Computing modular polynomials modulo large primes

Cryptography – Particular algorithmic function encoding

Reexamination Certificate

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

C380S030000

Reexamination Certificate

active

07623655

ABSTRACT:
Systems and methods for computing modular polynomials modulo large primes are described. In one aspect, the systems and methods generate 1-isogenous elliptic curves. A modular polynomial modulo a large prime p is then computed as a function of 1-isogenous elliptic curves modulo p.

REFERENCES:
Kohel, David. Endomorphism rings of elliptic curves over finite fields,1-104. Thesis UC Berkeley,1996. Berkeley:UCB, 1996.
Agashe, A., et al., “Constructing Elliptic Curves with a know number of points over a prime field”, in Lectures in honour of the 60th birthday of Hugh Cowie Williams, Fields Institute Cummunications Series, 1-17, 2003.
Blake, I., et al., “Elliptic Curves in Cryptography”, Lond. Math. Soc., Lecture Note Series, Cambridge University Press, 1999.
Bosma, W., et al., “Handbook of Magma Functions”, Sydney, 2003.
Burgess, D., et al., “On character sums and primitive roots”, Proc. London Math Soc., III, 179-192, 1962.
Elkies, Noam, et al., “Elliptic and modular curves over finite fields and related computational issues”, in Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A.O.L. Atkin (D.A. Buell and J.T. Teitelbaum, eds.), AMS/International Press, 21-76, 1998.
Lenstra, A. et al., “Algorithms in Number Theory”, Handbook of Theoretical Computer Science, vol. A. Elsevier 6730715, 1990.
Mestre, J-F.; “La methode des graphes. Exemples et applications”, Proceedings of the international conference on class numbers and fundamental units of algebraic number fields, Nagoya Univ., Nagoya, 217-242, 1986.
Schoof, Rene, “Nonsingular Plane Cubic Curves over Finite Fields”, J. Combinatorial Theory, 2, 183-208, 1987.
Shoup, Victor, “Fast construction of irreducible polynomials over finite fields”, J. Symbolic Computation, 471-391, 1994.
Silverman, Joseph H., “The Arithmetic of Elliptic Curves”, Graduate Texts in Mathematics, Springer-Verlag, 1986.

LandOfFree

Say what you really think

Search LandOfFree.com for the USA inventors and patents. Rate them and share your experience with other people.

Rating

Computing modular polynomials modulo large primes does not yet have a rating. At this time, there are no reviews or comments for this patent.

If you have personal experience with Computing modular polynomials modulo large primes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computing modular polynomials modulo large primes will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFUS-PAI-O-4083314

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.