同态加密方案及安全两点直线计算协议

近年来，安全多方计算一直是密码领域的一个研究热点，保密几何计算是其一个重要分支.过两私有点坐标安全地计算一条直线问题在空间信息安全方面有重要应用前景.本文首先提出一个由加密方计算（或选取）加密底数的Paillier变体同态加密方案，并证明了其在标准模型下对适应性选择明文攻击（adaptive chosen-plaintext attack，CPA）是安全的.然后在半诚实模型下，基于该变体同态加密方案设计了一个能够安全计算过两私有点直线的协议.还可以将此协议推广应用到那些可以归约为安全计算两私有点坐标差商的所有安全多方几何计算问题，从而解决了原有的基于同态加密体制的安全两方计算协议存在的信息泄露问题.

Homomorphic Encryption Scheme and A Protocol on Secure Computing a Line by Two Private Points

In recent years, secure multiparty computation is one of research focuses in the field of cryptography, and secret geometry calculation is an important branch of it. The problem that safely calculates a straight line by two private coordinate point has important application foreground in space information security. At first, we put forward a variant homomorphic encryption scheme of Paillier''s, where the base is calculated by sender during encryption, and it is proved to be indistinguishability under adaptive chosen-plaintext attack. And then, based on this homomorphic encryption scheme, we design a protocol that can safely calculate a straight line by two private coordinate point in semi-honesty model. More widely, we can apply this protocol to solve a type of secure multiparty computational geometry problem that can be reduced to compute coordinate difference quotient. Thus, the problem that there is a non-negligible probability of private information leakage in the current coordinate difference quotient calculation protocols based on homomorphic encryption has been solved.