Research On Lattice-based Signatures

Digital signature technology is an important content and research direction of cryptography.It can ensure the integrity and non-repudiation of information in the process of transmission,so it plays a cornerstone role in the construction of secure information systems.At present,the construction of digital signature schemes is mostly based on the difficult problems of classical mathematics such as the integer factorization problem,the discrete logarithm problem and the elliptic curve discrete logarithm problem.With the introduction of the Shor quantum algorithm,the integer factorization problem and the discrete logarithm problem can be broken in polynomial time.In this situation the existing digital signatures are no longer secure.Therefore,signatures which can resist quantum attacks have received widespread attention,especially lattice-based signature systems.In the application of digital signatures,there are two types of signatures with special properties: blind signatures and chameleon signatures.Blind signature is a kind of signature with anonymity attribute attached.This anonymity ensures that the signature obtained by the message provider is untraceable.Chameleon signature is a kind of non-interactive signature,appointing the only verifier,and it can guarantee the non-transmission,non-repudiation and non-forgeability of the signature.It is precisely because of the anonymity and nontransmissibility that blind signatures and chameleon signatures are widely used in areas that require privacy protection,such as electronic cash and electronic voting.In a security information system based on public key cryptography,the issuance of the public key is generally carried out through the CA,which is a time-consuming and laborious process.In order to solve this problem,Shamir proposed an identity-based cryptography.The idea is to use information disclosed by the user,such as name,email address,and address as the public key.Starting from the blind signature and the chameleon signature,combining the identity-based signature scheme,and on the basis of lattice theory,we proposed the following three signature scheme:1.A blind signature from lattices.According to the construction of qTESLA signature,this paper constructed a blind signature from lattices,which security was based on the intractability of RLWE and RSIS problems.The rejection sampling lemma was used in the process to ensure the security of the private key and the untraceability of messages and signatures.This scheme is blind and has one-more unforgeability under the random oracle model.2.According to the idea of the lattice-based identity-based signature by Yang Chunli and others,this paper constructed an identity-based blind signature from lattices,which security was based on the intractability of the SIS problem.Compared with the current identity-based signatures and blind signatures in the standard model,this scheme has certain advantages in terms of signature size.This scheme is blind,and has the one-more unforgeability under the selected message and identity attacks in the standard model.3.On the basis of the identity-based blind signature from lattices proposed in this paper,combined with the concept of chameleon hash,this paper constructed a first lattice-based identity-based chameleon hash,and based on this function,constructed a first latticebased identity-based chameleon signature.The security of this scheme was based on the inexplicability of the SIS problem.Most of the currently proposed chameleon signatures are designed based on discrete logarithms problem.Compared with these schemes,the scheme in this paper is resistant to quantum attacks.This scheme is also nontransmissible,non-forgeable and non-repudiation.