Secure Two-party Computation for Set Intersection and Set Equality Problems Based on LWE

Using Learning With Errors (LWE) in the lattice, the equation test is converted to a decryption ability of a random string. It solves the secure two-party computation such as the relationship of an element and a set, set intersection, and set equation etc. The simulations in the semi-honest model show that these two-party solutions are secure and efficient. Compared with protocols based on security assumptions in number theory, the proposed protocols not only have lower computational complexity without exponential operations but can also resist quantum attack because of the assumption on lattice problem.