Paper 2021/412

Uncloneable Encryption, Revisited

Prabhanjan Ananth and Fatih Kaleoglu

Abstract

Uncloneable encryption, introduced by Broadbent and Lord (TQC'20), is an encryption scheme with the following attractive feature: an adversary cannot create multiple ciphertexts which encrypt to the same message as the original ciphertext. We revisit this notion and show the following: - Reusability: The constructions proposed by Broadbent and Lord have the disadvantage that they either guarantee one-time security (that is, the encryption key can only be used once to encrypt the message) in the plain model or they guaranteed security in the random oracle model. We construct uncloneable encryption schemes, where the encryption key can be re-used to encrypt multiple messages. We present two constructions from minimal cryptographic assumptions: (i) a private-key uncloneable encryption scheme assuming post-quantum one-way functions and, (ii) a public-key uncloneable encryption scheme assuming a post-quantum public-key encryption scheme. - Lower Bound and Generalized Construction: We also revisit the information-theoretic one-time secure construction of Broadbent and Lord. The success probability of the adversary in their construction was guaranteed to be $0.85^n$, where $n$ is the length of the message. It was interesting to understand whether the ideal success probability of (negligibly close to) $0.5^n$ was unattainable. We demonstrate a simple attack that breaks the scheme with probability $0.71^n$. We also generalize their construction to be based on a broader class of monogamy of entanglement games (while their construction was based on BB84 game). - Implication to Copy-Protection: We also show that uncloneable encryption, satisfying a stronger property, called uncloneable-indistinguishability (defined by Broadbent and Lord), implies copy-protection for a simple class of unlearnable functions. While we currently don't have encryption schemes satisfying this stronger property, this implication demonstrates a new path to construct copy-protection.

Note: .