Quantum Encryption with Certified Deletion

Abstract

In the context of classical information, every message is composed of 0s and 1s; these messages can generally be copied at will. However, when quantum phenomena are used to model information, this guarantee no longer exists. This difference gives rise to a range of cryptographic possibilities when one considers encoding certain messages as quantum information. In our case, we analyze a potential benefit of encoding part of an encryption scheme’s ciphertext as quantum information. We call this type of ciphertext a quantum ciphertext. In particular, quantum ciphertexts are useful when one wants to be able to prove the deletion of the plaintext underlying a ciphertext. Since classical ciphertexts can be copied, clearly such feat is impossible using classical information alone. However, we show that quantum encodings allow such certified deletion. More precisely, we show that it is possible to encrypt classical data into a quantum ciphertext such that the recipient of the ciphertext can produce a classical string which proves to the originator that the recipient has relinquished any chance of recovering the plaintext, should the decryption key be revealed. Our scheme is feasible with current quantum technology: the honest parties only require quantum devices for single-qubit preparation and measurements, and the scheme is robust against noise in these devices. Furthermore, we provide a proof of security which requires only a finite amount of communication, and which therefore avoids the common technique of relying on the analysis of an asymptotic case.