CN113037474B - Asymmetric quantum conference key negotiation method and system - Google Patents

Asymmetric quantum conference key negotiation method and system Download PDF

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CN113037474B
CN113037474B CN202110226130.7A CN202110226130A CN113037474B CN 113037474 B CN113037474 B CN 113037474B CN 202110226130 A CN202110226130 A CN 202110226130A CN 113037474 B CN113037474 B CN 113037474B
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CN113037474A (en
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尹华磊
李昭
陈增兵
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Nanjing University
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    • 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 communications; Network security protocols
    • 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
    • H04L9/0838—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/50—Transmitters
    • H04B10/516—Details of coding or modulation
    • H04B10/524—Pulse modulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/50—Transmitters
    • H04B10/516—Details of coding or modulation
    • H04B10/548—Phase or frequency modulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/70—Photonic quantum communication
    • 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 communications; Network security protocols
    • 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
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Abstract

The invention provides an asymmetric quantum conference key negotiation method and system, which are implemented between any two sending ends and any receiving end, and channels between the two sending ends and the receiving end are asymmetric. The invention improves the original three-party quantum conference key negotiation system, considers the asymmetric scene of the channel, and provides an optimized safe code rate calculation method, thereby greatly improving the practicability of the asymmetric quantum conference key negotiation system, leading the safe code rate to be higher and leading the transmission distance to be longer.

Description

Asymmetric quantum conference key negotiation method and system
Technical Field
The invention relates to the technical field of quantum conference key negotiation, in particular to an asymmetric quantum conference key negotiation method and system.
Background
Quantum conference key agreement allows the sharing of identical unconditionally secure key strings between multiple parties based on the fundamental properties of quantum mechanics. However, because of the limitation of the linear boundary between the code rate and the channel distance, quantum conference key agreement has not been able to realize the key sharing at a longer distance, which also affects the practicability and greatly limits the development thereof. In order to solve the problem, the patent with application number 2020103489161 proposes a method and a system for quantum conference key agreement, and specifically discloses a method for quantum conference key agreement capable of realizing three remote parties, which breaks the linear limit of code rate and distance, greatly improves the practicality of quantum conference key agreement, and increases the transmission distance from the original 50km to more than 500 km. The method describes a three-way key sharing consisting of two senders and one receiver, which assumes that the two senders remain completely symmetrical to the receiver.
In reality, it is extremely difficult to ensure such symmetry, and therefore, the solution proposed in patent 2020103489161 does not adapt to the situation where the channel is asymmetric. Because perfect interference cannot be performed in interferometry, an inherent error rate is introduced, and the transmission distance of the interferometer is bound to be reduced while the safety is ensured.
Disclosure of Invention
The invention aims to: under the condition of asymmetric channels, signal lights sent by two sending ends cannot perform perfect interference in interference measurement, an inherent error rate is introduced, and if safety is guaranteed, a transmission distance is liable to be reduced. In order to eliminate the error rate and further improve the transmission distance on the premise of ensuring the safety, the invention provides an asymmetric quantum conference key negotiation scheme.
The technical scheme is as follows: in order to achieve the purpose, the invention provides the following technical scheme:
the invention provides an asymmetric quantum conference key negotiation method, which is implemented between any two sending ends and any two receiving ends, wherein channels from the two sending ends to the receiving ends are asymmetric, and the method comprises the following steps:
(1) randomly selecting an X basis vector or a Z basis vector by the first sending end and the second sending end; under the Z basis vector, a sending end randomly selects light intensity mu A Or 0 preparing weak coherent light pulse with random phase as signal state to be sent to receiving end, and selecting light intensity mu at random by sending end B Or 0, preparing weak coherent light pulses with random phases as signal states and sending the weak coherent light pulses to a receiving end; at the X basis vector, the sender-side randomly selects from { mu } A ，v A 0, the selected light forces the decoy state of random phase to be sent to the receiving end, and the second sending end randomly sends the decoy state from { mu } B ，ν B 0, selecting light to force the decoy state with random phase to be sent to a receiving end; v is A V and v B The following relation is satisfied:
Figure BDA0002956298760000021
wherein, t A Selecting light intensity mu for a transmitting end under Z basis vector A Probability of 1-t A Selecting light intensity 0, t for the transmitting end under Z basis vector B Selecting light intensity mu for the transmitting end two under the Z basis vector B Probability of 1-t B Selecting the probability of light intensity 0 for the second sending end under the Z basis vector;
(2) the receiving end randomly selects a Z basis vector or an X basis vector to measure; under the Z basis vector, the receiving end respectively measures two paths of weak coherent light pulses by adopting a first detector and a second detector, and when only the first detector or the second detector responds, a detection result is recorded; under X basis vector, the receiving end measures the interference light of two paths of weak coherent light pulses by adopting a detector III and a detector IV, and when only the detector III or the detector IV responds, a detection result is recorded;
(3) two sending ends and a receiving end publish the selected basis vectors and reserve data under the condition that all three parties select the Z basis vectors so as to generate original keys of all parties; in other cases, two transmitters will announce the selected light intensity as a first transmitter sends v A Weak coherent pulse of light intensity, sending end secondary sending v B The weak coherent pulse of light intensity, and when the receiving end chooses the X basis vector, two sending ends publish the phase, then choose and match after carrying on the phase; on the premise of successful phase selection and matching, calculating gains of different light intensities and bit error rates under X basis vectors through published phase data;
(4) estimating the possibility of data leakage by using a decoy method based on the published data under the condition that three parties do not select all Z basis vectors;
(5) on the premise that both the bit error rate and the data leakage possibility meet preset requirements, part of original keys are randomly selected by three parties to be published so as to carry out classical error correction, error verification and privacy amplification to obtain final keys of the three parties.
Several alternatives are provided below for the method, but not as an additional limitation to the above general solution, but merely as a further addition or preference, each alternative being combinable individually for the above general solution or among several alternatives without technical or logical contradictions.
Optionally, the method for selecting matching after the phase is as follows:
judging whether the phases of two paths of weak coherent light pulses sent by the first sending end and the second sending end meet a judgment formula:
Figure BDA0002956298760000022
if yes, the phases of the two weak coherent light pulses are matched, otherwise, the phases of the two weak coherent light pulses are not matched;
in the decision formula, r is a phase parameter, when r is 0, the detector four response represents a bit error of an X basis vector, and when r is 1, the detector three response represents a bit error of an X basis vector;
Figure BDA0002956298760000023
for phase differences, theta, between two weak coherent light pulses, due to reference frame and phase drift A For the phase, θ, of the weak coherent light pulse transmitted by the transmitting end B
The phase of the weak coherent light pulse sent by the sending end II; δ is a chosen constant parameter.
Optionally, in the step (4), the specific step of estimating the data leakage possibility includes:
method for estimating single photon response rate of signal state by decoy state method
Figure BDA0002956298760000031
And single photon phase error rate
Figure BDA0002956298760000032
Figure BDA0002956298760000033
Figure BDA0002956298760000034
Figure BDA0002956298760000035
Figure BDA0002956298760000036
Wherein, Y 1 d To representThe single photon responsivity of a signal state under a d-base vector, wherein d belongs to { X, Z };
Figure BDA0002956298760000037
the transmitting end under the d-base vector has the transmitting light intensity of k A The weak coherent state pulse and the sending light intensity of the sending end II is k B Gain, k, at weak coherent state of the pulse A ∈{μ A ,v A ,0}，k B ∈{μ B ,v B ,0}；
Figure BDA0002956298760000038
For the transmitting end, the transmitted light intensity is v A The weak coherent state pulse and the sending light intensity of the sending end two is nu B Selecting the error rate after matching after passing through the phase under the condition of weak coherent state pulse;
Figure BDA0002956298760000039
sending light intensity v for sending end A The weak coherent state pulse and the sending light intensity of the sending end two is nu B Under the condition of weak coherent state pulse, gain after phase selection and matching is carried out;
Figure BDA00029562987600000310
is the response rate of the vacuum state under the X basis vector,
Figure BDA00029562987600000311
optionally, the calculation formula of the security code rate in the classical error correction process is:
Figure BDA00029562987600000312
wherein R represents a security code rate, λ EC Representing the key revealed during classical error correction, h (x) is binary shannon entropy, h (x) is-xlog 2 x-(1-x)log 2 (1-x)。
Optionally, under the condition of a limited code length, in step (4), the specific step of estimating the data leakage possibility includes:
method for estimating vacuum state response number of signal state by using decoy state method
Figure BDA00029562987600000313
Number of single photon responses
Figure BDA00029562987600000314
And single photon phase error rate
Figure BDA00029562987600000315
Figure BDA0002956298760000041
Figure BDA0002956298760000042
Figure BDA0002956298760000043
Figure BDA0002956298760000044
Figure BDA0002956298760000045
Figure BDA0002956298760000046
Figure BDA0002956298760000047
Figure BDA0002956298760000048
Figure BDA0002956298760000049
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00029562987600000410
the expected value of the number of responses in the vacuum state,
Figure BDA00029562987600000411
indicating that the first sending end sends a single photon and the second sending end sends an expected value of the number of response measured under the Z basis vector in a vacuum state,
Figure BDA00029562987600000412
indicating that the first sending end sends a vacuum state, the second sending end sends single photons to measure the expected value of the response number under the Z basis vector,
Figure BDA00029562987600000413
the expected value of the response number after the transmitting terminal sends a single photon and the transmitting terminal sends a vacuum state under X basis vector and phase post selection is shown,
Figure BDA00029562987600000414
the expected value of the response number of the single photon sent by the sending terminal II after measurement under the X basis vector and phase post-selection is represented by the sending terminal I sending a vacuum state;
Figure BDA00029562987600000415
indicating that the transmitting end has a transmitting light intensity of k A The second sending end sends light intensity k B And the receiving end selects the total number of pulses of the Z or X basis vectors,
Figure BDA0002956298760000051
respectively the upper limit and the lower limit of the expected value of the corresponding response number,
Figure BDA0002956298760000052
respectively represent
Figure BDA0002956298760000053
The lower limit of (a) is,
Figure BDA0002956298760000054
Figure BDA0002956298760000055
respectively represent
Figure BDA0002956298760000056
The lower limit of (d);
Figure BDA0002956298760000057
representing single photon phase error rate in signal state
Figure BDA0002956298760000058
The upper limit of (a) is,
Figure BDA0002956298760000059
for the transmitting end, a transmitting light intensity v A The second sending end sends light intensity v B The total number of the weak coherent pulses after phase selection,
Figure BDA00029562987600000510
for the number of errors to be addressed,
Figure BDA00029562987600000511
the statistical fluctuation value of the random sampling without the return is obtained;
calculating the length of the security code:
Figure BDA00029562987600000512
wherein λ is EC Denotes the key revealed during classical error correction, h (x) -xlog 2 x-(1-x)log 2 (1-x) is binary Shannon entropy,
Figure BDA00029562987600000513
respectively, the code length leaked in the error verification and privacy amplification processes.
Optionally, the method for generating the receiving end data includes:
under the condition of selecting Z basis vector measurement, when a detector responds, the logic bit value of a receiving end is 1; when the detector II responds, the logic bit value of the receiving end is 0;
under the condition of selecting X basis vector measurement, when the detector responds to the three, the logic bit value of the receiving end is 0; and when the detector responds four times, the logic bit value of the receiving end is 1.
Optionally, the average photon number of the weak coherent light pulse is less than 1.
Optionally, the first sending end and the second sending end send weak coherent optical pulses to the receiving end through unsafe quantum channels, respectively.
Optionally, the three parties publishing data in step (3) are performed by authenticating a classical channel.
The invention also provides an asymmetric quantum conference key negotiation system, which comprises a first sending end, a second sending end and a receiving end, wherein channels from the two sending ends to the receiving end are asymmetric, and the first sending end, the second sending end and the receiving end adopt the method to carry out quantum conference key negotiation.
The technical effects are as follows: compared with the prior art, the invention considers the asymmetric scene of the channel, can optimize higher safe code rate, has farther transmission distance and greatly improves the practicability.
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FIG. 1 is a schematic structural diagram of a third embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a fourth embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a fourth embodiment of the present invention;
fig. 4 is a comparison between the scheme and the symmetric quantum conference key negotiation system proposed in patent 2020103489161 in the simulation graph of the security code rate and the transmission distance from the first sending end to the receiving end, when the channels are asymmetric and the transmission distance from the first sending end to the receiving end and the transmission distance from the second sending end to the receiving end differ by 50 kilometers in the fourth embodiment of the present invention.
Fig. 5 is a comparison between the scheme and the symmetric quantum conference key negotiation system proposed in patent 2020103489161 in the simulation diagram of the security code rate and the transmission distance from the first transmitting end to the receiving end, under the condition that the channels are asymmetric and the difference between the transmission distance from the first transmitting end to the receiving end and the transmission distance from the second transmitting end to the receiving end is 50 kilometers, considering the finite code length.
Detailed Description
The invention will be further described with reference to the accompanying drawings and specific embodiments. It is to be understood that the present invention may be embodied in various forms, and that there is no intention to limit the invention to the specific embodiments illustrated, but on the contrary, the intention is to cover some exemplary and non-limiting embodiments shown in the attached drawings and described below.
It is to be understood that the features listed above for the different embodiments may be combined with each other to form further embodiments within the scope of the invention, where technically feasible. Furthermore, the particular examples and embodiments of the invention described are non-limiting, and modifications may be made in the structure, steps, sequence of steps, or illustrated above without departing from the scope of the invention.
Example 1:
this embodiment proposes an asymmetric quantum conference key negotiation method, implemented between any two sending ends and receiving ends, where channels between the two sending ends and the receiving ends are asymmetric, where the method includes:
(1) randomly selecting an X basis vector or a Z basis vector by the first sending end and the second sending end; under the Z basis vector, a sending end randomly selects light intensity mu A Or 0 preparing weak coherent light pulse with random phase as signal state and sending to receiving end, and selecting light intensity mu at sending end B Or 0, preparing weak coherent light pulses with random phases as signal states and sending the weak coherent light pulses to a receiving end; at the X basis vector, the sender-side randomly selects from { mu } A ，v A 0-phase forced standby of selected lightSending the machine trap state to the receiving end, and sending the second random number from the { mu B ，ν B Selecting light from 0 to force a decoy state with random phase to be sent to a receiving end; v. of A And v B The following relation is satisfied:
Figure BDA0002956298760000061
wherein, t A Selecting light intensity mu for a transmitting end under Z basis vector A Probability of (1-t) A Selecting light intensity 0, t for the transmitting end under Z basis vector B Selecting light intensity mu for the transmitting end two under the Z basis vector B Probability of (1-t) B Selecting the probability of light intensity 0 for the second sending end under the Z basis vector;
(2) a receiving end randomly selects a Z basis vector or an X basis vector to measure; under the Z basis vector, the receiving end adopts a first detector and a second detector to respectively measure two paths of weak coherent light pulses, and when only the first detector or the second detector responds, a detection result is recorded; under X basis vector, the receiving end measures the interference light of two paths of weak coherent light pulses by adopting a detector III and a detector IV, and when only the detector III or the detector IV responds, a detection result is recorded;
(3) two sending ends and a receiving end publish the selected basis vectors and reserve data under the condition that all three parties select the Z basis vectors so as to generate original keys of all parties; in other cases, two transmitters will announce the selected light intensity as a first transmitter sends v A Weak coherent pulse of light intensity, sending end secondary sending v B When the receiving end selects X basis vector, two sending ends publish phase, and then select matching after phase; on the premise of successful phase selection and matching, calculating gains of different light intensities and bit error rates under X basis vectors through published phase data;
(4) estimating the possibility of data leakage by using a decoy state method based on the published data under the condition that three parties do not select all Z basis vectors;
(5) on the premise that both the bit error rate and the data leakage possibility meet preset requirements, part of original keys are randomly selected by three parties to be published so as to carry out classical error correction, error verification and privacy amplification to obtain final keys of the three parties.
Specifically, in step (1), the sending end selects the probabilities of the Z basis vector or the X basis vector as
Figure BDA0002956298760000071
And
Figure BDA0002956298760000072
at the Z basis vector, the transmitted light intensity is mu A Or 0 is t A And 1-t A With a transmitted light intensity of { mu ] at the basis of the X vectors corresponding to bit values 1 and 0 A ，v A Probability of 0 is respectively
Figure BDA0002956298760000073
The weak coherent pulse expression of random phase generated at the sending end is
Figure BDA0002956298760000074
k A ∈{μ A ,v A 0 }; similarly, the probability of selecting the Z basis vector or the X basis vector at the sending end is respectively
Figure BDA0002956298760000075
And
Figure BDA0002956298760000076
at the Z basis vector, the transmitted light intensity is mu B Or 0 is t B And 1-t B With a transmitted light intensity of { mu ] at the basis of the X vectors corresponding to bit values 0 and 1 B ，v B Probability of 0 is respectively
Figure BDA0002956298760000077
The weak coherent pulse expression of random phase generated by the second sending end is
Figure BDA0002956298760000078
k B ∈{μ B ,v B 0 }; wherein theta is A And theta B Indicating its phase.
Specifically, in the step (3), the data publishing is completed through the authenticated classical channel. After the data are published, the generation method of the data at the receiving end comprises the following steps:
under the condition of selecting Z basis vector measurement, when a detector responds, the logic bit value of a receiving end is 1;
when the detector II responds, the logic bit value of the receiving end is 0;
under the condition of selecting X basis vector measurement, when the detector responds to the three, the logic bit value of the receiving end is 0;
and when the detector responds four times, the logic bit value of the receiving end is 1.
After the data are published, the specific steps of selecting and matching after the phase position are as follows: judging whether the phases of two paths of weak coherent light pulses sent by the first sending end and the second sending end meet the following conditions:
Figure BDA0002956298760000081
if yes, the phases of the two weak coherent light pulses are matched, otherwise, the phases of the two weak coherent light pulses are not matched; in the formula, r is a phase parameter, and it is defined that when r is 0, the detector four response indicates a bit error of the X basis vector, and when r is 1, the detector three response indicates a bit error of the X basis vector, so that gains with different light intensities and a bit error rate of the X basis vector can be obtained through published data;
Figure BDA0002956298760000082
for phase differences, theta, between two weak coherent light pulses, due to reference frame and phase drift A Is the phase, θ, of the weak coherent light pulse transmitted by the transmitter B The phase of the weak coherent light pulse sent by the sending end II; δ is a chosen constant parameter.
Specifically, in the step (4), the specific step of estimating the possibility of data leakage includes:
method for estimating single photon response rate of signal state by decoy state method
Figure BDA0002956298760000083
And single photon phase error rate
Figure BDA0002956298760000084
The single photon responsivity is calculated by the following formula:
Figure BDA0002956298760000085
Figure BDA0002956298760000086
Figure BDA0002956298760000087
wherein, Y 1 d Representing the single photon responsivity of a signal state under a d-base vector, wherein d belongs to { X, Z };
Figure BDA0002956298760000088
the transmitting end under the d-base vector has the transmitting light intensity of k A The weak coherent state pulse and the sending light intensity of the sending end II is k B Gain k in weak coherent pulses A ∈{μ A ,v A ,0}，k B ∈{μ B ,v B ,0}。
Single photon phase error rate at the signal state, i.e. the Z basis vector
Figure BDA0002956298760000089
Approximately equal to the bit error rate after the selection of the decoy state, i.e., the phase under the X-basis vector, the single photon phase error rate is calculated as:
Figure BDA00029562987600000810
the formula can give the signal state single photon phase error rate
Figure BDA00029562987600000811
The upper limit of (1), wherein,
Figure BDA00029562987600000812
sending light intensity v for sending end A The weak coherent state pulse and the sending light intensity of the sending end two is nu B Selecting the error rate after matching after the phase is carried out under the condition of weak coherent state pulse;
Figure BDA00029562987600000813
sending light intensity v for sending end A The weak coherent state pulse and the sending light intensity of the sending end two is nu B Under the condition of weak coherent state pulse, gain after phase selection and matching is carried out;
Figure BDA0002956298760000091
is the response rate of the vacuum state under the X basis vector,
Figure BDA0002956298760000092
Figure BDA0002956298760000093
can be obtained from the data published in step three after experimental measurements.
Specifically, in the step (5), part of the secret keys are randomly selected in the step five to perform classical error correction, error verification and privacy amplification to obtain a final secret key, and the formula of the security code rate is as follows:
Figure BDA0002956298760000094
wherein R represents a security code rate, λ EC Representing the key revealed during classical error correction, h (x) is binary shannon entropy, h (x) is-xlog 2 x-(1-x)log 2 (1-x)。
Example 2:
embodiment 1 provides a method for calculating a security code rate under the condition of an infinite code length. However, in practical process, the transmitted code length cannot be infinite, and in case of the finite code length, a certain error may be caused due to the influence of statistical fluctuation, so the embodiment provides the lowest security code rate under the finite code length.
The rest of this embodiment is the same as the embodiment, and only the difference is found in the calculation formulas of step four and step five, specifically:
the implementation utilizes the decoy state method to estimate the number of the vacuum state responses of the signal state in the fourth step
Figure BDA0002956298760000095
Number of single photon responses
Figure BDA0002956298760000096
And single photon phase error rate
Figure BDA0002956298760000097
A calculation formula of finite code length is given below, and firstly, an expected value of the number of response states in a vacuum state under a Z-basis vector is given
Figure BDA0002956298760000098
Expected number of single photon responses
Figure BDA0002956298760000099
And expected value of number of single photon responses after phase post-selection under X-base vector
Figure BDA00029562987600000910
Lower limit of (2):
Figure BDA00029562987600000911
Figure BDA00029562987600000912
Figure BDA00029562987600000913
Figure BDA00029562987600000914
Figure BDA0002956298760000101
Figure BDA0002956298760000102
Figure BDA0002956298760000103
wherein the content of the first and second substances,
Figure BDA0002956298760000104
indicates that the transmitting end has a transmitting light intensity of k A The second sending end sends light intensity k B The total number of pulses when the receiving end selects the Z or X basis vector,
Figure BDA0002956298760000105
respectively the upper limit and the lower limit of the expected value of the corresponding response number,
Figure BDA0002956298760000106
respectively represent
Figure BDA0002956298760000107
The lower limit of (a) is,
Figure BDA0002956298760000108
Figure BDA0002956298760000109
respectively represent
Figure BDA00029562987600001010
The lower limit of (3). The observed value can be obtained from the data published in step three after specific experimental measurement, and the expected value and the upper and lower limits of the observed value conversion can be given by the chernoff limit and the inverse chernoff limit.
Single photon phase error rate at the signal state, i.e. the Z basis vector
Figure BDA00029562987600001011
Approximately equal to the bit error rate after selection of the decoy state, i.e., the lower phase of the X-base vector, so
Figure BDA00029562987600001012
Figure BDA00029562987600001013
The formula can give the signal state single photon phase error rate
Figure BDA00029562987600001014
An upper limit of (1), wherein
Figure BDA00029562987600001015
Sending light intensity v for sending end A The second sending end sends light intensity v B The total number of the weak coherent pulses after phase selection,
Figure BDA00029562987600001016
is the corresponding number of errors. Both quantities can be obtained from the data published in step three after experimental measurements,
Figure BDA00029562987600001017
statistical fluctuation values for random samples without payout.
In the fifth step, part of keys are randomly selected to carry out classical error correction, error verification and privacy amplification to obtain a final key, and the formula of the security code length is as follows:
Figure BDA00029562987600001018
wherein λ EC Representing keys revealed during classical error correction, h (x) -xlog 2 x-(1-x)log 2 And (1-x) is binary Shannon entropy, and the last two items are respectively the code length leaked in the error verification and privacy amplification processes.
Example 3:
in order to implement the asymmetric quantum conference key negotiation methods in the two embodiments, the present embodiment provides an asymmetric quantum conference key negotiation system, which includes a first sending end, a second sending end, and a receiving end; the function can be further divided into a plurality of modules as shown in fig. 1. The modules work cooperatively to complete a key distribution task, wherein the first sending end and the second sending end comprise a signal light sending module, a signal light intensity modulation module and a signal light phase modulation module, the receiving end comprises a signal light phase compensation module and a detection module, post-processing modules are arranged in the first sending end, the second sending end and the receiving end and are used for controlling the modules at the local end and screening out original key strings in subsequent processes of basis vector publishing, light intensity publishing, phase compensation, phase post-selection and the like, and then final keys are extracted through error correction and privacy amplification processes. To simplify the drawing, the post-processing module is not represented in the illustration. The functions realized by the modules are as follows:
the signal light sending module is used for sending continuous laser for preparing signal light, the light intensity, the phase, the frequency, the polarization and the like before and after the sent continuous laser are kept stable, and specific equipment can include but is not limited to a continuous laser with stable light intensity;
the signal light intensity modulation module is used for preparing weak coherent light pulses according with signal light conditions, and is required to realize control of light intensity and formation of the light pulses, and specific equipment can include but is not limited to an intensity modulator and a fixed attenuator;
the signal light phase modulation module modulates the signal light pulse into a weak coherent light pulse state which is randomly in any phase, and specific equipment can include but is not limited to a phase modulator and a random number generator;
the signal light phase compensation module is used for compensating phase drift generated by transmission of signal light in the quantum channel. The principle of the phase compensation process is as follows: since the signal light may cause a certain phase drift while propagating through the channel, the data needs to be subjected to phase compensation in a final post-processing module through algorithm processing or strong light reference. When implemented by a specific device, the following can be adopted: after the continuous laser is emitted by the continuous laser, a section of strong light without phase modulation and intensity attenuation is reserved in front of each beam of signal light pulse by the two transmitting ends and is transmitted to the receiving end adjacently with the signal light, and the receiving end detects the phase difference at the two ends and is used for performing phase post-compensation in the post-processing module.
The signal light is transmitted from the transmitting end to the receiving end through an unsafe quantum channel, and the detection module of the receiving end is used for realizing the measurement of the Z base and the X base.
Example 4:
this embodiment provides an asymmetric quantum conference key agreement system as shown in fig. 2, which is a preferred implementation of embodiment 3.
The first sending end and the second sending end both comprise a continuous laser, an intensity modulator and a phase modulator which are sequentially cascaded and are respectively used for realizing the functions of the signal light sending module, the signal light intensity modulation module and the phase modulation module. The two sending ends are connected with the receiving end through single mode fibers.
Continuum lasers are used to produce continuum laser light that is stable in intensity, phase, frequency, and polarization.
The intensity modulator chops continuous laser with certain intensity to obtain signal light pulse. A fixed attenuator is added behind the intensity modulator to reduce the intensity of the signal light pulse into weak coherent light pulse with average photon number less than 1.
The phase modulator adds a randomly selected phase to the weak coherent light pulse to prepare a phase random weak coherent state.
The receiving end comprises a first beam splitter, a second beam splitter, a third beam splitter, a first detector, a second detector, a third detector and a fourth detector; the four detectors respectively correspond to photon detection responses of the ports; the first beam splitter and the second beam splitter are used for passive selection of basis vectors, signal light entering the detection module from the first sending end and the second sending end respectively enters the first beam splitter and the second beam splitter, signal light photons of the first sending end randomly enter the first detector or the third beam splitter through the first beam splitter, and signal light photons of the second sending end randomly enter the second detector or the third beam splitter through the second beam splitter. And the detector I and the detector II measure the Z basis vector, the signal light entering the beam splitter III from two ends is interfered, and then the detector III and the detector IV measure the Z basis vector, so that the X basis vector is measured integrally. When only one response is detected in each pair of detectors, a success event is recorded.
And finally, the three parties publish the required data, and a post-processing module at the receiving end performs post-phase compensation on the obtained detection result and interacts with a post-processing module at the sending end to perform error correction and privacy amplification and obtain a final security key.
Example 5:
this embodiment is another preferred implementation of embodiment 3, and proposes an asymmetric quantum conference key agreement system as shown in fig. 3.
In this embodiment, the two transmitting ends are consistent with embodiment 4; the receiving end comprises a first dynamic polarization controller, a second dynamic polarization controller, a first rapid optical switch, a second rapid optical switch, a beam splitter, a first detector, a second detector, a third detector and a fourth detector.
The dynamic polarization controller is used for coordinating and keeping consistent polarization of signal light, so that the signal light at two ends keeps the same polarization direction, the influence of the polarization direction on interference is reduced, and the X-base vector measurement efficiency is improved.
The first fast optical switch and the second fast optical switch are used for selecting a measurement basis vector, and since the fast optical switches are controllable, active selection of the measurement basis vector can be performed, which is different from the passive selection of the beam splitter in the first embodiment.
The beam splitter functions the same as the beam splitter in example 4.
The four detectors are also the same as in example 4.
The specific steps are the same as those of embodiment 4, however, in this embodiment, because a dynamic polarization controller is added to ensure that the signal lights at the two ends keep the same polarization direction, the influence of the polarization direction on interference is reduced, and the additional error rate is reduced, in addition, different from the uncontrollable property of the first beam splitter and the second beam splitter in embodiment 4, because the fast optical switch is controllable, the signal lights at the two ends can be coordinated to randomly enter the same basis vector measuring end to perform active selection, so that one end of the signal light enters the Z basis vector detecting end, and the other end of the signal light enters the X basis vector detecting end, which causes waste, improves the efficiency, and further improves the security code rate.
The experimental results are as follows:
to verify the technical effect of the present invention, the applicant takes the system shown in fig. 3 as an experimental system, and performs experiments on the infinite code length case and the finite code length case respectively and provides the following data for explanation.
Under the condition of infinite code length and the condition of limited code length, the experimental parameter settings are the same, and the following table shows that:
p d η d α f e d
1×10 -8 56％ 0.167 1.1 3.5％
wherein p is d Is the secret mark rate, eta, of the detector d For the detection efficiency of the detector, alpha is the light attenuation rate, f is the error correction efficiency, e d For the phase imbalance rate, the optimal parameters of other adjustable parameters are optimized by the existing algorithm.
Fig. 4 is a comparison between the scheme and the symmetric quantum conference key negotiation system proposed in patent 2020103489161 in the simulation diagram of the security code rate and the transmission distance from the first sending end to the receiving end when the channel is asymmetric and the transmission distance from the first sending end to the receiving end and the transmission distance from the second sending end to the receiving end have a difference of 50 km.
Fig. 5 is a comparison between the scheme and the symmetric quantum conference key negotiation system proposed in patent 2020103489161 in the simulation diagram of the security code rate and the transmission distance from the first sending end to the receiving end, when the channel is asymmetric, and the difference between the transmission distance from the first sending end to the receiving end and the transmission distance from the second sending end to the receiving end is 50km, considering the finite code length. In simulation experiment of limited code length, the sending code length takes N as 10 14 The correctness parameter being epsilon cor ＝1×10 -10 Combining security parameters to take epsilon sec ＝1×10 -10 The security parameter ∈ ═ epsilon sec And/26, other parameters have the same value as the infinite code length, and the adjustable parameters are optimized by an algorithm to give the optimal value. As can be seen from fig. 5, the advantage of this scheme is still evident under the limited code length.
As can be seen from fig. 4 and fig. 5, the scheme is better than the original quantum conference key agreement scheme in both the case of channel symmetry and the case of channel asymmetry, and the advantages of the scheme are also particularly obvious in the case of channel asymmetry in reality.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent should be subject to the appended claims.

Claims (8)

1. An asymmetric quantum conference key negotiation method is implemented between any two sending ends and any two receiving ends, and is characterized in that channels from the two sending ends to the receiving ends are asymmetric, and the method comprises the following steps:
(1) randomly selecting an X basis vector or a Z basis vector by a first sending end and a second sending end; under the Z basis vector, the first preparation phase of the transmitting end is random, and the light intensity is mu A Or the weak coherent light pulse of 0 is sent to a receiving end as a signal state; the second sending end prepares the phase random and the light intensity is mu B Or the weak coherent light pulse of 0 is taken as a signal state to be sent to a receiving end; under the X basis vector, the sending end is from { mu A ，v A And 0 randomly selecting one of the two as a light intensity parameter to prepare a decoy state with random phase and sending the decoy state to a receiving end, wherein the sending end II randomly selects one of the two as a { mu } light intensity parameter B ，ν B And 0, randomly selecting one as a light intensity parameter, preparing a decoy state with random phase, and sending the decoy state to a receiving end; v. of A And v B The following relation is satisfied:
Figure FDA0003784748470000011
wherein, t A Selecting light intensity mu for the transmitting end under Z basis vector A Probability of 1-t A For the sending end under the Z basis vector, the probability of selecting the light intensity 0, t B Selecting light intensity mu for the second sending end under the Z basis vector B Probability of 1-t B Selecting the probability of light intensity 0 for the second sending end under the Z basis vector;
(2) the receiving end randomly selects a Z basis vector or an X basis vector to measure; under the Z basis vector, the receiving end adopts a first detector and a second detector to respectively measure two paths of weak coherent light pulses, and when only the first detector or the second detector responds, a detection result is recorded; under X-base vector, the receiving end measures the interference light of the two paths of weak coherent light pulses by adopting a detector III and a detector IV, and when only the detector III or the detector IV responds, the detection result is recorded;
(3) two sending ends and a receiving end publish the selected basis vectors and reserve data under the condition that all three parties select the Z basis vectors so as to generate original keys of all parties; in other cases, two transmitters will announce the selected light intensity as a first transmitter sends v A Weak coherent pulse of light intensity, sending end secondary sending v B The weak coherent pulse of light intensity, and when the receiving end chooses the X basis vector, two sending ends publish the phase, then choose and match after carrying on the phase; on the premise of successful phase selection and matching, calculating gains of different light intensities and bit error rates under X basis vectors through published phase data;
(4) the method for estimating the data leakage possibility by using the decoy state comprises the following steps of based on the published data under the condition that three parties do not select all Z basis vectors:
method for estimating single photon responsivity of signal state by decoy state method
Figure FDA0003784748470000012
And single photon phase error rate
Figure FDA0003784748470000013
Figure FDA0003784748470000014
Figure FDA0003784748470000015
Figure FDA0003784748470000021
Figure FDA0003784748470000022
Wherein, Y 1 d Representing the single photon responsivity of a signal state under a d-base vector, wherein d belongs to { X, Z };
Figure FDA0003784748470000023
the first sending light intensity of the sending end under the expression d base vector is k A The weak coherent state pulse and the sending light intensity of the sending end II is k B Gain k in weak coherent pulses A ∈{μ A ，v A ，0}，k B ∈{μ B ，v B ，0}；
Figure FDA0003784748470000024
For the transmitting end, the transmitted light intensity is v A The weak coherent state pulse and the second sending light intensity of the sending end is v B Selecting the error rate after matching after passing through the phase under the condition of weak coherent state pulse;
Figure FDA0003784748470000025
for the transmitting end, a transmitting light intensity v A The weak coherent state pulse and the second sending light intensity of the sending end is v B Under the condition of weak coherent state pulse, gain after phase selection and matching is carried out;
Figure FDA0003784748470000026
is the response rate of the vacuum state under the X basis vector,
Figure FDA0003784748470000027
(5) on the premise that both the bit error rate and the data leakage possibility meet preset requirements, part of original keys are randomly selected by three parties to be published so as to carry out classical error correction, error verification and privacy amplification to obtain final keys of the three parties.
2. The asymmetric quantum conference key agreement method according to claim 1, wherein the phase post-selection matching method is:
judging whether the phases of two paths of weak coherent light pulses sent by the first sending end and the second sending end meet a judgment formula:
Figure FDA0003784748470000028
if yes, matching the phases of the two weak coherent light pulses, otherwise, mismatching the phases of the two weak coherent light pulses;
in the decision formula, r is a phase parameter, when r is 0, the detector four response represents a bit error of an X basis vector, and when r is 1, the detector three response represents a bit error of an X basis vector;
Figure FDA0003784748470000029
the phase difference theta between two weak coherent light pulses caused by reference system and phase drift A For the phase, θ, of the weak coherent light pulse transmitted by the transmitting end B The phase of the weak coherent light pulse sent by the sending end II; δ is a chosen constant parameter.
3. The asymmetric quantum conference key agreement method according to claim 2, wherein a calculation formula of a security code rate in the classical error correction process is:
Figure FDA00037847484700000210
wherein R represents a security code rate, λ EC Representing the key revealed during classical error correction, h (x) is binary shannon entropy, h (x) is-xlog 2 x-(1-x)log 2 (1-x)。
4. The asymmetric quantum conference key agreement method according to claim 1, wherein the receiving end data is generated by:
under the condition of selecting Z basis vector measurement, when a detector responds, the logic bit value of a receiving end is 1; when the detector II responds, the logic bit value of the receiving end is 0;
under the condition of selecting X basis vector measurement, when the detector responds to the X basis vector measurement, the logic bit value of the receiving end is 0; and when the detector responds four times, the logic bit value of the receiving end is 1.
5. The asymmetric quantum conference key agreement method of claim 1, wherein an average photon number of the weak coherent light pulse is less than 1.
6. The asymmetric quantum conference key agreement method of claim 1, wherein the first sending end and the second sending end send weak coherent light pulses to the receiving end through the unsecured quantum channel, respectively.
7. The asymmetric quantum conference key agreement method according to claim 1, wherein the three parties publishing data in step (3) is performed by authenticating a classical channel.
8. An asymmetric quantum conference key negotiation system comprises a first sending end, a second sending end and a receiving end, and is characterized in that channels from the two sending ends to the receiving end are asymmetric, and the first sending end, the second sending end and the receiving end adopt the method of any one of claims 1 to 7 to carry out quantum conference key negotiation.
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