Research On Some Proxy Signature Schemes On Lattices

Digital signature is one of the indispensable key technologies in the current digital information era.In practical applications,the digital signature often needs to meet certain special properties,so that the corresponding research has very important theoretical significance and practical value.With the development of the quantum computer,the traditional cryptosystem will no longer be secure in the quantum environment.As one of the representatives of the resistance quantum attack cryptosystems,lattice cryptography has higher security and higher computational efficiency.However,few special signatures based on lattice have been proposed.Besides,they have some problems such as large key size and low communication efficiency,which restricts the theoretical development and application of special signatures based on lattice.To solve these problems,we have done some research on the special signatures based on lattice,including proxy signature,certificateless signature,and certificateless proxy re-signature.Compared with the existing schemes,they have improved in terms of safety or efficiency.The main work is as follows: Firstly,a proxy signature scheme is designed.Using a special structure of Ideal Lattice,G trapdoor generation algorithm,pre-image sampling algorithm and trapdoor delegation algorithm,a proxy signature scheme with an authorization certificate is constructed.Based on the hardness of Small Integer Solution(SIS)in the ideal lattice,it is proved that authorization is unforgeable,and the signature is strong unforgeable under the adaptive chosen-message and the chosen-identities attacks.Compared with the existing lattice-based proxy signature scheme,the public key and signature size of this scheme are relatively short,and the operating efficiency is improved.Secondly,a certificateless signature scheme is designed.A certificateless signature scheme under random oracle model is constructed by using signatures without trapdoors technology,trapdoor generation algorithm in lattice and pre-image sampling algorithm.Based on the hardness of the SIS problem,it is proved that this scheme is unforgeable for external or internal attacks under the adaptive chosen-message and chosen-identity.Compared with several existing lattice-based certificateless schemes,this scheme has a shorter key size and is more efficient.Thirdly,a certificateless proxy re-signature scheme is designed.Based on the design of the certificateless signature scheme given in 2,the proxy key generation and proxy re-signature are added,and a lattice-bassed certificateless proxy re-signature scheme is constructed.Among them,the proxy key generation requires only addition operations between the matrices,and the calculation complexity is low.Based on the hardness of the SIS problem,it is proved that this scheme is unforgeable under adaptive chosen-message attacks.Compared with the existing proxy re-signature scheme,this scheme has stronger security.