Many cyber-attach schemes and coding models established by algebra tools are build to address the problem of security of cyber-pysical systems (CPS). As an important field of algebra computing, Boolean Polynomial System Solving (PoSSo) problem plays a very important role in many algebra applications. In this article, we propose an efficient Parallel Boolean Characteristic Set method (PBCS) under the high-performance computing environment to improve the efficiency of solving Boolean polynomial systems. The PBCS is implemented based on the state-of-the-art Boolean Characteristic Set method (BCS). It adopts a master-slave parallel pattern, and distributes tasks based on the polynomial sets after initial zero decomposition. We design a strategy of dynamically reallocating tasks to ameliorate load imbalance, which is caused by dynamical zero decomposition of polynomials. Furthermore, we improve its performance by optimizing the parameter settings of PBCS, including the maximum number of polynomial branches that trigger the dynamic allocation policy and the scheduling time. Experimental results with solving several Boolean polynomial systems confirm that PBCS is efficient and scalable, especially for the equations generating from stream ciphers that have block triangular structure. Moreover, the method also has good scalability. It shows a stable speedup as well even extending to the size of thousands of CPU cores.

中文翻译：

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通过并行化信息物理系统的特征集方法求解布尔多项式系统

许多由代数工具建立的网络连接方案和编码模型都是为了解决网络物理系统（CPS）的安全问题而构建的。作为代数计算的一个重要领域，布尔多项式系统求解（PoSSo）问题在许多代数应用中扮演着非常重要的角色。在本文中，我们提出了一种 高性能计算环境下的高效并行布尔特征集方法（PBCS），以提高求解布尔多项式系统的效率。所述PBCS是基于国家的最先进的实现的布尔特征集方法 (BCS)。它采用主从并行模式，根据初始零分解后的多项式集分配任务。我们设计了一种动态重新分配任务的策略，以改善由多项式的动态零分解引起的负载不平衡。此外，我们通过优化 PBCS 的参数设置来提高其性能，包括触发动态分配策略的最大多项式分支数和调度时间。求解多个布尔多项式系统的实验结果证实 PBCS 是高效且可扩展的，特别是对于从具有块三角形结构的流密码生成的方程。而且，该方法还具有良好的可扩展性。它显示出稳定的加速，甚至扩展到数千个 CPU 内核的大小。