2002.
6. A. Enge and R. Schertz, Constructing Elliptic Curves from Modular Curves of Positive Genus, Preprint, March 2003.
7. GNU multiple precision library, edition 3.1.1, September 2000. Available at: http://www.swox.com/gmp.
8. N. Gura, H. Eberle, and S.C. Shantz, Generic Implementations of Elliptic Curve Cryptography using Partial Reduction, in Proc. 9th ACM Conf. on Computer and Communications Security - CCS'02, pp.108-116.
9. IEEE P1363/D13, Standard Specifications for Public-Key Cryptography, ballot draft, 1999. http://grouper.ieee.org/groups/1363/tradPK/draft.html.
10. E. Kaltofen, T. Valente, and N. Yui, An Improved Las Vegas Primality Test, in Proc. ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, pp. 26-33, 1989.
11. E. Kaltofen and N. Yui, Explicit construction of the Hilbert class fields of imaginary quadratic fields by integer lattice reduction. Research Report 89-13, Renseelaer Polytechnic Institute, May 1989.
12. E. Konstantinou, Y.C. Stamatiou, and C. Zaroliagis, On the Efficient Generation of Elliptic Curves over Prime Fields, in Cryptographic Hardware and Embedded Systems - CHES 2002, Lecture Notes in Computer Science Vol. 2523, Springer-Verlag, pp. 333-348, 2002.
13. G.J. Lay and H. Zimmer, Constructing Elliptic Curves with Given Group Order over Large Finite Fields, in Algorithmic Number Theory - ANTS-I, Lecture Notes in Computer Science Vol. 877, Springer-Verlag, pp.250-263, 1994.
14. LiDIA. A library for computational number theory, Technical University of Darmstadt. Available from http://www.Informatik.tu-darmstadt.de/TI/LiDIA/Welcome.html.
15. F. Morain, Computing the cardinality of CM elliptic curves using torsion points, Preprint, October 2002.
16. V. Müller and S. Paulus, On the Generation of Cryptographically Strong Elliptic Curves, preprint, 1997.
17. I. Niven, H.S. Zuckerman, and H.L. Montgomery, An Introduction to the Theory of Numbers, John Wiley & Sons, 5th edition, 1991.
18. E. Savaş, T.A. Schmidt, and Ç.K. Koç, Generating Elliptic Curves of Prime Order, in Cryptographic Hardware and Embedded Systems - CHES 2001, LNCS Vol. 2162 (Springer-Verlag, 2001), pp. 145-161.
19. R. Schertz, Weber's class invariants revisited, J. Théor. Nombres Bordeaux 14:1, 2002.
20. J. H. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, GTM 106, 1986.
21. A.-M. Spallek, Konstruktion einer elliptischen Kurve über einem endli-chen Körper zu gegebener Punktegruppe, Master Thesis, Universitäat GH Essen, 1992.
22. T. Valente, A distributed approach to proving large numbers prime, Rensselaer Polytechnic Institute Troy, New York, PhD Thesis, August 1992.
23. A. Weng, Konstruktion kryptographisch geeigneter Kurven mit komplexer Multiplikation, PhD thesis, Institut für Experimentelle Mathematik, Universität GH Essen, 2001.