Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Journal of Cryptology
Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve
Journal of Symbolic Computation
Computing Riemann---Roch spaces in algebraic function fields and related topics
Journal of Symbolic Computation
Counting Points on Hyperelliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Linear algebra algorithms for divisors on an algebraic curve
Mathematics of Computation
IEEE Transactions on Computers
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
Fast explicit formulae for genus 2 hyperelliptic curves using projective coordinates
ITNG '07 Proceedings of the International Conference on Information Technology
Explicit Formulas for Real Hyperelliptic Curves of Genus 2 in Affine Representation
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Efficient Pairing Computation on Genus 2 Curves in Projective Coordinates
Selected Areas in Cryptography
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
Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Efficient hyperelliptic arithmetic using balanced representation for divisors
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
An analysis of affine coordinates for pairing computation
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
An index calculus algorithm for plane curves of small degree
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Novel efficient implementations of hyperelliptic curve cryptosystems using degenerate divisors
WISA'04 Proceedings of the 5th international conference on Information Security Applications
Efficient scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Hi-index | 0.00 |
We derive an explicit method of computing the composition step in Cantor's algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor's general composition involves arithmetic in the polynomial ring $\mathbb{F}_q[x]$ , the algorithm we propose solves a linear system over the base field which can be written down directly from the Mumford coordinates of the group elements. We apply this method to give more efficient formulas for group operations in both affine and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form.