A Security Framework for Chemical Functions

TL;DR

The paper addresses authenticating and deriving keys from physical chemical substrates by introducing chemical functions as a unifying, cryptography-inspired framework. It formalizes CFIs and security properties—robustness, unclonability, and unpredictability—via security games and analyzes two DNA-based instantiations, ORDNA and GSE, to provide quantitative guarantees under lab noise. The framework translates laboratory operations into cryptographic resources, enabling principled design, analysis, and comparison of chemical-based authentication and key-generation schemes with practical parameters. The results indicate that DNA-based chemical-function schemes can offer strong security guarantees, including asymptotic unclonability and unpredictability, supporting in-product authentication, distributed key generation, and secure material provenance with reproducible extraction techniques.

Abstract

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.

Figures (7)

• Figure 1: Detailed view of the cf $\mathsf{CF}_{\mathrm{p}}$. The digital representation of the challenge $x$ is converted to chemical reactants $\tilde{x}$. These reactants are applied to the chemical substance with profile $\mathrm{p}$. After the reaction takes place, the output $\tilde{y}$ is measured and converted to a digital representation $y$. Note that all three steps are noisy.
• Figure 2: Architecture of the cfi, illustrating the three main layers: cfi $\mathsf{CFI}$, cfs $\mathsf{CFS}_{}$, and cf $\mathsf{CF}_{}$. Each layer contains specific processes and parameters contributing to the overall authentication mechanism.
• Figure 3: The structure of an ordna molecule. The outer handles can be used to amplify the sequences. The outer handles are blunted to prevent further amplification. The random inputs correspond to the challenges, as the selection pcr binds with these to perform the amplification process on these strands only. The random output part of multiple reads corresponds to the responses of the cf. Image replicated from luescher_2024_ChemicalUnclonablea.
• Figure 4: The structure of a two-stage ordna molecule.
• Figure 5: Illustration of how chemical functions can be used for authentication. For clarity, the evaluation parameter $\alpha_{\text{E}}$ and the extraction parameter $\alpha_{\text{X}}$ are omitted. The challenge is sent to both chemical functions and results in two noisy responses $y$ and $y'$. The extraction algorithm is applied to the first response with empty helper data to generate the output $z$ and helper data $h$. The same extraction algorithm is applied to the second response but this time with the helper data $h$ to generate the output $z'$. Finally, both outputs are compared using a verification algorithm. The verification algorithm outputs $1$ if both outputs are closer than a defined threshold and $0$ otherwise.

Theorems & Definitions (37)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Definition 6: Chemical Function
• Example 1
• Definition 7: Extraction Algorithm
• Definition 8: Chemical Function System
• Example 2