A key-exchange system based on imaginary quadratic fields
Journal of Cryptology
Journal of Cryptology
A key exchange system based on real quadratic fields
CRYPTO '89 Proceedings on Advances in cryptology
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
Key-Exchange in Real Quadratic Congruence Function Fields
Designs, Codes and Cryptography - Special issue dedicated to Gustavus J. Simmons
Discrete Logarithm Based Cryptosystems in Quadratic FunctionFields of Characteristic 2
Designs, Codes and Cryptography
Computing discrete logarithms in real quadratic congruence function fields of large genus
Mathematics of Computation
Real and imaginary quadratic representations of hyperelliptic function fields
Mathematics of Computation
Class group frequencies of real quadratic function fields: the degree 4 case
Mathematics of Computation
Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time
Mathematics of Computation
Cryptographic Protocols Based on Discrete Logarithms in Real-quadratic Orders
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Cryptographic Protocols Based on Real-Quadratic A-fields
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications 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
Comparing Real and Imaginary Arithmetics for Divisor Class Groups of Hyperelliptic Curves
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
On the complexity of the discrete logarithm and Diffie-Hellman problems
Journal of Complexity - Special issue on coding and cryptography
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
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We describe severalcryptographic schemes in quadratic function fields of odd characteristic.In both the real and the imaginary representation of such a field,we present a Diffie-Hellman-like key exchange protocol as wellas a public-key cryptosystem and a signature scheme of ElGamaltype. Several of these schemes are improvements of systems previouslyfound in the literature, while others are new. All systems arebased on an appropriate discrete logarithm problem. In the imaginarysetting, this is the discrete logarithm problem in the idealclass group of the field, or equivalently, in the Jacobian ofthe curve defining the function field. In the real case, theproblem in question is the task of computing distances in theset of reduced principal ideals, which is a monoid under a suitableoperation. Currently, the best general algorithms for solvingboth discrete logarithm problems are exponential (subexponentialonly in fields of high genus), resulting in a possibly higherlevel of security than that of conventional discrete logarithmbased schemes.