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.
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Publication details
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Cite this article
APA 7
Lim, C., & Ma, Y. (2026). On the Construction of Trapdoor Claw-Free Functions with Certifiable Key. https://omanscience.com/en/articles/on-the-construction-of-trapdoor-claw-free-functions-with-certifiable-key
MLA 9
Lim, Charles, and Yao Ma. "On the Construction of Trapdoor Claw-Free Functions with Certifiable Key." https://omanscience.com/en/articles/on-the-construction-of-trapdoor-claw-free-functions-with-certifiable-key.
Chicago (author–date)
Lim, Charles, and Yao Ma. 2026. "On the Construction of Trapdoor Claw-Free Functions with Certifiable Key." https://omanscience.com/en/articles/on-the-construction-of-trapdoor-claw-free-functions-with-certifiable-key.
Harvard
Lim, C. and Ma, Y. (2026) 'On the Construction of Trapdoor Claw-Free Functions with Certifiable Key', Available at: https://omanscience.com/en/articles/on-the-construction-of-trapdoor-claw-free-functions-with-certifiable-key.
Vancouver
Lim C, Ma Y. On the Construction of Trapdoor Claw-Free Functions with Certifiable Key. https://omanscience.com/en/articles/on-the-construction-of-trapdoor-claw-free-functions-with-certifiable-key
IEEE
C. Lim, and Y. Ma, "On the Construction of Trapdoor Claw-Free Functions with Certifiable Key," https://omanscience.com/en/articles/on-the-construction-of-trapdoor-claw-free-functions-with-certifiable-key.