The existing identity-based bidirectional proxy re-signature schemes require expensive bilinear pairing operations. Focused on the issue, an identity-based bidirectional proxy re-signature scheme without bilinear pairing was presented by using hash function. Under the assumption of discrete logarithm difficult problem, the proposed proxy re-signature scheme was proved secure against forgery under adaptive chosen message attacks. Furthermore, the proposed scheme was bidirectional, versatile, transparent and key optimal,which eliminated the bilinear pairing operations. Compared with the identity-based bidirectional proxy re-signature scheme — Shao scheme, the proposed scheme could reduce the computational complexity of re-signature algorithm and improve the computation efficiency of signature verification algorithm. Based on the proposed scheme, an aggregate proxy re-signature scheme was proposed. The new scheme can aggregate re-signatures only if they are generated in the same time period, which can greatly reduce the communication overhead.

Networks coding is highly susceptible to pollution attacks，but such attacks cannot be prevented by the standard technology of signature. Based on the vector hash which is secure if the discrete logarithm problem is infeasible，an efficient signature scheme for securing two-source networks coding against pollution attacks was proposed. In this scheme, each source node signed the files with its own private key, the intermediate nodes, with the merge algorithm, produced linear combinations of vectors from different files. The intermediate nodes could verify the received signature solely by the public key. The security of signature scheme relies on the hardness of the Co-Deffie-Hellman problem. Under the random oracle model, the new scheme is proved to be secure against the source nodes and intermediate nodes attacks.