Journal of Cryptology
Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
On the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Elliptic curves in cryptography
Elliptic curves in cryptography
Satoh's algorithm in characteristic 2
Mathematics of Computation
Use of Elliptic Curves in Cryptography
CRYPTO '85 Advances in Cryptology
Finding Secure Curves with the Satoh-FGH Algorithm and an Early-Abort Strategy
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
A Memory Efficient Version of Satoh's Algorithm
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Speeding up the Discrete Log Computation on Curves with Automorphisms
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Weil Descent of Elliptic Curves over Finite Fields of Characteristic Three
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Gaudry's Variant against Cab Curves
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Construction of Secure CabCurves Using Modular Curves
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Fast Jacobian Group Arithmetic on CabCurves
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Counting Points on Hyperelliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Arithmetic on superelliptic curves
Mathematics of Computation
An algorithm for solving the discrete log problem on hyperelliptic curves
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
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
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
On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Explicit bounds of polynomial coefficients and counting points on Picard curves over finite fields
Mathematical and Computer Modelling: An International Journal
Counting points on Cab curves using Monsky--Washnitzer cohomology
Finite Fields and Their Applications
Fast arithmetic in unramified p-adic fields
Finite Fields and Their Applications
| Hi-index | 0.00 |
We present an algorithm for counting points on superelliptic curves yr = f(x) over a finite field Fq of small characteristic different from r. This is an extension of an algorithm for hyperelliptic curves due to Kedlaya. In this extension, the complexity, assuming r and the genus are fixed, is O(log3+Ɛ q) in time and space, just like for hyperelliptic curves. We give some numerical examples obtained with our first implementation, thus provingthat cryptographic sizes are now reachable.