Research On Scalar Product Protocol Based On Paillier Cryptosystem

Secure multiparty computation which mainly studies how to compute an agreed function safely without a trusted third party is a hot potato in cryptographic community at present, and it has been gradually infiltrated into multiple branches of mathematics, such as data mining, computational geometry, scientific computing, statistical analysis, combinatorial optimization. Scalar product protocol is one of basic protocols for secure multiparty computation, which is often used in secure computational geometry, private statistical analysis as well as data mining, and provides the important security foundation for these applied protocols. The security of scalar product protocol based on homomorphic cryptosystem is higher than other solutions, so we mainly research the scalar product protocol which based on the Paillier cryptosystem, the related work are as follows:1. Paillier cryptosystem is a semantically secure additive homomorphic public-key cryptosystem, but the rate of whose key generation, encryption, decryption is slower than these algorithms such as RSA, ECC. So efficient algorithm of Paillier cryptosystem is studied, and the experimental results show that the key generation algorithm is efficient, moreover, the encryption algorithm and decryption algorithm based on the Chinese remainder theorem greatly improve the computational efficiency.2. Considering existing scalar product protocols are insecure and not practical, we presented a new parallel scalar product protocol which based on Paillier cryptosystem. The protocol with hypothesis equivalent computing power of the two participants can quickly run.3. Privacy-preserving determination protocol for point positioning is a secure two-party computational geometry problem, which researches two parties can determine the location relationship between a point and a polygon without leaking private information. According to polygon triangulation nature and based on scalar product protocol and comparison protocol, we design a secure protocol for determining the location relationship between a point and a polygon. Comparing with the similar literature, this protocol is more general and practical.4. As a part of larger trend of algorithmic game theory, rational cryptographic protocol is a rather new and emergent research area, the main purpose of which is to provide an understanding of secure multi-party computation based on the tools and language of game theory, and to analyze systems consisting of several participants with partially conflicting interests. It makes the protocols more practical and rational because computational model of cryptographic protocols are not just limited to semi-honest or malicious model. We use game theory to design a scalar product protocol in rational model, and theory proof and game analysis of this protocol are given.