Quantum Secret Permutating Protocol

Abstract

In modern cryptography, distributing a private and unique index number to each participant is an important cryptographic task, which can be adopted to efficiently solve many complicated secure multiparty computations. In this paper, we define this cryptographic primitive, called Secret Permutating, in which every one of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{n}}$</tex-math></inline-formula> participants can get a random but unique secret <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\bm{k}}}_{\bm{i}} \in \{ {1,2, \ldots ,{\bm{n}}} \}$</tex-math></inline-formula> . Furthermore, we focus on the unconditional security of Secret Permutating based on laws of quantum mechanics. Accordingly, by local Pauli operators and entanglement swapping of Bell states, we design novel quantum Secret Permutating protocols. What's more, to reduce the communicational complexity, we exploit the uniform, random and independent properties of quantum measurements to evenly divide all participants into many secret groups with the small approximate sizes. Finally, the analysis results and simulated experiments show that the proposed protocols have the unconditional security and the good feasibility.