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

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.

Cryptography and Security (cs.CR); Quantum Physics (quant-ph)

arXiv:2609.25819 [cs.CR]

(or arXiv:2609.25819v1 [cs.CR] for this version)

https://doi.org/10.48550/arXiv.2609.25819 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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