A key-exchange system based on imaginary quadratic fields
Journal of Cryptology
A Key Exchange System Based on Real Quadratic Fields
CRYPTO '89 Proceedings of the 9th 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
Selecting Cryptographic Key Sizes
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Asymptotically Fast Discrete Logarithms in Quadratic Number Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Strategies in Filtering in the Number Field Sieve
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
An Accelerated Buchmann Algorithm for Regulator Computation in Real Quadratic Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Designs, Codes and Cryptography
An Improved Real-Quadratic-Field-Based Key Exchange Procedure
Journal of Cryptology
Binary Quadratic Forms: An Algorithmic Approach (Algorithms and Computation in Mathematics)
Binary Quadratic Forms: An Algorithmic Approach (Algorithms and Computation in Mathematics)
Improved exponentiation and key agreement in the infrastructure of a real quadratic field
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
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We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic field. The algorithms used incorporate improvements over previously-used algorithms, and extensive numerical results are presented demonstrating their efficiency. This data is used as the basis for extrapolations, used to provide recommendations for parameter sizes providing approximately the same level of security as block ciphers with 80, 112, 128, 192, and 256-bit symmetric keys.