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