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This paper designs a system model of flexible proxy signature schemes and introduces some realizations for this model from pairings. The proxy signature scheme allows an original signer to delegate his signing authority to a designated person called proxy signer. With that the proxy signer can sign a message through anonymous or non-anonymous methods alternatively, which is depending on the different demand as well as the property of a message. For these reasons, we introduce message recovery and appendix approaches to satisfy the applications of short message and long message, respectively. From the perspective of any verifier, checking the validity of the proxy signature can be accomplished through the verification of the public key in a logically single step, which is advantageous in communication overhead. Finally, we analyze the proposed proxy signature schemes from several security points of view.
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