Deniable authentication protocols

Two deniable authentication schemes have been developed. One is based on the intractability of the factoring problem, and the other is based on the intractability of the discrete logarithm problem. The computation cost of the first scheme is about (t+2)/2s. The second scheme requires about (2t+3)/4s of a previous scheme; s is the length of a message block and t is the cost of multiplication mod N operations. It is shown that both protocols reserve all cryptographic characterisations of the previous scheme.