An Improved Real-Quadratic-Field-Based Key Exchange Procedure

The Efficiency and Security of a Real Quadratic Field Based-Key Exchange Protocol

Most cryptographic key exchange protocols make use of the presumed difficulty of solving the discrete logarithm problem (DLP) in a certain finite group as the basis of their security. Recently, real quadratic number fields have been proposed for use in the development of such protocols. Breaking such schemes is known to be at least as difficult a problem as integer factorization; furthermore, t...

Key-Exchange in Real Quadratic Congruence Function Fields

We show how the theory of real quadratic congruence function fields can be used to produce a secure key distribution protocol. The technique is similar to that advocated by Diffie and Hellman in 1976, but instead of making use of a group for its underlying structure, makes use of a structure which is “almost” a group. The method is an extension of the recent ideas of Scheidler, Buchmann and Wil...

Implementation of a Key Exchange Protocol Using Real Quadratic Fields

Improved Exponentiation and Key Agreement in the Infrastructure of a Real Quadratic Field

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-nea...

spKEX: An optimized lattice-based key exchange

The advent of large-scale quantum computers has resulted in significant interest in quantum-safe cryptographic primitives. Lattice-based cryptography is one of the most attractive post-quantum cryptographic families due to its well-understood security, efficient operation and versatility. However, LWE-based schemes are still relatively bulky and slow. In this work, we present spKEX, a forward-s...