Research Of Public-Key Cryptosystems Based On Hard Problems In Lattice

Public-key cryptosystem is the main technique to make sure the security of information. A good cryptosystem should be secure and efficient. In cryptosystem, it is a common way to use some known mathematical hard problems to construct cryptography schemes. At present, most public-key cryptosystems are based on traditional mathematical hard problems such as Integer Factoring problem and Discrete Logarithm Problem etc. However, these public-key cryptosystem are less efficient and can’t resist polynomial quantum attack and sub-exponent attack. These drawbacks limit their further applications. So more efficient and more secure cryptosystems based on new hard problems are needed.Ajtai96’s discovery, a connection between the worst-case and average-case hardness of some lattice problems, is the new direction of public-key cryptosystems. More efficient and more secure cryptography schemes can be designed based on the lattice theory. These schemes not only hold a great promise for post-quantum cryptography since there is no polynomial time algorithm and quantum algorithm to solve the lattice hard problems, but also enjoy high efficiency because of the lattice special structure and simple mathematical operation. This paper mainly focuses on the lattice theory and its application in cryptographic. Deeply research the cryptographic constructions based on lattice, especially based on the average-case hardness problems such as LWE problem and R-LWE problem. Then present some new public-key schemes based on the R-LWE problem. Compared with the schemes based on LWE, these ones not only enjoy lower computational complexity but also can resist quantum attack because of the assumption on lattice problem.