Deniable ring authenticated private key establishment

In this paper, we extend the work by M. Naor [7] on deniable ring authentication to include key establishment. Two secure deniable private key establishment protocols will be proposed. These two related schemes create only a secure private channel between Alice and Bob where the identity of Bob remains completely hidden. The first scheme does not require Alice to been within the user set S and in fact does not even require Alice to have a public-private key pair. The second scheme requires that Alice choose a user set S such that she is also within set S. This scheme also indirectly requires that Alice have a public-private key pair. Similar to the deniable ring authentication protocol by Naor, the protocols proposed here only assumes the existence of strong public key encryption schemes where all members have already established public and private keys. Finally, the problem of ciphertext search and ciphertext ambiguity will also be examined and a solution will be proposed.