Almost Tightly Secure Strongly Unforgeable And Hierarchical Identity-Based Signatures From Lattice

In recent years,with the rapid development of quantum computer technology,human society has entered the post quantum and big data era.The development of science and technology not only improves the quality of life for the public,but also exposes people to information security risks brought about by the development of the internet.The security of information has become a major issue that urgently needs to be addressed.Cryptography is the core and important research direction of information security,with digital signatures being an important component of cryptography.A digital signature is a string that can only be generated by the sender of information and cannot be tampered with by others.This string is a valid proof of the authenticity of the information sent by the sender.It can be verified by the recipient whether the electronic document has been forged during transmission.Due to the fact that traditional cryptosystems based on number theory will be cracked one by one in the future,they face significant security risks.In recent years,lattice based cryptography has received increasing attention from relevant scholars due to its strong anti quantum properties.In order to address the information security issues brought about by the development of quantum computing technology,it is particularly important to design signature schemes with higher security.Tight security and unforgeability are important indicators for measuring the security of a solution.This thesis proposes two lattice signature schemes with higher security under the standard model.The specific work is as follows:(1)A new almost tight secure strong unforgeable signature scheme for lattices under the standard model is proposed,and it is proved that the scheme itself has almost tight security and strong unforgeability.(2)A new identity based hierarchical signature scheme for lattices under the standard model has been proposed,and it has been proven that the scheme itself has almost tight security and strong unforgeability.(3)Comparing and analyzing the above two signature schemes with similar lattice schemes before,the improved signature scheme has significantly improved its security.