多方ARX系统的协作安全辨识——一种基于门限Paillier密码体制的最小二乘辨识方法

Cooperative secure parameter identification of multi-participant ARX systems—a threshold Paillier cryptosystem-based leastsquares identification algorithm

本文研究了多方参与的随机线性系统的协作安全参数辨识问题,提出了一种基于门限Paillier密码体制的安全多方最小二乘辨识算法.具体地,通过对正负整数的合理编码,将(门限)Paillier密码体制的加密对象及同态特性由非负整数扩展到了整数.利用门限Paillier密码体制和将数据沿时间轴切分的方法,设计了相应的安全多方参数辨识算法.给出了算法正确加解密所需的明文空间大小条件、保证隐私安全性的时间切分长度条件以及一定条件下估计误差与加密量化误差之间的定量关系.证明了,只要选取的时间切分长度合适,对于任意一个参与者,即使其他所有参与者联合起来仍然无法得到其具体的隐私信息.最后,通过数值仿真验证了算法的有效性.

In this paper,the cooperative secure parameter identification problem of stochastic linear systems with multiple participants is studied,and a threshold Paillier cryptosystem-based secure multiparty leastsquares identification algorithm is proposed.Specifically,by encoding positive and negative integers properly,the encryption object and homomorphic properties of the(threshold)Paillier cryptosystem are extended from nonnegative integers to integers.Using the threshold Paillier cryptosystem and the method for data segmentation along the time axis,the corresponding secure multiparty parameter identification algorithm is designed.The condition of plaintext space size required for correct encryption and decryption,the condition of the time slicing length to ensure privacy security,and the quantitative relationship between estimation error and encryption quantization error under certain conditions are given.We prove that as long as an appropriate length for time slicing is chosen,the specific private information of any given participant still cannot be obtained,even if all other participants colluded.Finally,the efficiency of the algorithm is verified using a numerical example.