A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Counting points on curves over finite fields
Journal of Symbolic Computation
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
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Counting Rational Points on Curves and Abelian Varieties over Finite Fields
ANTS-II Proceedings of the Second 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
Baby-Step Giant-Step Algorithms for Non-uniform Distributions
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Algebraic Function Fields and Codes
Algebraic Function Fields and Codes
On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
A Low-Memory Algorithm for Point Counting on Picard Curves
Designs, Codes and Cryptography
Generating Genus Two Hyperelliptic Curves over Large Characteristic Finite Fields
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
An Improvement to the Gaudry-Schost Algorithm for Multidimensional Discrete Logarithm Problems
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Computing L-series of hyperelliptic curves
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Genus 2 point counting over prime fields
Journal of Symbolic Computation
Counting points on genus 2 curves with real multiplication
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Explicit bounds of polynomial coefficients and counting points on Picard curves over finite fields
Mathematical and Computer Modelling: An International Journal
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Counting the number of points of Jacobian varieties of hyperelliptic curves over finite fields is necessary for construction of hyperelliptic curve cryptosystems. Recently Gaudry and Harley proposed a practical algorithm for point counting of hyperelliptic curves. Their algorithm consists of two parts: firstly to compute the residue modulo an integer m of the order of a given Jacobian variety, and then search for the order by a square-root algorithm. In particular, the parallelized Pollard's lambda-method was used as the square-root algorithm, which took 50CPU days to compute an order of 127 bits.This paper shows a new variation of the baby step giant step algorithm to improve the square-root algorithm part in the Gaudry-Harley algorithm. With knowledge of the residue modulo m of the characteristic polynomial of the Frobenius endomorphism of a Jacobian variety, the proposed algorithm provides a speed up by a factor m, instead of 驴m in square-root algorithms. Moreover, implementation results of the proposed algorithm is presented including a 135-bit prime order computed in 16 hours on Alpha 21264/667MHz.