### Limitations on Uncloneable Encryption and Simultaneous One-Way-to-Hiding

Christian Majenz, Christian Schaffner, and Mehrdad Tahmasbi

##### Abstract

We study uncloneable quantum encryption schemes for classical messages as recently proposed by Broadbent and Lord. We focus on the information-theoretic setting and give several limitations on the structure and security of these schemes: Concretely, 1) We give an explicit cloning-indistinguishable attack that succeeds with probability $\frac12 + \mu/16$ where $\mu$ is related to the largest eigenvalue of the resulting quantum ciphertexts. 2) For a uniform message distribution, we partially characterize the scheme with the minimal success probability for cloning attacks. 3) Under natural symmetry conditions, we prove that the rank of the ciphertext density operators has to grow at least logarithmically in the number of messages to ensure uncloneable security. 4) The \emph{simultaneous} one-way-to-hiding (O2H) lemma is an important technique in recent works on uncloneable encryption and quantum copy protection. We give an explicit example which shatters the hope of reducing the multiplicative "security loss" constant in this lemma to below 9/8.

Available format(s)
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
quantum cryptographyuncloneable encryptionno-cloninginformation theory
Contact author(s)
christian majenz @ gmail com
c schaffner @ uva nl
History
Short URL
https://ia.cr/2021/408

CC BY

BibTeX

@misc{cryptoeprint:2021/408,
author = {Christian Majenz and Christian Schaffner and Mehrdad Tahmasbi},
title = {Limitations on Uncloneable Encryption and Simultaneous One-Way-to-Hiding},
howpublished = {Cryptology ePrint Archive, Paper 2021/408},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/408}},
url = {https://eprint.iacr.org/2021/408}
}

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