Untelegraphable Encryption and its Applications
Jeffrey Champion, Fuyuki Kitagawa, Ryo Nishimaki, Takashi Yamakawa
TL;DR
This work introduces untelegraphable encryption (UTE), a principled relaxation of unclonable encryption (UE) grounded in the no-telegraphing paradigm, and proves information-theoretic security in the plain model. It develops a cascade of constructions and separations: UTE with indistinguishability security, collusion-resistant and everlasting UTE, and untelegraphable functional encryption (UTFE), each linked to classical and quantum cryptographic primitives (e.g., SKE, NCE, PRS/PRFS, and iO/PRF-based tools) and to broader quantum information tasks such as shadow tomography and leakage-resilient secret sharing. The results establish both upper and lower bounds: HEST is impossible under PRS or standard computational assumptions, while UTE can be extended to everlasting security in the QROM and to secret sharing schemes with joint leakage resilience. The paper further demonstrates separations between UE and UTE, provides practical encryption frameworks resilient to unbounded leakage, and lays the groundwork for UTFE and UTFE-based obfuscation. Collectively, these contributions advance the understanding of how quantum-information constraints interact with classical cryptographic notions and open avenues for resilient quantum-classical cryptography with provable guarantees.
Abstract
We initiate the study of untelegraphable encryption (UTE), founded on the no-telegraphing principle, which allows an encryptor to encrypt a message such that a binary string representation of the ciphertext cannot be decrypted by a user with the secret key, a task that is classically impossible. This is a natural relaxation of unclonable encryption (UE), inspired by the recent work of Nehoran and Zhandry (ITCS 2024), who showed a computational separation between the no-cloning and no-telegraphing principles. In this work, we define and construct UTE information-theoretically in the plain model. Building off this, we give several applications of UTE and study the interplay of UTE with UE and well-studied tasks in quantum state learning, yielding the following contributions: - A construction of collusion-resistant UTE from plain secret-key encryption, which we then show denies the existence of hyper-efficient shadow tomography (HEST). By building a relaxation of collusion-resistant UTE, we show the impossibility of HEST assuming only pseudorandom state generators (which may not imply one-way functions). This almost unconditionally answers an open inquiry of Aaronson (STOC 2018). - A construction of UTE from a one-shot message authentication code in the classical oracle model, such that there is an explicit attack that breaks UE security for an unbounded polynomial number of decryptors. - A construction of everlasting secure collusion-resistant UTE, where the decryptor adversary can run in unbounded time, in the quantum random oracle model (QROM), and formal evidence that a construction in the plain model is a challenging task. We leverage this construction to show that HEST with unbounded post-processing time is impossible in the QROM. - Constructions of secret sharing resilient to joint and unbounded classical leakage and untelegraphable functional encryption.