| Secure multi-party computation (SMC) is an important problem in cryp-tography. Existing solutions are mostly based on circuit evaluation protocols which are impractical. In this paper, two solutions are proposed by abstracting the Intersection problem and the Judging Private Path problem to a gener-al intersection problem, i.e., if two participants have a private curve and do not disclose their private curve data, how to solve the two free plane curves intersection problem in a cooperative environment.Firstly, by using curve approximation idea to tackle the free curve. After approximation phase, the secure two party quadratic curves intersection pro-tocol is proposed and it can be expanded to the secure two party cubic curves intersection protocol.A systematic Lagrange multiplier method is proposed to combat the gen-eral intersection problem instead of focusing on normal curves case. The pro-posed systematic method can systematically deal with various intersection problems faced in practical applications. In addition, the proposed method can also solve the normal curves cases. |
