Algebra and Logic for Policy and Utility in Information Security

管理人员、顾问和安全工程师有责任交付大型复杂系统的安全性。另一方面，政策制定者和行业/商业领袖有责任确保提供服务的信息生态系统的整体可持续性和弹性，包括商业、政府、情报、军事和科学领域的信息生态系统。尽管关注点和范围存在这些差异，但这两个小组都必须制定安全策略设计决策，这些决策必须结合广泛的相互竞争的、经常是相互矛盾的关注点。考虑到涉众的范围，我们受到以下密切相关的问题的激励：对于给定的系统，在给定的业务和威胁环境中操作的给定涉众集合，我们如何确定什么是适当的（即，有效的，负担得起的）安全策略？哪些属性应该受到保护，保护到什么程度，在什么情况下？对业务运营的影响是可以接受的，财务成本是多少？这样的分析，如果要实现和健全，将依赖于提供系统及其运作的严格的经济和数学模型。我们如何表达和推理策略，以便能够理解它们对期望的安全结果的有效性以及它们对涉众和业务操作的影响？我们的假设得到了广泛的工业背景工作和经验以及广泛的数学背景工作的支持，即逻辑建模技术与数学经济学建模技术的结合将提供一个适当的框架。我们的目标是为系统安全建模技术建立一个数学基础，该技术能够处理系统的结构方面，其环境的随机行为，特别是安全策略及其有效性的效用理论表示。这一理论的发展提出了重大挑战。我们需要重建效用理论，以利用理论计算机科学中常见的过程数学模型所提供的复杂的行为描述。理论计算机科学的另一种技术，Hennessy-Milner逻辑，提供了过程行为的逻辑表征；这将需要加强，以使涉及效用和博弈论概念的属性规范，如帕累托最优性和均衡属性。这种新数学的发展必须由政策决策应用驱动和指导，我们必须探索如何扩展和推广以前工作中使用的方法，以利用这种新数学。

Managers, consultants, and security engineers have responsibility for delivering the security of possibly large, complex systems. Policy-makers and industry/business leaders, on the other hand, have responsibility for ensuring the overall sustainability and resilience of information ecosystems that deliver services, including those in commercial, governmental, intelligence, military, and scientific worlds. Despite these differences in focus and scope, both groups must make security policy design decisions that combine a wide range of competing, often contradictory concerns.Considering this range of stakeholders, we are motivated by the following closely related questions: For a given system, with a given set of stakeholders operating in given business and threat environments, how do we determine what is an appropriate (i.e., effective, affordable) security policy? What attributes should be protected, to what extent, in what circumstances? What impact on business operations is acceptable, and at what financial cost? Such an analysis will, if it is to be achievable and robust, be dependent on the provision of rigorous economic and mathematical models of systems and their operations. How are we to express and reason about policies so that their effectiveness against the desired security outcomes and their impact upon the stakeholders and business operations can be understood?Our hypothesis, supported both by extensive background work and experience in an industrial setting and by extensive background mathematical work, is that a marriage of the modelling techniques of logic with those of mathematical economics will provide an appropriate framework. We aim to establish a mathematical basis for a systems security modelling technology that is able to handle the structural aspects of systems, the stochastic behaviour of their environments and, specifically, a utility-theoretic representation of security policies and their effectiveness.The development of this theory poses significant challenges. We need to reconstruct utility theory to take advantage of the sophisticated account of actions provided by the mathematical models of processes common in theoretical computer science. Another technique of theoretical computer science, Hennessy-Milner logic, provides a logical characterization of process behaviour; this will need to be enhanced to enable specification of properties involving utility- and game-theoretic concepts, such as Pareto optimality and equilibrium properties. The development of this novel mathematics must be driven and guided throughout by the policy decision-making applications, and we must explore how the methodology used in previous work can be extended and generalised to take advantage of this new mathematics.