Optimal Untelegraphable Encryption and Implications for Uncloneable Encryption
Anne Broadbent, Eric Culf, Denis Rochette
TL;DR
This work analyzes untelegraphable encryption ($UTE$) as a restriction of uncloneable encryption ($UE$) by restricting adversaries to classical outputs, and provides an unconditional Haar-measure construction achieving untelegraphable-indistinguishable security. It further extends to multi-copy and collusion-resistant settings, including everlasting security under pseudorandom unitaries, and establishes an asymptotic equivalence between $UTE$ and $UE$ as the number of receivers grows, offering a new pathway toward indistinguishability security for $UE$ in the plain model. The paper additionally derives concrete lower bounds and a minimality framework for Haar-based schemes, strengthening the understanding of security limits and connecting $UTE$ to the broader $UE$ landscape through a limit relationship. Overall, these results advance both the theory and practical prospects of quantum encryption primitives with indistinguishability guarantees, using unitary-design-based constructions and information-theoretic tools to bridge $UTE$ and $UE$.
Abstract
We investigate the notion of untelegraphable encryption (UTE), a quantum encryption primitive that is a special case of uncloneable encryption (UE), where the adversary's capabilities are restricted to producing purely classical information rather than arbitrary quantum states. We present an unconditionally secure construction of UTE that achieves untelegraphable-indistinguishability security, together with natural multi-ciphertext and bounded collusion-resistant extensions, without requiring any additional assumptions. We also extend this to the unbounded case, assuming pseudo-random unitaries, yielding everlasting security. Furthermore, we derive results on UE using approaches from UTE in the following ways: first, we provide new lower bounds on UTE, which give new lower bounds on UE; second, we prove an asymptotic equivalence between UTE and UE in the regime where the number of adversaries in UE grows. These results suggest that UTE may provide a new path toward achieving a central open problem in the area: indistinguishability security for UE in the plain model.