Algorithmica
Algorithmic algebraic number theory
Algorithmic algebraic number theory
Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Handbook of theoretical computer science (vol. A)
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
On some computational problems in finite Abelian groups
Mathematics of Computation
Handbook of Applied Cryptography
Handbook of Applied Cryptography
A Signature Scheme Based on the Intractability of Computing Roots
Designs, Codes and Cryptography
A One Way Function Based on Ideal Arithmetic in Number Fields
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Security of Cryptosystems Based on Class Groups of Imaginary Quadratic Orders
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
Computing Discrete Logarithms with the General Number Field Sieve
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Reducing Ideal Arithmetic to Linear Algebra Problems
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Public-key cryptosystems based on class semigroups of imaginary quadratic non-maximal orders
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
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We show for the first time how to implement cryptographic protocols based on class groups of algebraic number fields of degree 2. We describe how the involved objects can be represented and how the arithmetic in class groups can be realized efficiently. To speed up the arithmetic we present our new method for multiplication of ideals. Furthermore we show how to generate cryptographically suitable algebraic number fields. Besides,w e give a numerical example and analyse our run times.