Key-Exchange in Real Quadratic Congruence Function Fields
Designs, Codes and Cryptography - Special issue dedicated to Gustavus J. Simmons
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
Real and imaginary quadratic representations of hyperelliptic function fields
Mathematics of Computation
Comparing Real and Imaginary Arithmetics for Divisor Class Groups of Hyperelliptic Curves
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Pairings on Hyperelliptic Curves with a Real Model
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
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
Group law computations on jacobians of hyperelliptic curves
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
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We discuss arithmetic in the Jacobian of a hyperelliptic curveC of genus g. The traditional approach is to fix a point P∞ ∈ C and representdivisor classes in the form E - d(P∞) where E is effective and0 ≤ d ≤ g. We propose a different representation which is balancedat infinity. The resulting arithmetic is more efficient than previous approacheswhen there are 2 points at infinity.