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arXiv:1311.5212 · Physical Review A

Robust quantum data locking from phase modulation

Cosmo Lupo, Mark M. Wilde, Seth Lloyd

Published Aug 25, 2014• 21 citations

Abstract

Quantum data locking is a uniquely quantum phenomenon that allows a relatively short key of constant size to (un)lock an arbitrarily long message encoded in a quantum state, in such a way that an eavesdropper who measures the state but does not know the key has essentially no information about the message. The application of quantum data locking in cryptography would allow one to overcome the limitations of the one-time pad encryption, which requires the key to have the same length as the message. However, it is known that the strength of quantum data locking is also its Achilles heel, as the leakage of a few bits of the key or the message may in principle allow the eavesdropper to unlock a disproportionate amount of information. In this paper we show that there exist quantum data locking schemes that can be made robust against information leakage by increasing the length of the key by a proportionate amount. This implies that a constant size key can still lock an arbitrarily long message as long as a fraction of it remains secret to the eavesdropper. Moreover, we greatly simplify the structure of the protocol by proving that phase modulation suffices to generate strong locking schemes, paving the way to optical experimental realizations. Also, we show that successful data locking protocols can be constructed using random code words, which very well could be helpful in discovering random codes for data locking over noisy quantum channels.

DOI: 10.1103/physreva.90.022326

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Classical correlation can be locked via quantum means--quantum data locking. With a short secret key, one can lock an exponentially large amount of information, in order to make it inaccessible to unauthorized users without the key. Quantum data locking presents a resource-efficient alternative to one-time pad encryption which requires a key no shorter than the message. We report experimental demonstrations of quantum data locking scheme originally proposed by DiVincenzo et al. [Phys. Rev. Lett. 92, 067902 (2004)] and a loss-tolerant scheme developed by Fawzi, Hayde, and Sen [J. ACM. 60, 44 (2013)]. We observe that the unlocked amount of information is larger than the key size in both experiments, exhibiting strong violation of the incremental proportionality property of classical information theory. As an application example, we show the successful transmission of a photo over a lossy channel with quantum data (un)locking and error correction.

Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This violation mirrors a large gap existing between two security criteria for quantum cryptography quantified by two entropic quantities: the Holevo information and the accessible information. We show that the latter becomes a sensible security criterion if an upper bound on the coherence time of the eavesdropper's quantum memory is known. Under this condition, we introduce a protocol for secret key generation through a memoryless qudit channel. For channels with enough symmetry, such as the d-dimensional erasure and depolarizing channels, this protocol allows secret key generation at an asymptotic rate as high as the classical capacity minus one bit.

Quantum cryptography allows for unconditionally secure communication against an eavesdropper endowed with unlimited computational power and perfect technologies, who is only constrained by the laws of physics. We review recent results showing that, under the assumption that the eavesdropper can store quantum information only for a limited time, it is possible to enhance the performance of quantum key distribution in both a quantitative and qualitative fashion. We consider quantum data locking as a cryptographic primitive and discuss secure communication and key distribution protocols. For the case of a lossy optical channel, this yields the theoretical possibility of generating secret key at a constant rate of 1 bit per mode at arbitrarily long communication distances.

Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a quantum system, the phenomenon of quantum data locking allows one to encrypt a message with a shorter key and still provide information-theoretic security. We present one of the first feasible experimental demonstrations of quantum data locking for direct communication and propose a scheme for a quantum enigma machine that encrypts 6 bits per photon (containing messages, new encryption keys, and forward error correction bits) with less than 6 bits per photon of encryption key while remaining information-theoretically secure.

Quantum data locking is a quantum phenomenon that allows us to encrypt a long message with a small secret key with information-theoretic security. This is in sharp contrast with classical information theory where, according to Shannon, the secret key needs to be at least as long as the message. Here we explore photonic architectures for quantum data locking, where information is encoded in multi-photon states and processed using multi-mode linear optics and photo-detection, with the goal of extending an initial secret key into a longer one. The secret key consumption depends on the number of modes and photons employed. In the no-collision limit, where the likelihood of photon bunching is suppressed, the key consumption is shown to be logarithmic in the dimensions of the system. Our protocol can be viewed as an application of the physics of Boson Sampling to quantum cryptography. Experimental realisations are challenging but feasible with state-of-the-art technology, as techniques recently used to demonstrate Boson Sampling can be adapted to our scheme (e.g., Phys. Rev. Lett. 123, 250503, 2019).

Quantum data locking is a quantum communication primitive that allows the use of a short secret key to encrypt a much longer message. It guarantees information-theoretical security against an adversary with limited quantum memory. Here we present a quantum data locking protocol that employs pseudorandom circuits consisting of Clifford gates only, which are much easier to implement fault tolerantly than universal gates. We show that information can be encrypted into

n

-qubit code words using order $n\ensuremath{-}{H}_{\mathrm{min}}(\mathsf{X})$ secret bits, where

{H}_{\mathrm{min}}(\mathsf{X})

is the min-entropy of the plain text, and a min-entropy smaller than

n

accounts for information leakage to the adversary. As an application, we discuss an efficient method for encrypting the output of a quantum computer.