On the Construction of Trapdoor Claw-Free Functions with Certifiable Key

2026-09-22

AI Summary

研究解决了TCF协议中密钥认证问题，通过构建可认证密钥关系和生成方法，并应用零知识证明来增强量子证明的安全性。

Abstract

Trapdoor claw-free functions (TCFs) underpin much of classical-quantum cryptographic interaction, yet every TCF-based protocol states its guarantees relative to an honestly generated key. We give a family-agnostic abstraction of key certification for (noisy) TCF constructions, built on two notions: a certifiable key relation, an NP relation capturing a family's honest keys with witnesses recoverable from the trapdoor; and certified key generation, which emits with each key a certificate of membership satisfying completeness, certificate soundness with extractability, and key privacy. We instantiate certifiable key relations for different constructions, each met generically by a zero-knowledge argument of knowledge for the relation. As our main application, a generic compiler turns any TCF-based proof of quantumness into a zero-knowledge one, with each security property following from its counterpart in the certification scheme. Finally, we delimit the primitive's reach: for protocols resting on injective invariance, an accepting certificate is itself a family distinguisher, leaking exactly the bit such protocols must hide.

Problem

• Trapdoor Claw-Free Functions
• Key Certification
• Quantum Cryptography

Innovation

• certifiable key relation
• certified key generation
• zero-knowledge argument of knowledge