A course in computational algebraic number theory
A course in computational algebraic number theory
Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve
Journal of Symbolic Computation
Key-Exchange in Real Quadratic Congruence Function Fields
Designs, Codes and Cryptography - Special issue dedicated to Gustavus J. Simmons
Computing discrete logarithms in real quadratic congruence function fields of large genus
Mathematics of Computation
Real and imaginary quadratic representations of hyperelliptic function fields
Mathematics of Computation
Voronoi's algorithm in purely cubic congruence function fields of unit rank 1
Mathematics of Computation
Computing in the jacobian of a plane algebraic curve
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
On Integral Basis Reduction in Global Function Fields
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Lattice Basis Reduction in Function Fields
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Computing Riemann---Roch spaces in algebraic function fields and related topics
Journal of Symbolic Computation
Computing Zeta Functions of Hyperelliptic Curves over Finite Fields of Characteristic 2
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Supersingular Curves in Cryptography
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Computation of Discrete Logarithms in F2607
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
An Extension of Kedlaya's Point-Counting Algorithm to Superelliptic Curves
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Linear algebra algorithms for divisors on an algebraic curve
Mathematics of Computation
The arithmetic of certain cubic function fields
Mathematics of Computation
Efficient Computation of Roots in Finite Fields
Designs, Codes and Cryptography
A new cryptography algorithm using cab curves an LDPC for wireless communication systems
MATH'06 Proceedings of the 10th WSEAS International Conference on APPLIED MATHEMATICS
An addition algorithm in Jacobian of C34 curve
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
A general methodology for pipelining the point multiplication operation in curve based cryptography
ACNS'06 Proceedings of the 4th international conference on Applied Cryptography and Network Security
Explicit bounds of polynomial coefficients and counting points on Picard curves over finite fields
Mathematical and Computer Modelling: An International Journal
Algebraic curves and cryptography
Finite Fields and Their Applications
| Hi-index | 0.00 |
This paper is concerned with algorithms for computing in the divisor class group of a nonsingular plane curve of the form yn = c(x) which has only one point at infinity. Divisors are represented as ideals, and an ideal reduction algorithm based on lattice reduction is given. We obtain a unique representative for each divisor class and the algorithms for addition and reduction of divisors run in polynomial time. An algorithm is also given for solving the discrete logarithm problem when the curve is defined over a finite field.