Paper 2025/1662

The Affine One-Wayness (AOW): A Transparent Post-Quantum Temporal Verification via Polynomial Iteration

Abstract

Distributed systems require robust, transparent mechanisms for verifiable temporal ordering to operate without trusted authorities or synchronized clocks. This paper introduces Affine One-Wayness (AOW), a new cryptographic primitive for post-quantum temporal verification based on iterative polynomial evaluation over finite fields. AOW provides strong temporal binding guarantees by reducing its security with a tight reduction to the hardness of the dis crete logarithm problem in high-genus hyperelliptic curves (HCDLP) and with a reduction to the Affine Iterated Inversion Problem (AIIP), which possesses dual foundations in multivariate quadratic algebra and the arithmetic of high-genus hyperelliptic curves. We present a con struction with transparent setup and prove formal security against both classical and quantum adversaries. Furthermore, we demonstrate efficient integration with STARK proof systems for zero-knowledge verification of sequential computation with logarithmic scaling. As the core reliability component of the Chaotic Affine Secure Hash (CASH) framework, AOW enables practical applications in Byzantine-resistant event ordering and distributed synchronization with provable security guarantees under standard cryptographic assumptions.

Note: This manuscript on the Affine One-Wayness (AOW) primitive constitutes the formalization of the core reliability and temporal verification component for the broader research program on legally explainable post-quantum cryptography. It is the second defined component of the CASH framework (CEE, AOW, SH), which itself is a primitive-level instantiation of the abstract Q2CSI infrastructure (ePrint 2025/1380). The design of AOW directly enforces the Reliability property of the CRO Trilemma (ePrint 2025/1348), providing the temporal binding and verifiable sequentiality necessary to resolve the incompatibility with Confidentiality and Opposability. This submission is a theoretical and foundational contribution. It focuses exclusively on the definition, temporal binding properties, tight security reduction to high-genus HCDLP, reduction to the MQ problem, and cryptanalysis of the new AOW primitive. It does not include implementation artifacts or performance benchmarks. All contributions are original. This manuscript is not under submission or review elsewhere. The author may reference this work in future publications detailing the instantiation of the full CASH framework or its integration into higher-level protocols (e.g., Byzantine-resistant consensus mechanisms), ensuring no duplication of content and a clear progression from foundational primitive to applied construction.