Algorithmic number theory
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Isomorphism Classes of Hyperelliptic Curves of Genus 2 over Fq
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Elliptic Scalar Multiplication Using Point Halving
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
An Algorithm for Computing Weierstrass Points
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Linear algebra algorithms for divisors on an algebraic curve
Mathematics of Computation
Efficient divisor class halving on genus two curves
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
A complete divisor class halving algorithm for hyperelliptic curve cryptosystems of genus two
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
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We give a deterministic polynomial time algorithm to find the structure of the 2-Sylow subgroup of the Jacobian of a genus 2 curve over a finite field of characteristic 2. Our procedure starts with the points of order 2 and then performs a chain of successive halvings while such an operation makes sense. The stopping condition is triggered when certain polynomials fail to have roots in the base field, as previously shown by I. Kitamura, M. Katagi and T. Takagi. The structure of our algorithm is similar to the already known case of genus 1 and odd characteristic.