Untelegraphable Encryption and its Applications

TL;DR

This paper introduces untelegraphable encryption (UTE), a new cryptographic primitive that prevents ciphertexts from being decrypted by the secret key, and explores its theoretical foundations and applications in quantum and classical cryptography.

Contribution

It provides the first information-theoretic construction of UTE, explores its relationship with unclonable encryption, and demonstrates applications including collusion resistance and security against quantum attacks.

Findings

UTE denies the existence of hyper-efficient shadow tomography.

A classical oracle-based UTE construction breaks UE security.

Everlasting secure collusion-resistant UTE is achievable in the QROM.

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.