Limitations on Uncloneable Encryption and Simultaneous One-Way-to-Hiding
This work addresses foundational security issues in quantum cryptography, specifically for uncloneable encryption and copy protection, by providing concrete limitations and counterexamples, which is incremental but crucial for understanding and improving these schemes.
The paper tackles limitations in uncloneable quantum encryption schemes for classical messages, showing explicit cloning attacks with success probability at least 1/2 + μ/16, characterizing minimal attack success, proving ciphertext rank must grow logarithmically with messages, and demonstrating that the simultaneous one-way-to-hiding lemma cannot reduce its security loss constant below 9/8.
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 $\frac12 + μ/16$ where $μ$ 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.