The Wrestlers Protocol: A simple, practical, secure, deniable protocol for key-exchange

We describe and prove (in the random-oracle model) the security of a simple but efficient zero-knowledge identification scheme, whose security is based on the computational Diffie-Hellman problem. Unlike other recent proposals for efficient identification protocols, we don’t need any additional assumptions, such as the Knowledge of Exponent assumption. From this beginning, we build a simple key-exchange protocol, and prove that it achieves ‘SK-security’ – and hence security in Canetti’s Universal Composability framework. Finally, we show how to turn the simple key-exchange protocol into a slightly more complex onewhich provides a number of valuable ‘real-life’ properties, without damaging its security.