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arXiv:quant-ph/0211155 · Journal of Modern Optics

Eavesdropping on practical quantum cryptography

Mark Williamson, Vlatkovedral

Published Sep 1, 2003• 12 citations
arXivHTMLPDF

Abstract

Practical implementations of quantum cryptography use attenuated laser pulses as the signal source rather than single photons. The channels used to transmit are also lossy. Here we give a simple derivation of two beamsplitting attacks on quantum cryptographic systems using laser pulses, either coherent or mixed states with any mean photon number. We also give a simple derivation of a photon-number splitting attack, the most advanced, both in terms of performance and technology required. We find bounds on the maximum disturbance for a given mean photon number and observed channel transmission efficiency for which a secret key can be distilled. We start by reviewing two incoherent attacks that can be used on single photon quantum cryptographic systems. These results are then adapted to systems that use laser pulses and lossy channels.

DOI
10.1080/09500340308235253

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Practical implementations of quantum cryptography use attenuated laser pulses as the signal source rather than single photons. The channels used to transmit are also lossy. Here we give a simple derivation of two beamsplitting attacks on quantum cryptographic systems using laser pulses, either coherent or mixed states with any mean photon number. We also give a simple derivation of a photon-number splitting attack, the most advanced, both in terms of performance and technology required. We find bounds on the maximum disturbance for a given mean photon number and observed channel transmission efficiency for which a secret key can be distilled. We start by reviewing two incoherent attacks that can be used on single photon quantum cryptographic systems. These results are then adapted to systems that use laser pulses and lossy channels.
Practical implementations of quantum cryptography use attenuated laser pulses as the signal source rather than single photons. The channels used to transmit are also lossy. Here we give a simple derivation of two beamsplitting attacks on quantum cryptographic systems using laser pulses, either coherent or mixed states with any mean photon number. We also give a simple derivation of a photon-number splitting attack, the most advanced, both in terms of performance and technology required. We find bounds on the maximum disturbance for a given mean photon number and observed channel transmission efficiency for which a secret key can be distilled. We start by reviewing two incoherent attacks that can be used on single photon quantum cryptographic systems. These results are then adapted to systems that use laser pulses and lossy channels.
Practical implementations of quantum cryptography use attenuated laser pulses as the signal source rather than single photons. The channels used to transmit are also lossy. Here we give a simple derivation of two beam-splitting attacks on quantum cryptographic systems using laser pulses, either coherent or mixed states with any mean photon number. We also give a simple derivation of a photon-number splitting attack, the most advanced, both in terms of performance and technology required. We find bounds on the maximum disturbance for a given mean photon number and observed channel transmission efficiency for which a secret key can be distilled. We start by reviewing two incoherent attacks that can be used on single photon quantum cryptographic systems. These results are then adapted to systems that use laser pulses and lossy channels.
We propose a class of quantum cryptography protocols that are robust against photon-number-splitting attacks (PNS) in a weak coherent-pulse implementation. We give a quite exhaustive analysis of several eavesdropping attacks on these schemes. The honest parties (Alice and Bob) use present-day technology, in particular an attenuated laser as an approximation of a single-photon source. The idea of the protocols is to exploit the nonorthogonality of quantum states to decrease the information accessible to Eve due to the multiphoton pulses produced by the imperfect source. The distance at which the key distribution becomes insecure due to the PNS attack is significantly increased compared to the existing schemes. We also show that strong-pulse implementations, where a strong pulse is included as a reference, allow for key distribution robust against photon-number-splitting attacks.
Quantum cryptography in theory allows distributing secure keys between two users so that any performed eavesdropping attempt would be immediately discovered. However, in practice an eavesdropper can obtain key information from multi-photon states when attenuated laser radiation is used as a source. In order to overcome this possibility, it is generally suggested to implement special cryptographic protocols, like decoy states or SARG04. We present an alternative method based on monitoring photon number statistics after detection. This method can therefore be used with any existing protocol.
A new family of two-parameter quantum key distribution protocols is discussed where eavesdropping is detected by using two parameters: bit error rate Q and photon count rate q in control time slots. When a single-photon source is used and mutually orthogonal states are prepared in each basis, the protocol’s maximum tolerable error rate for secure key distribution is the highest, reaching a theoretical upper limit of 50%. When the signal states emitted by the source of attenuated laser light include multiphoton coherent states, the protocol also guarantees secure key distribution over the longest distance as compared to other quantum cryptography systems, up to the channel length for which the channel losses are sufficiently high that all five-photon pulses can be blocked by an eavesdropper.
Based on practical implementations of quantum cryptography with the attenuated laser pulses as the signal source rather than single photon, as well as lossy channels, detection efficiency, dark count of singlephoton counter, and technological possibilities of a realistic eavesdropping, we discuss a combining eavesdropping strategy of Breidbart basis and beamsplitting, and give a bound on maximum disturbance for a given mean photon number and transmission length for which a secret key can be distilled.