Secure Scalar Product Protocols

Abstract

Secure scalar product computation is a special secure multi-party computation problem. A secure scalar product protocol can be used by two parties to jointly compute the scalar product of their private vectors without revealing any information about the private vector of either party. Secure scalar product protocol is of great significance in privacy-preserving scientific computing, privacy preserving data mining, privacy-preserving cooperative statistical analysis and privacy-preserving geometry computation, etc. Many privacy preserving computing problems can be transformed to secure scalar product computation. At present, existing scalar product protocols cannot be used to privately compute scalar product of private vectors with both positive and negative components. Based on homomorphic encryption scheme, we design three protocols to compute scalar product of three different kinds of private vectors. The components of the first kind vector are arbitrary integers; those of the second kind are positive rational numbers and those of the third kind are arbitrary rational numbers. We use simulation paradigm proving that the protocols are secure in the semi-honest model. Theoretical analysis and experimental results show that the protocols designed in this paper are efficient.