Implementation of a Key Exchange Protocol Using Real Quadratic Fields
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In  Buchmann and Williams introduced a key exchange protocol which is based on the Diffie-Hellman protocol (see ). However, instead of employing arithmetic in the multiplicative group F* of a finite field F (or any finite Abelian group G), it uses a finite subset of an infinite Abelian group which itself is not a subgroup, namely the set of reduced principal ideals in a real quadratic field. As the authors presented the scheme and its security without analyzing its actual implementation, we will here discuss the algorithms required for implementing the protocol.
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