Game-based proofs are a well-established paradigm for structuring security arguments and simplifying their understanding. We present a novel framework, CryptHOL, for rigorous game-based proofs that is supported by mechanical theorem proving. CryptHOL is based on a new semantic domain with an associated functional programming language for expressing games. We embed our framework in the Isabelle/HOL theorem prover and, using the theory of relational parametricity, we tailor Isabelle’s existing proof automation to game-based proofs. By basing our framework on a conservative extension of higher-order logic and providing automation support, the resulting proofs are trustworthy and comprehensible, and the framework is extensible and widely applicable. We evaluate our framework by formalising different game-based proofs from the literature and comparing the results with existing formal-methods tools.

中文翻译：

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CryptHOL：高阶逻辑中基于游戏的证明

基于游戏的证明是构建安全论点和简化其理解的完善范例。我们提出了一个新颖的框架 CryptHOL，用于由机械定理证明支持的严格的基于游戏的证明。CryptHOL 基于一个新的语义域，并带有用于表达游戏的相关函数式编程语言。我们将我们的框架嵌入到 Isabelle/HOL 定理证明器中，并使用关系参数化理论，将 Isabelle 现有的证明自动化定制为基于游戏的证明。通过将我们的框架基于对高阶逻辑的保守扩展并提供自动化支持，由此产生的证明是可信且易于理解的，并且该框架具有可扩展性和广泛适用性。