Robust quantum data locking from phase modulation

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.

Quantum Data Locking for Secure Communication against an Eavesdropper with Time-Limited Storage

“…First, since γ is only determined by the first and second moments of the distribution, quantum data locking protocols with the same performances can be obtained by choosing random codewords from a spherical 2-design. Second, non-uniform distributions can also be used and may lead to similar results (see [4,14]). …”

“…To ensure the security of the quantum data locking protocol, K must be chosen large enough to make Eve's mutual information negligibly small. It was shown in [12] (see also [11,13,14]) that for n large enough, there exist choices of log K = 4 log 1/ϵ + O(log log 1/ϵ) bases such that I acc (X; E) ≤ ϵ log d n .…”

Controllable quantum private queries using an entangled Fibonacci-sequence spiral source

“…Typical quantum data locking protocols exist [16,[19][20][21][22][23][24][25]. In these protocols, as in our protocol it is also assumed that Alice and Bob share a fixed number of secret key bits in advance.…”

Quantum-Locked Key Distribution at Nearly the Classical Capacity Rate

“…From this set, they then use a short shared private key of log K bits to select a set of M codewords that they will use for sending information. In the strongest QDL protocols known up to now, a key of constant length of about Oðlog 1=ϵÞ bits allows one to encrypt a message of n bits, in such a way that if an eavesdropper Eve intercepts and measures the quantum system, then she cannot access more than about ϵn bits of information about the message [6,8].A number of works have been devoted to the role of QDL in physics and information theory [3][4][5][6][7][8][9][10][11]. However, only recently has QDL been considered in the presence of noise.…”

“…A number of works have been devoted to the role of QDL in physics and information theory [3][4][5][6][7][8][9][10][11]. However, only recently has QDL been considered in the presence of noise.…”