Secure Computing Scheme Based On LWE Problem On

Secure Computation is an important field of cryptography, which has important applications in network communication and e-government. One of the common methods to construct secure encryption scheme in information security is using known mathematical difficult problem.In information security, the secure encryption scheme based on known mathematical difficult problem is one of the common methods. The security of most of secure computation schemes that we currently studying is based on either the difficulty of factoring large numbers or the difficulty of finding discrete logarithms in a finite group. But these computation schemes have slow speed of implementation and can not resist quantum attacks and sub-index attacks, so it is necessary to construct more efficient and secure computation schemes based on a new difficult structure.In recent years, schemes using the theory based on lattice to learn public key cryptography have become a hotspot in the academia of cryptography. This innovative research provides a new direction to construct new cryptosystem. Cryptographic schemes based on difficult problems on lattice have been widely studied because of their following advantages:(1) Simple descriptions and implementations;(2) Very parallelizable;(3) Resists quantum attacks;(4) Security based on worst-case problems;(5) high efficiency.Encryption schemes based on the Learning With Error Problem (LWE problem) have been studied deeply. In this paper, we mainly study the application of LWE problem in the design of cryptography system. And we analyze the public-key encryption scheme based on LWE difficult problem to construct a new public key encryption scheme using the latest research findings and design methods. The two main constructions based on LWE problem in this paper are the secure two-party computation scheme, which can effectively resist the attacks from the malicious adversary, and public key encryption with keyword search on clod computing. All in all, the main results of this paper are as follows:· According to the defects existing in the protocols of comparing two data based on security under the semi-honesty model, this paper proposes a secure computation protocol for two-party numbers equality test in the malicious model. We use the public-key encryption mechanism based on lattice Learning With Error(LWE) difficult problem and Paillier encryption scheme to construct a secure two-party computation protocol that can prevent malicious attacks.· We present an efficient and secure public key encryption scheme with keyword search based on LWE problem, which is mainly used in the email search service. It enables the mail server to perform keyword search for users and identify all messages containing some specific keywords.· The two solutions prove that they are secure in the random oracle model, and the analysis results tell that after the implementations are completed, no private information in both communication parties is revealed.