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This paper investigates the minimal assumptions required for constructing many-time secure uncloneable encryption, a form of symmetric key encryption resistant to ciphertext cloning. They demonstrate that the existence of a one-time secure uncloneable bit, combined with either standard symmetric key encryption or pseudorandom unitaries, is sufficient to construct many-time secure uncloneable encryption for arbitrary-length messages. This result establishes a tight connection between fundamental cryptographic primitives and uncloneable encryption, potentially grounding it in the "microcrypt" setting.
Uncloneable encryption, a powerful defense against ciphertext cloning, may be achievable under surprisingly weak assumptions, potentially residing within the realm of "microcrypt".
In this note, we consider the setting of uncloneable encryption satisfying uncloneable indistinguishability, a form of symmetric key encryption that prevents the cloning of ciphertexts in a very strong sense. Our goal is to minimize the assumptions under which (many-time secure) uncloneable encryption is known to exist, assuming the existence of an information-theoretic"uncloneable bit", i.e. a one-time secure uncloneable encryption scheme for one-bit messages. We observe that if a t ->t'uncloneable bit exists, then the following implications hold. 1. If many-time secure symmetric key encryption exists, then many-time secure t ->t'uncloneable encryption for arbitrary-length messages exists. Since many-time secure uncloneable encryption implies many-time secure symmetric key encryption, this result is tight. 2. If pseudorandom unitaries exist, then many-time secure t ->t'uncloneable encryption for arbitrary-length messages with identical copy security exists. These results together show that many-time secure uncloneable encryption may follow from concrete assumptions in"microcrypt", the world of unstructured quantum cryptography that plausibly exists even if P = NP.