Affine One-Wayness: Post-Quantum Temporal Verification Primitive ∞ Research

A close-up view presents a translucent, cylindrical device with visible internal metallic structures. Blue light emanates from within, highlighting the precision-machined components and reflective surfaces

A precisely cut transparent cube, featuring a perfect spherical droplet, is positioned on a detailed blue circuit board, indicative of advanced technological infrastructure. Surrounding it are smaller, dark blue cubic elements, reminiscent of digital data blocks or encrypted nodes

Briefing

This research introduces Affine One-Wayness (AOW), a novel cryptographic primitive for post-quantum temporal verification based on iterative polynomial evaluation over finite fields. AOW provides robust temporal binding guarantees, reducing its security to the hardness of the discrete logarithm problem in high-genus hyperelliptic curves and the Affine Iterated Inversion Problem. The construction features a transparent setup and formal security proofs against both classical and quantum adversaries, enabling practical applications in Byzantine-resistant event ordering and distributed synchronization.

A clear cubic prism sits at the focal point, illuminated and reflecting the intricate blue circuitry beneath. White, segmented tubular structures embrace the prism, implying a sophisticated technological framework

Context

Distributed systems fundamentally require robust and transparent mechanisms for verifiable temporal ordering, traditionally relying on trusted authorities or synchronized clocks. The advent of quantum computing poses a significant threat to existing cryptographic foundations, necessitating new primitives that can provide provable security against both classical and quantum adversaries while ensuring temporal integrity in a trustless environment.

A vibrant blue metallic, cross-shaped component, possibly an ASIC or validator node, is partially submerged in a dense layer of white foam. The intricate design of the object, featuring various slots and reflective surfaces, is accentuated by the delicate, bubbly texture clinging to its form

Analysis

The core mechanism of Affine One-Wayness (AOW) is its reliance on iterative polynomial evaluation over finite fields to establish temporal binding. This primitive reduces its security to the computationally hard discrete logarithm problem in high-genus hyperelliptic curves (HCDLP) and the Affine Iterated Inversion Problem (AIIP), which draws from multivariate quadratic algebra and hyperelliptic curve arithmetic. The construction is designed with a transparent setup, eliminating trusted third parties, and integrates efficiently with STARK proof systems for zero-knowledge verification of sequential computation, achieving logarithmic scaling. This approach fundamentally differs by offering a post-quantum secure primitive for temporal verification, moving beyond pre-quantum assumptions.

A sophisticated, metallic cylindrical mechanism, predominantly silver with striking blue internal components, is presented in a close-up, shallow depth of field perspective. The device's intricate design reveals layers of precision-engineered elements and illuminated blue structures that resemble advanced microcircuitry

Parameters

Core Concept ∞ Affine One-Wayness (AOW)
Problem Addressed ∞ Post-quantum temporal verification in distributed systems
Key Mechanism ∞ Iterative polynomial evaluation over finite fields
Security Reduction ∞ Hardness of Discrete Logarithm Problem in high-genus hyperelliptic curves (HCDLP) and Affine Iterated Inversion Problem (AIIP)
Integration ∞ STARK proof systems for zero-knowledge verification
Applications ∞ Byzantine-resistant event ordering, distributed synchronization
Key Author ∞ MINKA MI NGUIDJOI Thierry Emmanuel
Publication Date ∞ September 17, 2025

A sleek, reflective metallic shaft connects to a multifaceted, spherical object rendered in varying shades of translucent blue. The sphere's surface is composed of numerous irregular, geometric panels, creating a complex, fragmented yet unified appearance

Outlook

The development of Affine One-Wayness (AOW) opens new research avenues in post-quantum cryptography and its application to decentralized systems. Future work will likely involve further optimizing its integration with various zero-knowledge proof systems and exploring its deployment in real-world blockchain architectures to enhance verifiable event ordering and secure distributed synchronization against quantum threats. This primitive lays a crucial groundwork for building resilient and trustless temporal verification mechanisms for the quantum era.

A brilliant, square-cut crystal is held within a segmented white ring, suggesting a secure element or core processing unit. This assembly is intricately connected to a vibrant blue, illuminated circuit board, indicative of advanced computational infrastructure

Verdict

Affine One-Wayness establishes a critical post-quantum cryptographic primitive, fundamentally advancing the security and verifiability of temporal ordering in future decentralized architectures.

Signal Acquired from ∞ iacr.org