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This paper presents a novel password-based remote user authentication scheme using bilinear pairings by introducing the concept of private key proxy quantity. In the proposed scheme, an authorized user is allowed to login to the remote system if and only if the login request is verified. And by assigning each user his corresponding private key proxy quantity, the collusion-resistance security of the proposed scheme is enhanced. The scheme provides a flexible password change strategy and eliminates the need of the password table. In addition, the proposed scheme can efficiently resist message replaying attack, forgery attack, Masquerade attack, guessing and stolen verifier attack and collusion attack. [ABSTRACT FROM AUTHOR]

Aggregate signatures are digital signatures that allown players to sign n different messages and all these signatures can be aggregated into a single signature. This single signature enables the verifier to determine whether then players have signed the n original messages. Verifiably encrypted signatures are used when Alice wants to sign a message for Bob but does not want Bob to possess her signature on the message until a later date. In this paper, we first propose an identity (ID)-based signature scheme from bilinear pairing and show that such a scheme can be used to generate an ID-based aggregate signature. Then, combining this ID-based signature with the short signature given by Boneh, Lynn and Shacham, we come up with an ID-based verifiably encrypted signature. Due to the nice properties of the bilinear pairing, the proposed signatures are simple, efficient and have short signature size. [ABSTRACT FROM AUTHOR]