CN113037474A - Asymmetric quantum conference key negotiation method and system - Google Patents

Asymmetric quantum conference key negotiation method and system Download PDF

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CN113037474A
CN113037474A CN202110226130.7A CN202110226130A CN113037474A CN 113037474 A CN113037474 A CN 113037474A CN 202110226130 A CN202110226130 A CN 202110226130A CN 113037474 A CN113037474 A CN 113037474A
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CN113037474B (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
    • H04L9/0858—Details about key distillation or coding, e.g. reconciliation, error correction, privacy amplification, polarisation coding or phase coding

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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 three-way key sharing described by the method consists 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 purpose of the invention is as follows: 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 receiving end, wherein channels between the two sending ends and the receiving end 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 muAOr 0 preparing weak coherent light pulse with random phase as signal state and sending to receiving end, and selecting light intensity mu at sending endBOr 0, preparing weak coherent light pulses with random phases as signal states and sending the weak coherent light pulses to a receiving end; under the X basis vector, a first terminal is sentRandom from muA，v A0, 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，νBSelecting light from 0 to force a decoy state with random phase to be sent to a receiving end; v isAV and vBThe following relation is satisfied:
Figure BDA0002956298760000021
wherein, tASelecting light intensity mu for a transmitting end under Z basis vectorAProbability of 1-tASelecting light intensity 0, t for the transmitting end under Z basis vectorBSelecting light intensity mu for the transmitting end two under the Z basis vectorBProbability of 1-tBSelecting 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 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 vAWeak coherent pulse of light intensity, sending end secondary sending vBThe 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 driftAFor the phase, θ, of the weak coherent light pulse transmitted by the transmitting endB
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 responsivity 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, Y1 dRepresenting the 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 kAThe weak coherent state pulse and the sending light intensity of the sending end II is kBGain k in weak coherent pulsesA∈{μA,vA,0}，kB∈{μB,vB,0}；
Figure BDA0002956298760000038
For the transmitting end, a transmitting light intensity vAThe weak coherent state pulse and the sending light intensity of the sending end two is nuBSelecting the error rate after matching after the phase is carried out under the condition of weak coherent state pulse;
Figure BDA0002956298760000039
sending light intensity v for sending endAThe weak coherent state pulse and the sending light intensity of the sending end two is nuBIn the case of weak coherent pulsesUnder the condition, the gain after phase selection matching is carried out;
Figure BDA00029562987600000310
is the response rate of the vacuum state under the X basis vector,
Figure BDA00029562987600000311
optionally, a calculation formula of the security code rate in the classical error correction process is as follows:
Figure BDA00029562987600000312
wherein R represents a security code rate, λECRepresenting the key revealed during classical error correction, h (x) is binary shannon entropy, h (x) is-xlog2x-(1-x)log2(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 content of the first and second substances,
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 a single photon to measure the expected value of the response number under the Z basis vector,
Figure BDA00029562987600000413
hair with indicationOne transmitting end transmits a single photon, the other transmitting end transmits an expected value of response number after the vacuum state is measured under X basis vector and phase post-selection,
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 kAThe second sending end sends light intensity kBAnd 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 vAThe second sending end sends light intensity vBThe 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;
and (4) calculating the security code length:
Figure BDA00029562987600000512
wherein λ isECRepresenting keys revealed during classical error correction, h (x) -xlog2x-(1-x)log2(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 case that the channel is asymmetric and the transmission distance between the first sending end and the receiving end differs from the transmission distance between the second sending end and the receiving end by 50km according to the fourth embodiment of the present invention in the simulation diagram of the security code rate and the transmission distance between the first sending end and the receiving end.
Fig. 5 is a comparison between the scheme and the symmetric quantum conference key negotiation system proposed in patent 2020103489161 in the case that 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 the simulation diagram of the security code rate and the transmission distance from the first sending end to the receiving end.
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 various modifications may be made in the structure, steps, and sequence set forth 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 muAOr 0 preparing weak coherent light pulse with random phase as signal state and sending to receiving end, and selecting light intensity mu at sending endBOr 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 A0, 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，νBSelecting light from 0 to force a decoy state with random phase to be sent to a receiving end; v. ofAAnd vBThe following relation is satisfied:
Figure BDA0002956298760000061
wherein, tASelecting light intensity mu for a transmitting end under Z basis vectorAProbability of 1-tASelecting light intensity 0, t for the transmitting end under Z basis vectorBSelecting light intensity mu for the transmitting end two under the Z basis vectorBProbability of 1-tBSelecting 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 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 vAWeak coherent pulse of light intensity, sending end secondary sending vBThe 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.
Specifically, in step (1), the probability of selecting the Z basis vector or the X basis vector at the sending end is respectively
Figure BDA0002956298760000071
And
Figure BDA0002956298760000072
at the Z basis vector, the transmitted light intensity is muAOr 0 is tAAnd 1-tAWith a transmitted light intensity of { mu ] at the basis of the X vectors corresponding to bit values 1 and 0A，vAProbability of 0 is respectively
Figure BDA0002956298760000073
The weak coherent pulse expression of random phase generated at the sending end is
Figure BDA0002956298760000074
kA∈{μA,vA0 }; 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 muBOr 0 is tBAnd 1-tBWith a transmitted light intensity of { mu ] at the basis of the X vectors corresponding to bit values 0 and 1B，vBProbability of 0 is respectively
Figure BDA0002956298760000077
The weak coherent pulse expression of random phase generated by the second sending end is
Figure BDA0002956298760000078
kB∈{μB,vB0 }; wherein theta isAAnd thetaBIndicating its phase.
Specifically, in the step (3), the data publishing is completed through an 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 so, twoThe phases of the two paths of weak coherent light pulses are matched, otherwise, the phases of the two paths of 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 driftAFor the phase, θ, of the weak coherent light pulse transmitted by the transmitting endBThe 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 responsivity of signal state by decoy state method
Figure BDA0002956298760000083
And single photon phase error rate
Figure BDA0002956298760000084
The calculation formula of the single photon responsivity is as follows:
Figure BDA0002956298760000085
Figure BDA0002956298760000086
Figure BDA0002956298760000087
wherein, Y1 dRepresenting the single photon responsivity of the 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 kAThe weak coherent state pulse and the sending light intensity of the sending end II is kBGain k in weak coherent pulsesA∈{μA,vA,0}，kB∈{μB,vB,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 endAThe weak coherent state pulse and the sending light intensity of the sending end two is nuBSelecting 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 endAThe weak coherent state pulse and the sending light intensity of the sending end two is nuBUnder 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, λECRepresenting the key revealed during classical error correction, h (x) is binary shannon entropy, h (x) is-xlog2x-(1-x)log2(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
indicating that the transmitting end has a transmitting light intensity of kAThe second sending end sends light intensity kBAnd the receiving end selects the total number of pulses of the Z or X basis vectors,
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 endAThe second sending end sends light intensity vBThe total number of the weak coherent pulses after phase selection,
Figure BDA00029562987600001016
is the corresponding error number. 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 the secret keys are randomly selected for classical error correction, error verification and privacy amplification to obtain a final secret key, and the formula of the safe code length is as follows:
Figure BDA00029562987600001018
wherein λECRepresenting keys revealed during classical error correction, h (x) -xlog2x-(1-x)log2And (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; further decomposition into a plurality of modules is possible according to the function, 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 is a preferred implementation manner of embodiment 3, and proposes an asymmetric quantum conference key agreement system as shown in fig. 2.
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 lasers that are stable in intensity, phase, frequency, and polarization.
The intensity modulator chops the 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 the 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 from the first sending end randomly enter the first detector or the third beam splitter through the first beam splitter, and signal light photons from the second sending end randomly enter the second detector or the third beam splitter through the second beam splitter. And the first detector and the second detector measure the Z basis vector, the signal light entering the third beam splitter from two ends interferes, and then the third detector and the fourth detector measure the X basis vector as a whole. 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, the post-processing module of the receiving end performs post-phase compensation on the obtained detection result, and interacts with the post-processing module of 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 specific parameters are shown in the following table:
pd ηd α f ed
1×10-8 56％ 0.167 1.1 3.5％
wherein p isdIs the secret mark rate, eta, of the detectordFor the detection efficiency of the detector, alpha is the light attenuation rate, f is the error correction efficiency, edFor 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 shows that when the channel is asymmetric, 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 5Under the condition of considering limited code length at 0 kilometer, the scheme is compared with a symmetric quantum conference key negotiation system provided by the patent 2020103489161 in a simulation graph of the security code rate and the transmission distance from the sending end to the receiving end. In simulation experiment of limited code length, the sending code length takes N as 1014The correctness parameter being epsiloncor＝1×10-10Combining security parameters to take epsilonsec＝1×10-10The security parameter ∈ ═ epsilonsecAnd/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 shall be subject to the appended claims.

Claims (10)

1. An asymmetric quantum conference key negotiation method is implemented between any two sending ends and any receiving end, 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 the first sending end and the second sending end; under the Z basis vector, the sending end randomly selectsLight intensity muAOr 0 preparing weak coherent light pulse with random phase as signal state and sending to receiving end, and selecting light intensity mu at sending endBOr 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，νA0, 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，νBSelecting light from 0 to force a decoy state with random phase to be sent to a receiving end; v isAV and vBThe following relation is satisfied:
Figure FDA0002956298750000011
wherein, tASelecting light intensity mu for a transmitting end under Z basis vectorAProbability of 1-tASelecting light intensity 0, t for the transmitting end under Z basis vectorBSelecting light intensity mu for the transmitting end two under the Z basis vectorBProbability of 1-tBSelecting 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 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; under other conditions, the two sending ends publish the selected light intensity, and when the sending end sends vAWeak coherent pulse of light intensity, v sent by sending endBThe 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 post-selection matching, the increase of different light intensities is calculated through published phase dataThe bit error rate under the X basis vector is benefited;
(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.
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 FDA0002956298750000021
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 FDA0002956298750000022
for phase differences, theta, between two weak coherent light pulses, due to reference frame and phase driftAFor the phase, θ, of the weak coherent light pulse transmitted by the transmitting endBThe 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 in the case of an infinite code length, the specific step of estimating the possibility of data leakage in step (4) comprises:
method for estimating single photon responsivity of signal state by decoy state method
Figure FDA0002956298750000023
And single photon phase error rate
Figure FDA0002956298750000024
Figure FDA0002956298750000025
Figure FDA0002956298750000026
Figure FDA0002956298750000027
Figure FDA0002956298750000028
Wherein, Y1 dRepresenting the single photon responsivity of a signal state under a d-base vector, wherein d belongs to { X, Z };
Figure FDA0002956298750000029
the transmitting end under the d-base vector has the transmitting light intensity of kAThe weak coherent state pulse and the sending light intensity of the sending end II is kBGain k in weak coherent pulsesA∈{μA，νA，0}，kB∈{μB，νB，0}；
Figure FDA00029562987500000210
Sending light intensity v for sending endAThe weak coherent state pulse and the sending light intensity of the sending end two is nuBIn the case of weak coherent state pulsesThen, selecting the error rate after matching after the phase;
Figure FDA00029562987500000211
sending light intensity v for sending endAThe weak coherent state pulse and the sending light intensity of the sending end two is nuBUnder the condition of weak coherent state pulse, gain after phase selection and matching is carried out;
Figure FDA00029562987500000212
is the response rate of the vacuum state under the X basis vector,
Figure FDA00029562987500000213
4. the asymmetric quantum conference key agreement method according to claim 2, wherein the calculation formula of the security code rate in the classical error correction process is:
Figure FDA00029562987500000214
wherein R represents a security code rate, λECRepresenting the key revealed during classical error correction, h (x) is binary shannon entropy, h (x) is-xlog2x-(1-x)log2(1-x)。
5. The asymmetric quantum conference key agreement method according to claim 2, wherein in the case of a finite code length, the specific step of estimating the possibility of data leakage in step (4) comprises:
method for estimating vacuum state response number of signal state by using decoy state method
Figure FDA0002956298750000031
Number of single photon responses
Figure FDA0002956298750000032
And single photon phase error rate
Figure FDA0002956298750000033
Figure FDA0002956298750000034
Figure FDA0002956298750000035
Figure FDA0002956298750000036
Figure FDA0002956298750000037
Figure FDA0002956298750000038
Figure FDA0002956298750000039
Figure FDA00029562987500000310
Figure FDA00029562987500000311
Figure FDA00029562987500000312
Wherein the content of the first and second substances,
Figure FDA00029562987500000313
the expected value of the number of responses in the vacuum state,
Figure FDA00029562987500000314
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 FDA00029562987500000315
indicating that the first sending end sends a vacuum state, the second sending end sends a single photon to measure the expected value of the response number under the Z basis vector,
Figure FDA0002956298750000041
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 FDA0002956298750000042
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 FDA0002956298750000043
indicating that the transmitting end has a transmitting light intensity of kAThe second sending end sends light intensity kBAnd the receiving end selects the total number of pulses of the Z or X basis vectors,
Figure FDA0002956298750000044
respectively the upper limit and the lower limit of the expected value of the corresponding response number,
Figure FDA0002956298750000045
respectively represent
Figure FDA0002956298750000046
The lower limit of (a) is,
Figure FDA0002956298750000047
Figure FDA0002956298750000048
respectively represent
Figure FDA0002956298750000049
The lower limit of (d);
Figure FDA00029562987500000410
representing single photon phase error rate in signal state
Figure FDA00029562987500000411
The upper limit of (a) is,
Figure FDA00029562987500000412
sending light intensity v for sending endAThe second sending end sends light intensity vBThe total number of the weak coherent pulses after phase selection,
Figure FDA00029562987500000413
for the number of errors to be addressed,
Figure FDA00029562987500000414
the statistical fluctuation value of the random sampling without the return is obtained;
and (4) calculating the security code length:
Figure FDA00029562987500000415
wherein λ isECRepresenting keys revealed during classical error correction, h (x) -xlog2x-(1-x)log2(1-x) is binary incenseThe agricultural entropy is the sum of the agricultural entropy,
Figure FDA00029562987500000416
respectively, the code length leaked in the error verification and privacy amplification processes.
6. 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 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.
7. 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.
8. 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.
9. 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.
10. An asymmetric quantum conference key negotiation system, comprising a first sending end, a second sending end and a receiving end, characterized in that the 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 9 to perform quantum conference key negotiation.
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