Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
A key-exchange system based on imaginary quadratic fields
Journal of Cryptology
A double-digit Lehmer-Euclid algorithm for finding the GCD of long integers
Journal of Symbolic Computation - Special issue on design and implementation of symbolic computation systems
A Key Exchange System Based on Real Quadratic Fields
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
An Improved Real-Quadratic-Field-Based Key Exchange Procedure
Journal of Cryptology
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
Security estimates for quadratic field based cryptosystems
ACISP'10 Proceedings of the 15th Australasian conference on Information security and privacy
SP 800-57. Recommendation for Key Management, Part 1: General (revised)
SP 800-57. Recommendation for Key Management, Part 1: General (revised)
New directions in cryptography
IEEE Transactions on Information Theory
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We describe improvements to the performance of a key agreement protocol based in the infrastructure of a real quadratic field through investigating fast methods for exponentiating ideals. We present adaptations of non-adjacent form and signed base-3 exponentiation and compare these to the binary method. To adapt these methods, we introduce new algorithms for squaring, cubing, and dividing w-near (f,p) representations of ideals in the infrastructure. Numerical results from an implementation of the key agreement protocol using our new algorithms and all three exponentiation methods are presented, demonstrating that non-adjacent form exponentiation improves the speed of key establishment for most of the currently recommended security levels.