International Association
for Cryptologic Research

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.