Research On Efficient Lattice-based Ring Signature Schemes

With the development of network information technology,digital signatures have been widely used in various fields.Specially,ring signature is often used in e-voting,cryptocurrency,anonymous reporting and other applications because of its full anonymity.Most of the existing ring signature schemes are based on the traditional number theory assumptions such as discrete logarithm and large integer decomposition.Unfortunately,these assumptions have been proved to be unsecure in quantum computers,and the quantum-secure alternative schemes have become the urgent needs of ring signature research.In addition to being able to resist the attack of quantum algorithm,lattice-based ring signature is also efficient in computation.And importantly,the hardness assumptions on lattices enjoy the reduction from average-case to worst-case,which brings great convenience to the instantiation of ring signature schemes.Up to now,some ring signature schemes based on lattices have been proposed,but there are still some drawbacks,such as higher overhead,lower efficiency and lower security.Aiming at these problems in ring signatures,this thesis has done the following researches:1.This thesis proposes a new lattice-based ring signature scheme,and proves its security.In this scheme,the ring signature is generated without trapdoor.The sampling process in the signature generation algorithm can be completed offline.The actual generation process of the ring signature only involves simple linear operations and modular operations.Compared with the ring signature schemes using the trapdoor sampling algorithm,this scheme greatly improves the efficiency of signature generation.2.This thesis proposes an efficient identity-based ring signature scheme from lattices.Compared with the general lattice-based ring signature,this scheme eliminates the additional storage and computation overhead caused by the public key certificates.By introducing an efficient trapdoor delegation algorithm,the efficiency of private key extraction can be improved.In addition,the signature generation algorithm only involves simple linear operations and rejection sampling.Finally,we analyze the efficiency of the scheme and prove its security.