Eavesdropping on practical quantum cryptography

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.

arXiv:quant-ph/0211155Journal of Modern OpticsSep 1, 200312 citations

Mark S. Williamson, Vlatko Vedral

Journal of Modern OpticsJan 1, 20033 citations

Coherent-pulse implementations of quantum cryptography protocols resistant to photon-number-splitting attacks

Antonio Acín, Nicolas Gisin, Valerio Scarani

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.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.

arXiv:quant-ph/0302037Physical Review AJan 15, 2004136 citations

Security of a two-parameter quantum cryptography system using time-shifted states against photon-number splitting attacks

Dmitry Anatolevich Kronberg, S. N. Molotkov

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.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.

Journal of Experimental and Theoretical PhysicsOct 1, 200911 citations

Revealing of photon-number splitting attack on quantum key distribution system by photon-number resolving devices

Andrei Gaidash, V. I. Egorov, Artur V. Gleim

Quantum cryptography 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 of quantum states. In order to prevent actions of an eavesdropper, it is generally suggested to implement special cryptographic protocols, like decoy states or SARG04. In this paper, we describe an alternative method based on monitoring photon number statistics after detection. We provide a useful rule of thumb to estimate approximate order of difference of expected distribution and distribution in case of attack. Formula for calculating a minimum value of total pulses or time-gaps to resolve attack is shown. Also formulas for actual fraction of raw key known to Eve were derived. This method can therefore be used with any system and even combining with mentioned special protocols.Quantum cryptography 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 of quantum states. In order to prevent actions of an eavesdropper, it is generally suggested to implement special cryptographic protocols, like decoy states or SARG04. In this paper, we describe an alternative method based on monitoring photon number statistics after detection. We provide a useful rule of thumb to estimate approximate order of difference of expected distribution and distribution in case of attack. Formula for calculating a minimum value of total pulses or time-gaps to resolve attack is shown. Also formulas for actual fraction of raw key known to Eve were derived. This method can therefore be used with any system and even combining with mentioned special protocols.

Journal of Physics Conference SeriesAug 1, 201616 citations

Security of two quantum cryptography protocols using the same four qubit states

Cyril Branciard, Nicolas Gisin, Barbara Kraus +1 more

The first quantum cryptography protocol, proposed by Bennett and Brassard in 1984 (BB84), has been widely studied in recent years. This protocol uses four states (more precisely, two complementary bases) for the encoding of the classical bit. Recently, it has been noticed that by using the same four states, but a different encoding of information, one can define a protocol which is more robust in practical implementations, specifically when attenuated laser pulses are used instead of single-photon sources [V. Scarani et al., Phys. Rev. Lett. 92, 057901 (2004), referred to as the SARG04 protocol]. We present a detailed study of SARG04 in two different regimes. In the first part, we consider an implementation with a single-photon source: we derive bounds on the error rate $Q$ for security against all possible attacks by the eavesdropper. The lower and the upper bound obtained for SARG04 ($Q\ensuremath{\lesssim}10.95%$ and $Q\ensuremath{\gtrsim}14.9%$, respectively) are close to those obtained for BB84 ($Q\ensuremath{\lesssim}12.4%$ and $Q\ensuremath{\gtrsim}14.6%$, respectively). In the second part, we consider a realistic source consisting of an attenuated laser and improve on previous analysis by allowing Alice to optimize the mean number of photons as a function of the distance. The SARG04 protocol is found to perform better than BB84, both in secret-key rate and in maximal achievable distance, for a wide class of Eve's attacks.The first quantum cryptography protocol, proposed by Bennett and Brassard in 1984 (BB84), has been widely studied in recent years. This protocol uses four states (more precisely, two complementary bases) for the encoding of the classical bit. Recently, it has been noticed that by using the same four states, but a different encoding of information, one can define a protocol which is more robust in practical implementations, specifically when attenuated laser pulses are used instead of single-photon sources [V. Scarani et al., Phys. Rev. Lett. 92, 057901 (2004), referred to as the SARG04 protocol]. We present a detailed study of SARG04 in two different regimes. In the first part, we consider an implementation with a single-photon source: we derive bounds on the error rate $Q$ for security against all possible attacks by the eavesdropper. The lower and the upper bound obtained for SARG04 ($Q\ensuremath{\lesssim}10.95%$ and $Q\ensuremath{\gtrsim}14.9%$, respectively) are close to those obtained for BB84 ($Q\ensuremath{\lesssim}12.4%$ and $Q\ensuremath{\gtrsim}14.6%$, respectively). In the second part, we consider a realistic source consisting of an attenuated laser and improve on previous analysis by allowing Alice to optimize the mean number of photons as a function of the distance. The SARG04 protocol is found to perform better than BB84, both in secret-key rate and in maximal achievable distance, for a wide class of Eve's attacks.

arXiv:quant-ph/0505035Physical Review ASep 1, 2005146 citations

Q

for security against all possible attacks by the eavesdropper. The lower and the upper bound obtained for SARG04 ($Q\ensuremath{\lesssim}10.95%$ and $Q\ensuremath{\gtrsim}14.9%$, respectively) are close to those obtained for BB84 ($Q\ensuremath{\lesssim}12.4%$ and $Q\ensuremath{\gtrsim}14.6%$, respectively). In the second part, we consider a realistic source consisting of an attenuated laser and improve on previous analysis by allowing Alice to optimize the mean number of photons as a function of the distance. The SARG04 protocol is found to perform better than BB84, both in secret-key rate and in maximal achievable distance, for a wide class of Eve's attacks.