E cient and Provably Secure Identity Based Aggregate Signature Schemes With Partial and Full Aggregation

An identity based signature allows users to sign their documents using their private keys and the signature can be verified by any user by using the identity of the signer and public parameters of the system. This allows secure communication between the users without any exchange of certificates. An aggregate signature scheme is a digital signature scheme which allows aggregation of di erent signatures by di erent users on di erent messages. An aggregate signature on n messages mi by n users Ui convinces the verifier that each user Ui has signed the corresponding message mi. The primary objective of the aggregate signature scheme is to achieve both computational and communication e⇤ciency. Here we discuss two identity based aggregate signature schemes. The first aggregate scheme IBAS-1 uses a variation of light weight Schnorr based signature. IBAS-1 does not involve any pairing operations in signature verification. IBAS-1 is computationally e⇤cient since it avoids the costlier operation in elliptic curve groups(pairings). Also because of the light weight property of IBAS-1, it is much suitable for practice. The second aggregate signature scheme IBAS-2, which also has Schnorr type key construct, achieves full aggregation of signatures without agreeing on common randomness and without having any kind of interaction among all the signers. IBAS-2 achieves communication e⇤ciency. But the computational complexity of IBAS-2 is higher than the IBAS-1 because it involves