Matrix rank is an important tool for mathematical analysis, it is hard to compute cooperatively in an insecure distributed network. For the purpose to solve this problem, we put forward a privacy-preserving rank compu...
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Matrix rank is an important tool for mathematical analysis, it is hard to compute cooperatively in an insecure distributed network. For the purpose to solve this problem, we put forward a privacy-preserving rank computation protocol for the first time. In this paper, the pro-rata protocol is improved to an optimal complexity of O(m) through comparing the collective information to reduce the round number, it performs better when the disproportional pairs distribute dispersedly or appear at later part of the sequence. Then, we propose a protocol to calculate matrix rank by the help of privacy-preserving technology, this protocol implements securely step by step according to the procedure in linear algebra. The protocol achieves the goal in secure two-party model without leaking other message. After that, their applications in mean square error and square sum error are considered. At last, we analyze all the protocols appeared in this paper to investigate their correctness, complexity and security by means of mathematical induction and cryptographic primitive.
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