Research And Design Of Provable Security Digital Signature Based On Lattice

Digital signature scheme is an essential component of the public key cryptography, and is widely applied in military, communications, e-commerce and other fields. With the rapid development of information technology, some specific scenarios require signature with additional features, such as group signature, proxy signature, threshold signature, re-signature, blind signature and so on, so it has abroad application foreground to research the special signatures. With the rapid development of quantum computer, traditional signature schemes are no longer secure. The digital signature based on lattice has the advantages of simple and efficient linear operation, quantum-resistant and flexible structure, so how to design the security and efficient digital signature is the research contents in this paper, and our research is as follows:Firstly, the theories of lattice, digital signature are stated in our article. In order to design new digital signature from lattice, we describes sampling functions and rejection sampling technique. At the same time, we introduction the methodology and models of provable security, which can help us to design secure signature scheme.Secondly, two group signature schemes which satisfy provable security are proposed. The first one is an improved signature based on paillier, the efficiency is improved. On the basis of this scheme, we propose a group signature scheme and prove it is secure. The second one is an group signature scheme based on SIS and LWE is proposed, its security of CPA-anonymous and CCA-traceable was proved based on the hardness of the LWE or SIS problems in the random oracle model. The group members can be added or revoked efficiently by only updating a fraction of group public keys and group member keys, and the size of the signature does not rely on the number of group members any more.Thirdly, two proxy signature schemes based on lattice which satisfy provable security are proposed. On the basis of blind technique of Wang Dr., an proxy blind signature scheme based on SIS problem is designed, which is secure against framing attack of original signer. And the proposed scheme is proved to be strongly unforgeable under adaptive chosen message attacks. The second one is a threshold proxy re-signature scheme over lattice, which uses preimage sampleable functions and(k,l) threshold technique. Its security is based on ISIS problem, and its ECF-ACMA secure is proved under random model.At last, a proxy re-encryption scheme from lattice which satisfy provable security is proposed. Through the study of proxy re-encryption scheme, we construct a proxy re-encryption scheme from lattice, and embed a type information to a ciphertext. The type of ciphertext can be modified dynamically. We prove that it is IND-p-CPA secure under random model, and also, it can resist collusion attack.