Research On The Traceable Signature Scheme Based On Lattice

In recent years,quantum computer has been one of the key research projects in many countries and large companies,and many achievements have been made.Under quantum computers,traditional public key cryptography system is not safe.With the increasing success of quantum computers,a new public key cryptosystem is urgently needed to replace the traditional public key cryptosystem.As a recognized cryptosystem that can resist quantum computation,lattice cipher is very promising.At present,the research of lattice cryptosystem is still in the transition stage from embryonic stage to mature stage.Therefore,there are still many plans worthy of our development and research.The lattice-based signature scheme is a research focus at present.Anonymity as a security requirement for signature schemes in the information age has always been a focus of research.However,in case of anonymity,it will be difficult to trace the identity of the signer if there are disputes.Aiming at anonymity and traceability,we focus on group signature and ring signature scheme.The main work is:(1)Aiming at the problem of dynamic join and exit of members in lattice-based group signature schemes,a dynamic group signature scheme based lattice(LL scheme)is proposed.First,a new revocation mechanism is constructed based on the existing revocation mechanism,which enables users to withdraw from groups at any time.In this mechanism,each user has the unique revocation token.No information is needed to update for the group manager and group members.A revocation Turing is needed to interact with the group manager to verify the identity of a group member.After that,the group manager adds the revocation token to the revocation list.Secondly,in the process of constructing signature and member public and private key,we use the way of password construction based on SIS problem and LWE problem to ensure the security of the scheme.Finally,a Stern zero knowledge proof based on SIS problem is constructed by decomposing and extending technology in the signature to ensure the verifiability of the signature.Compared with existing schemes,group public key is fixed in the length and shorter.When a user joins into the group,he needs less downloads.So,we can provide a higher efficiency in practical applications.(2)Due to the lack of traceable ring signature schemes based lattice,we constructed such a scheme based on SIS problem and the decisional Diffie-Hellman assumption.Traceable ring signature scheme is proposed for hidden dangers caused by unconditional anonymity of ring signature.The user identity can be tracked in some cases.While protecting the privacy of users,it also protects the security of the system.The scheme is divided into two parts: the signature based on the decisional Diffie-Hellman assumption and the signature based on the SIS problem.First,we use Trap Gen algorithm to generate the lattice-based key pair.The key pair based on the discrete logarithm is generated by the one-way function,so that even if the quantum computer completely attacks the signature based on the decisional Diffie-Hellman assumption,the private key based on the lattice cannot be effectively derived from the key pair based on the decisional Diffie-Hellman assumption.Finally,we use the collision resistance of hash function to ensure that the first part of the signature is unforgeable.