In this paper, we introduce chemical functions, a unified framework that models chemical systems as noisy challenge--response primitives, and formalize the associated chemical function infrastructure. Building on the theory of physical functions, we rigorously define robustness, unclonability, and unpredictability for chemical functions in both finite and asymptotic regimes, and specify security games that capture the adversary's power and the security goals. We instantiate the framework with two existing DNA-based constructions (operable random DNA and Genomic Sequence Encryption) and derive quantitative bounds for robustness, unclonability, and unpredictability. Our analysis develops maximum-likelihood verification rules under sequencing noise and partial-edit models, and provides high-precision estimates based on binomial distributions to guide parameter selection. The framework, definitions, and analyses yield a reproducible methodology for designing chemically unclonable authentication mechanisms. We demonstrate applications to in-product authentication and to shared key generation using standard extraction techniques.

翻译：本文提出化学功能这一统一框架，将化学系统建模为带噪声的挑战-响应原语，并形式化定义了相关的化学功能基础设施。基于物理功能理论，我们严格定义了化学功能在有限域和渐近域中的鲁棒性、不可克隆性和不可预测性，并制定了刻画攻击者能力与安全目标的安全博弈。我们通过两种现有的DNA构建方案（可操作随机DNA与基因组序列加密）实例化该框架，并推导出鲁棒性、不可克隆性和不可预测性的量化边界。我们的分析建立了测序噪声和部分编辑模型下的最大似然验证规则，并基于二项分布提供了高精度估计以指导参数选择。该框架、定义及分析形成了一套可复现的化学不可克隆认证机制设计方法。我们通过标准提取技术展示了其在产品内认证和共享密钥生成中的应用。