  Quantum information is well-known to achieve cryptographic feats that are
unattainable using classical information alone. Here, we add to this repertoire
by introducing a new cryptographic functionality called uncloneable encryption.
This functionality allows the encryption of a classical message such that two
collaborating but isolated adversaries are prevented from simultaneously
recovering the message, even when the encryption key is revealed. Clearly, such
functionality is unattainable using classical information alone. We formally
define uncloneable encryption, and show how to achieve it using Wiesner's
conjugate coding, combined with a quantum-secure pseudorandom function (qPRF).
Modelling the qPRF as a quantum random oracle, we show security by adapting
techniques from the quantum one-way-to-hiding lemma, as well as using bounds
from quantum monogamy-of-entanglement games.
