Research On Lattice-based Ring Signature Schem

Public key cryptography and digital signature have been playing an important role in various fields since they were proposed.As a special digital signature,ring signature is often used in various e-commerce activities due to its anonymity,such as e-voting,etransaction and so on.Traditional number theory or algebraic problems,such as discrete logarithms or bilinear maps,are the security cornerstone of most current ring signatures.These schemes cannot prevent the attack of quantum algorithms.Therefore,finding post-quantum cryptography schemes that can resist quantum attacks has become a hot spot in cryptography research.Lattice cryptography stands out from various postquantum cryptography schemes because of its outstanding advantages.Lattice-based ring signature has strong resistance to quantum algorithm attacks.Although the current ring signature technology is relatively mature and has certain advantages,there are also many shortcomings,such as low computational efficiency,high storage costs,and difficulty in resisting quantum attacks.In response to these issues,this article will explore several different types of lattice-based ring signature schemes.The specific content is as follows:Firstly,a ring signature scheme without trapdoors from lattice is proposed.For the reason that we need to improve the computational efficiency caused by sampling technology,a ring signature scheme without trapdoors is constructed by using the sampling rejection technology.The scheme takes the SVP from lattice as the underlying difficult assumption,and neither the trapdoor generation technology nor the Gaussian sampling technology is used to improve the computational efficiency.Under the ROM model,our scheme has been proven not only achieves anonymity but also satisfies strong unforgeability.Compared to other schemes,it has better security.Secondly,an identity-based linkable ring signature scheme from lattice is proposed.The scheme combines identity-based cryptography with ring signature to solve the problems of system resource waste caused by certificate authority and low computational efficiency in public key infrastructure(PKI).It is also based on the lattice approximate shortest vector problem,without using trapdoor technology and Gaussian sampling technology,which improves the computational efficiency and verifies the security of the ring signature under the ROM.Finally,an identity-based threshold ring signature scheme from lattice is proposed.This scheme can be used in electronic voting and other activities.First,the message is preprocessed using the " pad-then-permute" technology,so that the signature size is basically not affected by the threshold value.Then,the message block sharing technology is used to evenly distribute the message blocks to the ring signers,so that the scheme meets the threshold mechanism.The scheme takes the SVP from lattice as the underlying security basis,and is limited to the solution of SIS problem in the average case.It introduces a small size G-trapdoor,which requires a small storage cost,in addition,it also improves the computational efficiency of the entire process of key generation,signature,and verification.Our scheme has been proved to be correct and meets indistinguishable source hiding and unforgeability.