Self-certified identity information using the minimum knowledge

We propose the new notion of self-certified identity information that applies the notion of self-certified public key to the case in which the public key is just the identity information. Using the notion of self-certified identity information, we propose a truly “paradoxical” identity-based identification scheme, the corresponding signature scheme which any user can choose his(her) own secret key though it is an identity-based method (that is, it is not a certification-based method). Also as an application of self-certified self-certified information, we propose a practical group signature which was proposed by Chaum (1991). The security of our schemes is based on the difficulty of the γ^th-residuosity problem and discrete logarithm problem simultaneously. Also our schemes are in the level 2 of trust or in the level 3 of trust. In particular, our schemes are almost as efficient as the Schnorr´s (1989) scheme