CN105743882B  Quantum key distribution based on BB84 agreement eavesdrops method of discrimination  Google Patents
Quantum key distribution based on BB84 agreement eavesdrops method of discrimination Download PDFInfo
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 CN105743882B CN105743882B CN201610040486.0A CN201610040486A CN105743882B CN 105743882 B CN105743882 B CN 105743882B CN 201610040486 A CN201610040486 A CN 201610040486A CN 105743882 B CN105743882 B CN 105743882B
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 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L63/00—Network architectures or network communication protocols for network security
 H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
 H04L63/1441—Countermeasures against malicious traffic
 H04L63/1475—Passive attacks, e.g. eavesdropping or listening without modification of the traffic monitored

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L63/00—Network architectures or network communication protocols for network security
 H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
 H04L63/1441—Countermeasures against malicious traffic
 H04L63/1466—Active attacks involving interception, injection, modification, spoofing of data unit addresses, e.g. hijacking, packet injection or TCP sequence number attacks

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communication
 H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
 H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
 H04L9/0852—Quantum cryptography
Abstract
Description
Technical field
The invention belongs to quantum communications field, in particular to a kind of quantum key distribution based on BB84 agreement, which is eavesdropped, to be differentiated The analysis method of scheme, for solving quantum information efficiency of transmission lowly and by nonideal device and incomplete experiment condition institute The problem of safety in the quantum cryptography of generation.
Background technique
Quantum communications are the technologies communicated using quantummechanical basic principle, and concrete form includes quantum secure Communication, quantum teleportation and Quantum Secure Direct Communication etc..Quantum teleportation is based on Entanglement, can be remote real The transfer of existing quantum state.Quantum Secure Direct Communication can realize the transmission of information under the premise of guaranteeing channel safety.Quantum is protected It is close communication based on quantum key distribution guarantee key distribution unconditional security, it can be achieved that data safe transmission.By Bennett The quantum key distribution QKD proposed jointly with Brassard is considered first application of quantum information science, and Commercial product is practical.Theoretically, the safety that QKD agreement resists the several variables generally attacked has been proven.It is real The technology tested, which has had developed to, makes it possible that key is distributed beyond the stage of the distance of 300km.Due to reality realize in this The nonideal experimental situation of kind, always some are imperfect in safety and efficiency.
QKD needs between two legal participants, is generally termed as Alice and Bob, generates from a primary key The key of one secret and shared key.Pass through the classical channel between access Alice and Bob, the part letter of primary key Breath can be used to distinguish that eavesdropping whether there is.If it turn out that coming from an illegal participant, it is generally termed as the eavesdropping of Eve Really it is not present, then remaining partial information can be used as last key after completing by privacy amplification and data harmonization. The agreement of first completion is exactly the BB84 agreement that is proposed jointly by Bennett and Brassard.Facts proved that the source of coming from The multiphoton signal of pole and the loss in quantum channel may result in the constraint of rate and distance.
Ideal QKD protocol requirement uses special state, such as single photon and Entangled State.However more tend in practice In using substitute, with transmission of quantum information, such as weak incoherent light, the preparation for it is in current experimental ability Within the scope of.This faulty quantum source provides possibility, commonly referred to as Eve for eavesdropping.It multiphoton signal source and is passing Loss in defeated route, which combines, can be obtained some strong eavesdropping attacks.This light proposed first by He Te and well this Rong Subnumber divides PNS attack, and usually substituting this by a better route of performance has noisy and loss transmission line.It is measuring During son encryption, the signal comprising single photon and at least two photons can be separated by Eve by physical schemes.Legal Loss in quantum channel can be divided into two parts, respectively transmission loss and nontransmitting loss.The generation of transmission loss It is low from minimum transfer loss and detector efficiency.Rather than transmission loss is introduced by illegal participant.Work as transmission When the ratio of loss is sufficiently large, transmission will become dangerous.Because the threshold value of the encryption about loss is discussed determination, surreptitiously The quantum channel that hearer Eve can replace this legal with an ideal channel, intercept all single photon signal and The information for only meeting Bob with multiphoton receives.If loss is not serious, listenerin Eve can intercept a part of monochromatic light Subsignal and these details, and listenerin's Eve energy are collected from remaining single photon by other best eavesdropping attacks Enough hide his behavior.Optical fiber attack includes that blinding is attacked.In addition, even if only single linear optics device, it is strong in thread Big attack can also be initiated.After listenerin Eve has grasped the basis of polarization according to BB84 agreement in public consulting, he Partial photonic in hand will reveal these polarization informations.
In short, listenerin Eve in transmission loss after being benefited, he may be collected into the letter shifted between legal participant Breath, and his behavior is made not to be disclosed for out.
Never stopped about the detection listenerin Eve research for executing the scheme of PNS attack.By utilizing average photon Several variations will not be stolen the fact that hearer Eve is obtained, and impulse method is inveigled to be used by most of BB84 protocol realization devices, with Solve the PNS attack there are the loss of channel height.In practical applications, since the imperfection of experiment and channel can Bypass message can be generated, perhaps listenerin Eve can be unfolded a kind of attack using them.And it is real for the trick state of progress It tests, even if it is also highly difficult for avoiding the eavesdropping from attack based on the more brilliant performance of the prior art.
Summary of the invention
It is an object of the invention to be directed to the deficiency of abovementioned prior art, the quantum key based on BB84 agreement is provided Distribution eavesdropping method of discrimination, to solve the safety in the quantum cryptography as caused by nonideal device and incomplete experiment condition The problem of property.
The technical scheme is that by analyzing the mathematical statistics characteristic of quantum in pulse, being based in the presence of eavesdropping The statistical property of their variation and photon in practical quantum channel, differentiates the presence of eavesdropping, and implementation step includes the following:
(1) according to the average photon number parameter in BB84 agreement, the Poisson formula of number of photons distribution is defined, i.e.,
Wherein, μ is the number of photons sent in pulse, and η is the efficiency of transmission under the conditions of different channels, and η≤1, μ η are through believing Road loses the average photon number in afterpulse, and k is the average photon number in pulse, P_{1}[k] is that number of photons channel damages in pulse Probability after mistake, k！It is the factorial of k, e is natural Exponents；
(2) after according to a part of photon of listenerin's interception is set, the distribution that number of photons is met is retransmitted, judgement obtains Receive the entire probability distribution situation of number of photons in pulse train:
If retransmitting number of photons after setting a part of photon of listenerin's interception and meeting Poisson distribution, and be sent to legal arteries and veins It rushes in sequence, then according to the arrival time of photon in the discontinuously arranged characteristic of single photon pulses and reception pulse, convolution < 1 >, determine that the entire probability distribution for receiving number of photons in pulse train is destroyed；
If retransmitting number of photons after setting a part of photon of listenerin's interception and meeting normal distribution:
(3) are thened follow the steps, wherein f (x) is the probability density of number of photons, and e is natural Exponents, and μ is mean value or distribution Expectation, σ is standard variance, σ^{2}It is variance ,∞ < x <+∞；
(3) following analysis is carried out to determine:
3a) according to μ=0, σ=1, convolution<2>obtains standardized normal distribution:
3b) according to the value of number of photons in Poisson distribution, convolution<3>obtains the discrete probability distribution of number of photons, i.e.,
Wherein, the value of k is 0.1,0.2,0.3 ..., P_{3}[k] is the probability of number of photons in pulse；
3c) according to the number of photons from listenerin Yu the different proportion of legal participant, convolution<1>,<3>and<4>is obtained It is to the probability distribution for receiving number of photons in pulse
Wherein α, β come from the ratio of the number of photons of legal participant and listenerin, α, β >=0 and alpha+beta=1, f respectively (k) be number of photons in pulse probability, k is the average photon number in each pulse, m！It is the factorial of m；
3d) according to BB84 agreement, monochromatic light subnumber in each pulse of faint incoherent light is obtained close to 0.1, in conjunction with Formula<7>, then set μ>=0.1；
3e) according to μ=0.1, the probability distribution of the number of photons of the different proportion of listenerin and legal person is emulated, determines to receive The entire probability distribution of number of photons is destroyed in pulse train；
(4) according to the entire probability distribution of number of photons, judgement receives the source of information error:
If the entire probability distribution of number of photons is destroyed, determine that information error comes from eavesdropping attack, legal participation Person thinks that this communication is dangerous, cancels communication；
Otherwise it is assumed that information error is from nonideal communication channel, legal participant by adjusting nonideal communication channel parameter, To reduce the error of information.
The present invention has the advantages that compared with traditional scheme
1) legal participant can distinguish information error source
Traditional scheme cannot distinguish between information error source；The present invention can be according to the whole probability of receiving end number of photons point Cloth, identifying information error are as caused by nonideal communication channel or eavesdropping attack.
2) efficiency of quantum information transmission is improved
For traditional scheme, legal participant may be misinterpreted as some mistakes as caused by nonideal communication channel to be to come from In eavesdropping attack, then cancel this communication, quantum information transmission process will restart；But due to not eavesdropping The decaying of channel is always high in the presence of attack, will lead to legal participant and will not may collect from beginning to end and takes office What useful information, makes the efficiency degradation of quantum communications.
Presence of the present invention due to that can perceive eavesdropping attack, improves the efficiency of quantum communications.
Detailed description of the invention
Implementation flow chart Fig. 1 of the invention；
Fig. 2 is to retransmit the entire probability distribution that number of photons meets number of photons in reception pulse under normal distribution in listenerin Figure.
Specific embodiment
Below in conjunction with attached drawing, the present invention will be described in detail:
One, technical principle
Although theoretically the quantum key distribution safety based on BB84 agreement has obtained compellent proof, Due to the imperfection of real device, ideal singlephoton light source is such as substituted using weak coherent light source, listenerin Eve can be used and be cut The mode for obtainingretransmitting eavesdrops quantum key distribution process, and quantum key distribution system is caused to lose safety.According to amount The safety detection of quantum key distribution agreement is based on Probability Statistics Theory, so the present invention uses quantum mathematical statistics method, analysis The probability distribution situation of number of photons in pulse.Application of Statistic Methods is in many researchs and industrial circle, especially in actual rings In border, they are played a very important role.Medical worker tests, with the effect of the various drugs of determination and control people The environmental condition of class, to infer the suitable treatment of various diseases.Engineer is according to sampling product quality characteristics and various controllable Process variable, to determine key variables relevant to product quality.In the past decade, to the probabilistic statistical characteristics of number of photons into The research gone in terms of some quantum.The distribution character of quantum has obtained, and becomes the one of quantum communications and field of cryptography A important basis.
BB84 agreement uses four quantum states for the carrier of quantum information, this four states belong to two groups of conjugated radicles, and every group Two states in base are mutually orthogonal.Two groups of bases are conjugated each other to be referred to: any basic vector in one group of base is any in another group of base Projection on basic vector is all equal, can not thoroughly be differentiated by measuring between nonorthogonal states.
In BB84 agreement, a kind of binary sequence photonic modulation that sender will transmit to polarization state, recipient's selection It is corresponding to measure base to measure the polarization state of the photon received, and convert it into corresponding binary sequence.
The first experiment of feasibility about BB84 agreement achieved success in 1992.Hereafter, several research groups The long distance transmission of quantum key distribution is realized in the past twenty years.However these practical approaches are in many basic aspects It is different from initial theoretical suggestion, because current experimental ability is not able to satisfy technical need.Such as, it is ensured that the peace of BB84 scheme Full property also needs perfect singlephoton source, and in practice, replace singlephoton source to realize BB84 quantum key point with weak laser pulse Originating party case is then transmitted in the quantum channel of height loss, if number of photons included in a weak laser pulse is more than 1, so that it may There can be the leakage of quantum information.Therefore, all these ideal BB84 agreement and it is practical realize between modification may The safety of agreement can be jeopardized, and cause to include efficiency and apart from upper limitation.Although Heisenberg uncertainty principle and quantum are not Can cloning theorem ensure that the Unconditional security of BB84 agreement, but due to the deficiency of current conditions, or it is difficult to ensure that amount The efficiency of subinformation transmission.
The method that the present invention manages statistical property using analysis quantum number, to try to differentiate by nonideal communication channel and eavesdropping attack Quantum information efficiency of transmission can be improved in caused information error.
There are many attack strategies can collect not detectedly useful information.Listenerin Eve is in order in attack process It is middle to intercept more photons, and retransmit the photon of regeneration or manipulate legal detection according to the measurement result of malice Device has made many effort.It include vacuum, single photon and multiphoton pulses in quantum channel.According to the demand of BB84 agreement And quantum nature, it is difficult the attack for detecting that quantum channel is vacuum and single photon both types.Therefore, it is necessary to analyze measuring There are the attacks of multiphoton pulses in subchannel.
The present invention is exactly that can be able to satisfy Poisson distribution and normal distribution according to the photon retransmitted from listenerin Eve These two types of distribution situations, to analyze the entire probability distribution situation for receiving number of photons in pulse, to judge coming for information error Source.
Two, embodiments
Referring to Fig.1, steps are as follows for realization of the invention:
Step 1, according to the average photon number parameter in BB84 agreement, definition sends the Poisson point that number of photons is obeyed in pulse Cloth formula, i.e.,
Wherein, μ is the number of photons sent in pulse, and η is the efficiency of transmission under the conditions of different channels, and η≤1, μ η are through believing Road loses the average photon number in afterpulse, and k is the average photon number in pulse, P_{1}[k] is that number of photons channel damages in pulse Probability after mistake, k！It is the factorial of k, e is natural Exponents.
Step 2, after according to a part of photon of listenerin's interception is set, the distribution that number of photons is met is retransmitted, judgement Obtain receiving the entire probability distribution situation of number of photons in pulse train:
It after listenerin intercepts a part of photon, retransmits there are two types of the distributions that number of photons is met: first is that meeting Poisson distribution, second is that meeting normal distribution.
If retransmitting number of photons after setting a part of photon of listenerin's interception and meeting Poisson distribution, then steal in this case Hearer Eve makes its probability distribution and initial to the photon pulse of forgery is resend in legal inceptive impulse sequence The probability distribution of number of photons is identical, but due to actually due to using substitution of the faint incoherent light as single photon signal, Faint incoherent light has good characteristic of the single photon in pulse train, and the specific location of single photon is difficult to determine, because This cannot achieve the number of photons of listenerin's interception as the position where this original partial photonic number, so can be according to monochromatic light The time that the discontinuity and photon of the distribution of subpulse successively reach learns that the entire probability distribution of number of photons is destroyed；
If retransmitting number of photons after setting a part of photon of listenerin's interception and meeting normal distribution, deterministic process such as step 3。
Step 3, judge to receive and retransmit the entire probability distribution situation that number of photons meets normal distribution in pulse train:
As the continuous probability distribution of a very universal generation, ignorant realvalued random variable is distributed for it, Normal distribution is a most suitable function to be used to describe nature and social science.
When listenerin Eve retransmit forge photon when, usual light pulse be it is independent, and number of photons be it is random, Therefore normal distribution can be used to indicate the probability distribution of this event, i.e.,
For convenience, μ=0 is allowed, σ=1 obtains standardized normal distribution:
Because normal distribution is a continuous probability distribution, it describes the distribution of any time on entire time shaft, And stochastic variable of the number of photons in pulse as an independent same distribution, its distribution are discrete.So can lead to Cross the discrete variable for changing traditional normal distribution form to describe number of photons；
According to the value of number of photons in Poisson distribution, convolution<1>and<3>obtain the discrete probability distribution of number of photons, i.e.,
Wherein, the value of k is taken as 0.1,0.2,0.3 ..., these values are all the reasonable values about pulse subnumber.
After listenerin Eve is sent to the photon of forgery in legal pulse train, according to from listenerin Eve and legal The different proportion of the number of photons of participant can be obtained the entire probability distribution for receiving number of photons in pulse by formula<1>and<4>, it may be assumed that
Wherein α, β come from the ratio of the number of photons of legal participant and listenerin, α, β >=0 and alpha+beta=1, f respectively (k) be number of photons in pulse probability, k is the average photon number in each pulse, m！It is the factorial of m；
Monochromatic light subnumber in each pulse of usually weak incoherent light can set μ >=0.1 close to 0.1.
This example sets μ=0.1, and ensures that the value of the entire probability distribution f (k) of number of photons meets f (k) >=0, and emulation is being stolen Hearer retransmits number of photons and meets the entire probability distribution for receiving number of photons in pulse under normal distribution.In order to facilitate observation, this hair It is bright to use a continuous curve, as shown in Figure 2.
Step 4, according to the entire probability distribution of number of photons, judgement receives the source of information error:
Referring to Fig. 2, learn that the entire probability distribution of number of photons is intended to by fixation in legal number of photons and each pulse Number of photons determines together.When forgery number of photons is more than the 25% of overall number of photons, it can be seen that the entire probability distribution of number of photons Significantly it is destroyed.In this case, according to BB84 agreement, this ratio can be received accurately well below listenerin Eve Collect the probability 50% of information, therefore for listenerin Eve, this ratio value is not enough to be collected into from legal participant useful Information, it can be ensured that the safety communicated between legal person.Therefore it can judge to receive letter by the entire probability distribution of number of photons Cease the source of error:
If the entire probability distribution of number of photons is destroyed, determine that information error comes from eavesdropping attack, legal participation Person thinks that this communication is dangerous, cancels communication；
Otherwise it is assumed that information error is from nonideal communication channel, legal participant by adjusting nonideal communication channel parameter, To reduce the error of information.
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