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arXiv:1206.1287 · Physical Review A

Weak randomness seriously limits the security of quantum key distribution

Jan Bouda, Matej Pivoluska, Martin Plesch, Colin Wilmott

Published Dec 7, 2012• 59 citations
arXivHTMLPDF

Abstract

In usual security proofs of quantum protocols the adversary (Eve) is expected to have full control over any quantum communication between any communicating parties (Alice and Bob). Eve is also expected to have full access to an authenticated classical channel between Alice and Bob. Unconditional security against any attack by Eve can be proved even in the realistic setting of device and channel imperfection. In this paper we show that the security of quantum key distribution protocols is ruined if one allows Eve to possess a very limited access to the random sources used by Alice. Such knowledge should always be expected in realistic experimental conditions via different side channels.

DOI
10.1103/physreva.86.062308

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In usual security proofs of quantum protocols the adversary (Eve) is expected to have full control over any quantum communication between any communicating parties (Alice and Bob). Eve is also expected to have full access to an authenticated classical channel between Alice and Bob. Unconditional security against any attack by Eve can be proved even in the realistic setting of device and channel imperfection. In this paper we show that the security of quantum key distribution protocols is ruined if one allows Eve to possess a very limited access to the random sources used by Alice. Such knowledge should always be expected in realistic experimental conditions via different side channels.
Quantum key distribution allows two parties, traditionally known as Alice and Bob, to establish a secure random cryptographic key if, firstly, they have access to a quantum communication channel, and secondly, they can exchange classical public messages which can be monitored but not altered by an eavesdropper, Eve. Quantum key distribution provides perfect security because, unlike its classical counterpart, it relies on the laws of physics rather than on ensuring that successful eavesdropping would require excessive computational effort. However, security proofs of quantum key distribution are not trivial and are usually restricted in their applicability to specific protocols. In contrast, we present a general and conceptually simple proof which can be applied to a number of different protocols. It relies on the fact that a cryptographic procedure called privacy amplification is equally secure when an adversary's memory for data storage is quantum rather than classical.
It has been established that the security of quantum key distribution protocols can be severely compromised were one to permit an eavesdropper to possess a very limited knowledge of the random sources used between the communicating parties. While such knowledge should always be expected in realistic experimental conditions, the result itself opened a new line of research to fully account for real-world weak randomness threats to quantum cryptography. Here we expand of this novel idea by describing a key distribution scheme that is provably secure against general attacks by a post-quantum adversary. We then discuss possible security consequences for such schemes under the assumption of weak randomness.
Several protocols are presented that allow two parties Alice and Bob not sharing any secret information initially (except possibly a short key to be used for authentication) to generate a long shared secret key such that even an enemy Eve with unlimited computing power is unable to obtain a non-negligible amount of information (in Shannon's sense) about this key. Two different models are considered. In a first model we assume that Alice can send information to Bob over a noisy main channel but that Eve is able to receive the same information over a parallel independent noisy channel from Alice to Eve. In a second, more general model we assume that Alice, Bob and Eve receive the output of a random source (e.g., a satellite broadcasting random bits) over three independent individual channels. The condition that the channels be independent can be replaced by the condition that they be independent only to a known, arbitrarily small degree. We demonstrate that even when Eve's channel is sup...
Quantum cryptography shows that one can guarantee the secrecy of correlation on the sole basis of the laws of physics, that is, without limiting the computational power of the eavesdropper. The usual security proofs suppose that the authorized partners, Alice and Bob, have a perfect knowledge and control of their quantum systems and devices; for instance, they must be sure that the logical bits have been encoded in true qubits and not in higher dimensional systems. In this paper, we present an approach that circumvents this strong assumption. We define protocols, both for the case of bits and for generic ddd-dimensional outcomes, in which the security is guaranteed by the very structure of the Alice-Bob correlations, under the no-signaling condition. The idea is that if the correlations cannot be produced by shared randomness, then Eve has poor knowledge of Alice's and Bob's symbols. The present study assumes on the one hand that the eavesdropper Eve performs only individual attacks (this is a limitation to be removed in further work), and on the other hand that Eve can distribute any correlation compatible with the no-signaling condition (in this sense her power is greater than what quantum physics allows). Under these assumptions, we prove that the protocols defined here allow extracting secrecy from noisy correlations, when these correlations violate a Bell-type inequality by a sufficiently large amount. The region in which secrecy extraction is possible extends within the region of correlations achievable by measurements on entangled quantum states.
In a two-way deterministic quantum key distribution (DQKD) protocol, Bob randomly prepares qubits in one of four states and sends them to Alice. To encode a bit, Alice performs an operation on each received qubit and returns it to Bob. Bob then measures the backward qubits to learn about Alice's operations and hence the key bits. Recently, we proved the unconditional security of the final key of this protocol in the ideal device setting. In this paper, we prove that two-way DQKD protocols are immune to all detector-side-channel attacks at Bob's side, while we assume ideal detectors at Alice's side for error testing. Our result represents a step forward in making DQKD protocols secure against general detector-side-channel attacks.
We present general security proof for quantum key distribution (QKD) with imperfect states in whole space including both the operational space and the other space (side-channel space). We show that in a protocol where Alice (Bob) uses two states, the secure key rate for a real protocol using imperfect (mixed) states is the same as that of a perfect protocol if the real protocol can be mapped from the perfect protocol. The calculation of the secure key rate for imperfect sources is reduced to the lower bound of projection probability to vacuum for each state. This paves the operable way to side-channel-secure QKD under more realistic conditions, including imperfections of whole-space states, mixed states, and finite data size. Taking the sending-or-not-sending encoding as an example in calculation, we obtain good key rates and long secure distance for QKD that is both measurement-device-independent and secure with imperfect whole-space source states. Published by the American Physical Society 2024