某信息系统二次规划同态加密梯度下降算法研究

Research on quadratic programming homomorphic encrypted gradient descent algorithm for an information system

同态加密方法能够实现在不泄露内容情况下分析或操作加密数据的功能,但该方法计算开销大,一直以来难以在控制领域的实践中实现。为解决这一问题,首先计算分析梯度下降算法在同态加密方法中解决二次规划的适用性,降低了同态加密电路乘法深度对梯度下降算法迭代的限制,并量化了原型示例,为后续的研究打下基础。其次,对梯度下降及加速梯度下降方法的选择进行了权衡和评估,为同态加密技术的工程应用开辟了道路。所采用的CKKS方案,通过选择合适的步长使程序实现收敛,直接展示了同态加密梯度下降算法的可行性。

The homomorphic encryption method can realize the function of analyzing or operating encrypted data without leaking the content.However,this method has a heavy computational overhead and has been very hard to achieve in practice within the control domain..In order to solve this problem,we first calculated and analyzed the applicability of the gradient descent algorithm in solving quadratic programming in the homomorphic encryption method,reduced the limitation of the multiplication depth of the homomorphic encryption circuit on the iteration of the gradient descent algorithm,and quantified the prototype example.Lay the foundation for further research.Secondly,the choice of gradient descent and accel-erated gradient descent methods was weighed and evaluated,which opened up a path for the engineering application of ho-momorphic encryption technology.The adopted CKKS scheme allows the program to achieve convergence by selecting an appropriate step size,directly demonstrating the feasibility of the homomorphic encryption gradient descent algorithm.