Security of the Fischlin Transform in Quantum Random Oracle Model

2026-02-19

AI Summary

This work investigates whether the Fischlin transformation retains straight-line extractability in the quantum random oracle model (QROM), thereby establishing its post-quantum security. By introducing a compressed oracle technique and combining it with tail-bound analyses of independent random variables and martingales, symmetrization arguments, query amplitude estimation, and a quantum union bound, the authors provide the first proof of straight-line extractability for the Fischlin transformation in the QROM. This result not only confirms its security against quantum adversaries but also yields a more compact non-interactive zero-knowledge (NIZK) construction compared to the Pass transformation, significantly reducing proof size.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

The Fischlin transform yields non-interactive zero-knowledge proofs with straight-line extractability in the classical random oracle model. This is done by forcing a prover to generate multiple accepting transcripts through a proof-of-work mechanism. Whether the Fischlin transform is straight-line extractable against quantum adversaries has remained open due to the difficulty of reasoning about the likelihood of query transcripts in the quantum-accessible random oracle model (QROM), even when using the compressed oracle methodology. In this work, we prove that the Fischlin transform remains straight-line extractable in the QROM, via an extractor based on the compressed oracle. This establishes the post-quantum security of the Fischlin transform, providing a post-quantum straight-line extractable NIZK alternative to Pass' transform with smaller proof size. Our techniques include tail bounds for sums of independent random variables and for martingales as well as symmetrization, query amplitude and quantum union bound arguments.

Problem

• Fischlin transform
• quantum random oracle model
• straight-line extractability
• post-quantum security
• non-interactive zero-knowledge

Innovation

• Fischlin transform
• quantum random oracle model
• straight-line extractability
• compressed oracle
• post-quantum NIZK