Abstract: There are many problems in the multiple grade proxy signature schemes that are used nowadays. For example, the original signer and the proxy signers sometimes deny the truth of their signatures; the multiple grade proxy signatures usually have to be very long and the validating process of them are too complicated. To solve all these problems, a more secure multiple grade proxy signature scheme is proposed in this paper based on the study of a difficult mathematical concept, the discrete logarithm. Firstly, to ensure that none of the signers of all grades can deny their signatures, the private keys of all the proxy signers are put into the final proxy-signing key. Another feature of this scheme is that some calculation in the validating process is somehow transferred into the process of producing proxy-signing key. In this way, not only the validating of the signature is simplified, but also the multiple grade proxy signature can be effectively shortened. As a result, this paper achieve an efficient, secure multiple grade proxy signature scheme.

Key words: Proxy signature, Mulitiple grade proxy signature, Undeniable, Secure, The discrete logarithm