CN113037475A - Quantum secret sharing method and system under asymmetric channel - Google Patents
Quantum secret sharing method and system under asymmetric channel Download PDFInfo
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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
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- 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
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- 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
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- 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
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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
- H04L9/0852—Quantum cryptography
- H04L9/0858—Details about key distillation or coding, e.g. reconciliation, error correction, privacy amplification, polarisation coding or phase coding
Abstract
The invention provides a quantum secret sharing method and system under an asymmetric channel. On the other hand, the invention provides a modeling method of an asymmetric channel and a new scheme for calculating the total error rate of a system based on the problem that the distances between a plurality of senders and a credible detector are respectively different, namely the transmission rates of channels from the senders to the detector are different. Compared with a symmetrical channel scheme, the method has higher practicability, and obtains higher safe code rate and longer transmission distance.
Description
Technical Field
The invention relates to the field of quantum communication, in particular to a quantum secret sharing method and system under an asymmetric channel
Background
The cipher is an important secret means for information transmission between two communication parties according to the agreed rule. Cryptography in the modern sense is mainly to ensure the security of cryptographic communication systems with computational complexity. However, such modern cryptographic algorithms based on computational complexity cannot theoretically provide unconditional security of cryptographic systems. This is mainly because the computational complexity is limited by the computational speed, computing power, network construction and communication techniques of the computer, and the progress of these techniques will cause the security of the corresponding cryptographic algorithm to be challenged.
As an emerging interdisciplinary formed by the combination of classical cryptography and quantum mechanics, the security of quantum cryptography is based on quantum theory rather than computational complexity. Currently, research on Quantum cryptography mainly focuses on three fields of Quantum Key Distribution (QKD), Quantum Secret Sharing (QSS), and Quantum Secure Direct Communication (QSDC). Secret sharing is an important branch of cryptography, and the main task of the secret sharing is to divide a secret message and distribute the divided sub-secrets to a plurality of legitimate users, who can recover the original secret by combining their sub-secrets. While any single user or unauthorized user cannot recover the original secret, quantum secret sharing mainly solves the problem of how to transfer information by establishing a quantum information channel and ensures the absolute safety and efficiency of the transferred information.
The theory of three entangled states (GHZ) proposed by Hillery, Buzek and Berthaume in 1999 firstly provides the concept of Quantum Secret Sharing (QSS), and theoretically overcomes the defect of the classical information channel in the traditional secret sharing, thereby raising the enthusiasm of QSS research. However, the code rate is low, and the prepared GHZ state is difficult to be put into practical use.
To solve the above problem, patent application No. 202010957892.X discloses a quantum secret sharing method based on differential phase shift, in which weak coherent light with an average photon number less than 1, which is easy to prepare, is used, and a code rate is improved from 80km to 600 km.
However, this scheme requires that the transmission channels are symmetrical and the intensity of the transmitted light is the same, and the symmetry of the transmission channels means that the transmission rates of the channels are the same. The channel transmission rate is related to the distance from the sender to the detector, provided that the detector is equally efficient. That is, the scheme requires that the distances from a plurality of senders to a detector are consistent, in this case, the senders and the detector perform symmetric communication, and the scheme is difficult to be applied to actual lives with different distances between the senders and the credible detector, and the practical effect is poor.
Disclosure of Invention
The purpose of the invention is as follows: based on the defect of the quantum secret sharing scheme in the patent 202010957892.X, the invention provides a quantum secret sharing method and system under an asymmetric channel, which not only reduces photon loss, but also considers the problem that the distances between a plurality of senders and a credible detector are different respectively in a real scene, and has the advantages of simple experimental device and simple and convenient operation.
The technical scheme is as follows: in order to achieve the purpose, the invention provides the following technical scheme:
a quantum secret sharing method under an asymmetric channel is implemented between any two sending ends and any two receiving ends participating in secret sharing, and comprises the following steps:
(1) the first and second sending ends respectively use light intensity mua、μbWeak coherent light pulse signals with the period of 2T and the average photon number less than 1 are prepared, phase coding of 0/pi is carried out on the prepared light pulse signals respectively at random according to 50% of possibility to obtain signal light, the signal light prepared by the first sending end is A, and the signal light prepared by the second sending end is B;
(2) the first sending end and the second sending end send the prepared signal light to the receiving end through an unsafe quantum channel, and the time of the signal light B reaching the receiving end lags behind the time of the signal light A by a half period T;
(3) the receiving end is provided with a Mach Zehnder interferometer and two detectors; the signal light enters the Mach-Zehnder interferometer and is divided into two beams which are respectively transmitted through the upper arm and the lower arm of the Mach-Zehnder interferometer, and the signal light component transmitted through the upper arm is introduced into a delay T, so that the component of the signal light A/B transmitted through the upper arm is interfered with the component of the signal light B/A transmitted through the lower arm; the receiving end respectively detects interference results of two output ends of the Mach-Zehnder interferometer through the first detector and the second detector;
(4) the receiving end publishes the response time, and the first sending end and the second sending end respectively reserve phase coding results of the response time to obtain an original key of the local end; the receiving end encodes the response data to obtain an original key of the receiving end;
(5) the receiving end calculates all gains for code forming based on the response data and the sending data amount of the two sending ends; then the receiving end randomly selects a plurality of response moments, the first sending end and the second sending end of the command signal alternately transmit the logic bits at the corresponding moments in the original secret keys to the receiving end through the public channel, and the receiving end calculates the total error rate of the system according to the logic bits at the corresponding moments in the original secret keys of the receiving end and judges whether the preset requirements are met;
(6) and (5) on the premise that the total error rate of the system calculated in the step (5) meets the preset requirement, performing classical error correction, error verification and privacy amplification on the residual original keys by the first sending end, the second sending end and the receiving end, and extracting the keys for quantum secret sharing by the first sending end and the second sending end respectively.
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, in step (4), the specific step of encoding the response data by the receiving end is:
in case of only one detector response:
when the occurrence time of the interference event is T-2N T, if the relative phase of the signal light A and the signal light B is 0, the first detector responds, and the logic bit of the receiving end is 0; if the relative phase of the signal light A and the signal light B is pi, the second detector responds, and the logic bit of the receiving end is 1;
when the occurrence time of the interference event is T ═ 2N +1 × T, if the relative phase of the signal light a and the signal light B is 0, the second detector responds, and the logic bit of the receiving end is 0; if the relative phase of the signal light A and the signal light B is pi, the first detector responds, and the logic bit of the receiving end is 1;
when two detectors respond simultaneously, the receiving end randomly selects 0 or 1 for encoding with a 50% probability.
Optionally, the gains for all coding are:
Qμ＝Q1(1-Q2)+Q2(1-Q1)+Q1Q2＝Q1+Q2-Q1Q2
Q1and Q2The response probabilities of the two detectors at the receiving end are respectively.
Optionally, the calculation formula of the total error rate of the system is as follows:
wherein, muaAnd mubThe intensity of the signal light, D, respectively prepared by the first and second transmitting terminals1And D2The intensities of the interference light detected by the two detectors at the receiving end are respectively, and e is a constant; e.g. of the typedRepresenting the basis vector calibration error rate, p, of the detectordRepresenting the dark count rate, eta, of the detectoraAnd ηbRespectively indicating the channel transmission rate from the sending end one to the receiving end and the channel transmission rate from the sending end two to the receiving end.
Optionally, when the channel loss from the first sending end to the receiving end is larger than the channel loss from the second sending end to the receiving end, the receiving end adds extra loss to the channel from the second sending end to the receiving end, so that the channel transmission efficiency from the first sending end to the receiving end is the same as the channel transmission efficiency from the second sending end to the receiving end, i.e. η is obtaineda＝ηbη', the total error rate of the system is calculated as:
the invention also provides a quantum secret sharing system under the asymmetric channel, which comprises any two sending ends and receiving ends which participate in secret sharing; the two sending ends and the receiving end adopt the method to carry out quantum secret sharing.
Further, the transmitting end comprises a signal light transmitting module, a signal light intensity modulation module and a signal light phase modulation module; the signal light sending module is used for generating continuous laser with consistent and continuous light intensity, frequency, phase and polarization maintaining time; the signal light intensity modulation module performs chopping on continuous laser to obtain signal light pulses, and then performs weak light modulation on the signal light pulses to obtain weak coherent light pulses with the average photon number smaller than 1; the signal light phase modulation module carries out phase coding with the phase of 0 or pi on the weak coherent light pulse to obtain required signal light;
the receiving end comprises a first beam splitter, a second beam splitter, a first detector and a second detector, the first beam splitter and the second beam splitter form an unbalanced Mach Zehnder device and are used for interfering two beams of signal light sent by a first sending end and a second sending end, and the first detector and the second detector are respectively used for measuring interference results.
Furthermore, the two sending ends send the signal light simultaneously, and the channel from the sending end two to the receiving end has a section of delay line more than the path from the sending end one to the receiving end, so as to realize that the time when the signal light B reaches the receiving end lags behind the signal light A by half a period T.
Further, the receiving end further comprises a first polarization controller and a second polarization controller, and the first polarization controller and the second polarization controller are respectively used for adjusting the signal light A and the signal light B to the same polarization angle and then sending the signal light A and the signal light B to the first beam splitter.
Has the advantages that: compared with the prior art, the invention has the following advantages:
1. the coding mode is improved, the device is simplified, and the complexity of system operation is reduced.
2. The invention considers the problem that the distances between a plurality of senders and the credible detector are respectively different, and has more practicability compared with the symmetrical channel scheme in the prior art that the distances between the senders and the credible detector are the same; by providing a new modeling method for the asymmetric channel, higher security code rate and longer transmission distance are obtained.
Drawings
Fig. 1 is a schematic structural diagram of a quantum secret sharing system based on differential phase shift under an asymmetric channel according to embodiment 1;
fig. 2 is a schematic structural diagram of a signal light phase modulation module according to embodiment 1;
fig. 3 is a schematic structural diagram of a quantum secret sharing system based on differential phase shift under an asymmetric channel according to embodiment 2;
fig. 4 is a schematic structural diagram of a quantum secret sharing system based on differential phase shift under an asymmetric channel according to embodiment 3;
FIG. 5 shows the distance l from the transmitting end two to the receiving end in embodiment 1bDistance l from the sending end to the receiving endaUnder the condition of 12 km difference, obtaining a safe code rate comparison graph by adopting a channel model provided by the first calculation method and an original symmetrical channel model;
FIG. 6 shows the distance l from the transmitting end two to the receiving end in embodiment 1bDistance l from the sending end to the receiving endaAnd under the condition of 12 km difference, obtaining a safety code rate comparison graph by adopting the channel model provided by the second calculation method and the original symmetrical channel model.
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.
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:
the embodiment provides a quantum secret sharing system based on differential phase shift under an asymmetric channel, which comprises a first sending end, a second sending end and a receiving end. As shown in fig. 1. The first sending end and the second sending end both comprise a signal light sending module, a signal light intensity modulation module and a signal light phase modulation module. And the corresponding modules in the first sending end and the second sending end have the same function. The receiving end comprises a signal light beam splitting module and a signal light detection module. And the first sending end, the second sending end and the receiving end are respectively provided with a post-processing module which has the functions of carrying out subsequent classical error correction, error verification and privacy amplification processing so as to finish the sharing of the secret key. The functions realized by the modules are as follows:
the function of the signal light sending module is to send continuous laser by using a continuous laser, and the light intensity, frequency, phase and polarization of the laser should be kept consistent and continuous in time.
The signal light intensity modulation module has the function of chopping continuous laser with certain intensity which leaves the signal light phase modulation module and reaches the signal light intensity modulation module to obtain signal light pulse. The light can be modulated in weak light to generate weak coherent light pulses with average photon number less than 1, and the specific device can use an intensity modulator and a signal attenuator.
The signal light phase modulation module has a function of performing phase coding with a phase of 0 or pi on a signal light pulse which leaves the signal light intensity modulation module and reaches the signal light phase modulation module, so that a required pulse sequence signal light A and a required pulse sequence signal light B are obtained, and a phase modulator can be used for specific equipment.
The apparatus used for the signal light splitting module comprises a first splitter and a second splitter, both of which constitute the unbalanced mach zehnder, the detailed structure of which is shown in fig. 2. The first beam splitter has the function of splitting the signal light A leaving the signal light phase modulation module into signal light A1 and signal light A2, and splitting the signal light B into signal light B1 and signal light B2; as can be seen from fig. 2, the signal light a1 passing through the long arm and the signal light B1 are relaxed by a half period T (by the second delay line shown in the figure) compared with the signal light a2 and the signal light B2 passing through the short arm. The second beam splitter has a function of splitting the signal light a1, the signal light a2, the signal light B1 and the signal light B2 into the signal light a11, the signal light a12, the signal light a21, the signal light a22, the signal light B11, the signal light B12, the signal light B21 and the signal light B22. Wherein the signal light a11, the signal light a21, the signal light B11, and the signal light B21 reach the first detector, and the signal light a12, the signal light a22, the signal light B12, and the signal light B22 reach the second detector. The signal light B12 and the signal light a21 have an incidental phase of pi due to the beam splitter property, and the remaining signal light has an incidental phase of 0.
The signal light detection module comprises a first detector and a second detector. When the signal light transmission time is an even number of cycle times (T is 2N × T), the signal light a1 and the signal light B2 interfere with each other, the first detector responds when the relative phase of the signal light a and the signal light B is 0, and the second detector responds when the relative phase of the signal light a and the signal light B is pi. When the signal light transmission time is an odd number of times of the cycle (T ═ 2N +1) × T), the signal light a2 and the signal light B1 interfere with each other, the second detector responds when the relative phase of the signal light a and the signal light B is 0, and the first detector responds when the relative phase of the signal light a and the signal light B is pi. In order to unify the above detector response results, let the signal light sending time be an odd number of cycle times (T ═ 2N-1) × T), and the first (second) detector response corresponds to logic bit 0 (pi); when the signal light transmission time is an even number of cycle times (T2N × T), the first (second) detector responds to the corresponding logical bit pi (0).
The embodiment also provides a quantum secret sharing method based on differential phase shift under the asymmetric channel, which is realized by the system, and the method comprises the following specific steps:
step 1: the signal light sending modules of the sending end A and the sending end B independently send signal light A and signal light B at the same period 2T by using continuous lasers at the same time, and then chopping continuous lasers with certain intensity, which leave the signal light sending modules and reach the signal light intensity modulation module, by using the intensity modulator to obtain signal light pulses. Then uses signal attenuator to make weak light modulation to make it produce weak coherent light pulse whose average photon number is less than 1, and its light intensity is respectively set as mua,μbI.e. has mua＜1，μb＜1。
After the signal light a and the signal light B reach the signal light phase modulation module, the phase modulator randomly performs phase encoding of 0 (pi) on the optical pulse signal with a probability of 50% (50%), wherein the phase 0 corresponds to a logic bit 0, and the phase pi corresponds to a logic bit 1. The signal light B is then delayed by a time T by a delay line so as to interfere with the signal light a at the receiving end C.
Step 2: when two weak coherent light pulses with the average photon number less than 1 reach a signal receiving end C through an unsafe quantum channel, the weak coherent light pulses enter a signal light beam splitting module and interfere at an unequal-arm Mach-Zehnder interferometer formed by two beam splitters. After passing through the signal light beam splitting module, the signal light enters the signal light detection module, and the two detectors can perform detection response on the interference result. When there is no detector response, no encoding is performed. When only one detector has response, the coding mode is as follows:
when the occurrence time of the interference event is T2N T, if the relative phase of the signal light A and the signal light B is 0, the first detector responds; if the relative phase of the signal light A and the signal light B is pi, the second detector responds;
when the occurrence time of the interference event is T ═ 2N +1 × T, if the relative phase of the signal light a and the signal light B is 0, the second detector responds; the first detector responds if the relative phase of the signal light a and the signal light B is pi.
In order to unify the response results of the detectors, the following method is adopted to map the detection result of the receiving end into a logic bit, specifically:
the interference event occurs at T2N T, the first detector responds, and the receiving end corresponds to a logic bit 0;
the interference event occurs at T2N T, the second detector responds, and the receiving end corresponds to a logic bit 1;
the interference event occurs at T ═ 2N +1 × T, the first detector responds, and the receiving end corresponds to logic bit 1;
the interference event occurs at T ═ 2N +1 × T, the second detector responds, and the receiving end corresponds to logic bit 0;
wherein N is a positive integer.
In summary, the interference event occurs at T ═ 2N × T and the first detector responds, and the interference event occurs at T ═ 2N +1 × T and the second detector responds, the logical bit value at the receiving end is 0, and the phase difference between the corresponding signal light a and the corresponding signal light B is 0;
on the contrary, the interference event occurs at T ═ 2N × T and the second detector responds, and the interference event occurs at T ═ 2N +1 × T and the first detector responds, the logical bit value at the receiving end is 1, and the phase difference between the corresponding signal light a and the corresponding signal light B is pi.
When two detectors respond simultaneously, the interference result is unknown, so the receiving end randomly selects 0 or 1 for encoding with 50% (50%) probability. And obtaining the original key of the receiving end by the coding mode.
And step 3: the signal light detection module publishes response time, and the first sending end and the second sending end can correspond to the phase coding result in the signal light phase modulation module according to the published result, so that sub-keys are respectively generated for subsequent secret sharing.
And 4, step 4: after the signal light detection module finishes counting calculation, the receiving end counts the number and the sending data amount of the first sending end and the second sending end calculates all gains for code forming. And then the receiving end randomly selects a plurality of response moments, the first sending end and the second sending end of the command signal alternately transmit the logic bit value of the sub-key corresponding to the selected response moments to the receiving end through the public channel, and the receiving end records the detection result and the coding logic bit value of the receiving end at the response moments in step 2 and then combines the logic bits of the first sending end and the second sending end to calculate the total error rate of the system.
Specifically, two asymmetric channel modeling approaches are provided in this step.
The first method is as follows:
in order to solve the problem of the asymmetric channel, a modeling mode different from that of the symmetric channel is adopted for simulation calculation. Setting the distances between a first sending end and a second sending end and a receiving end as la、la. It can be known that the transmission rates of the first and second channels at the transmitting end are respectively:
where α is the attenuation ratio of the optical fiber, ηdIs the detection efficiency of the detector.
The light intensities received by the first detector and the second detector after passing through the second beam splitter are respectively as follows:
wherein, mua、μbThe light intensity of the signal light prepared by the first sending end and the second sending end is respectively.
The probabilities of the first and second detectors responding are respectively:
the total gain for all coding is:
Qμ＝Q1(1-Q2)+Q2(1-Q1)+Q1Q2＝Q1+Q2-Q1Q2
the error rate can be obtained by the following formula:
in summary, the gain formula is given by
Total error rate of the system is
The second method comprises the following steps:
using the same illuminant parameter, we assume l without loss of generality in case of channel asymmetryb＝la+50. By
From this, η at this time is knowna＞ηb. In this case, the channel loss from the first sending end to the receiving end is larger than the channel loss from the second sending end to the receiving end, and in order to overcome the difficulty in the original modeling method caused by the difference of the channel losses, the modeling method in the first method is still adopted. Different from the first calculation method, the receiving end adds extra to the channel from the first sending end to the receiving endSo that the channel from the transmitting end to the receiving end and the channel from the transmitting end to the receiving end are both etabI.e. etaa＝ηbEta'. The total error rate of the system is calculated as follows:
the light intensities received by the first detector and the second detector after passing through the second beam splitter are respectively as follows:
the probabilities of the first and second detectors responding are respectively:
the total system gain is:
Qμ＝Q1(1-Q2)+Q2(1-Q1)+Q1Q2＝Q1+Q2-Q1Q2
the error rate can be obtained by the following formula:
wherein edIndicating the basis vector calibration error rate of the detector.
In summary, the gain formula is given by
The total error rate of the system is:
and 5: the first sending end, the second sending end and the receiving end carry out classical error correction, error verification and privacy amplification processing on the residual original secret keys, the first sending end and the second sending end respectively extract secret keys for quantum secret sharing, and secret sharing of the receiving end can be achieved according to the respective secret keys under the condition of resisting independent attacks.
To verify the technical effect of the present embodiment, the following description is provided with specific experimental results.
The parameters used in the experiment are first given:
parameter table for experiment
Wherein p isdIs the dark count rate of the detector, feIs the error correction efficiency, alpha is the fiber attenuation ratio, etadIs the detection efficiency of the detector, edIs the basis vector calibration error rate of the detector.
Then, a code rate calculation formula is given:
Rdps＝Qμ[1-(1-2μmax)log2(Pc0)-feh(Eμ)]
wherein, Pc0Maximum value of collision probability h (E) for the attacker to carry out entanglement attackμ) Is the Shnnon entropy, and the calculation formulas are respectively as follows:
h(x)＝-xlog2(x)-(1-x)log2(1-x)
μmax＝max(μa，μb)
when l isb＝la+50, the rate of the security code and the transmission distance obtained by the first method are as shown in fig. 5, which is a comparison graph of the first method and a symmetric protocol, wherein the symmetric protocol refers to the same source parameters and asymmetric parameters. The safe bit rate and transmission distance obtained by the second method are shown in fig. 6, which is a comparison graph of the second calculation method and the symmetric channel. It can be known that the two asymmetric channel modeling schemes proposed in this embodiment have higher code rate and longer transmission distance than the original symmetric channel scheme.
Some preferred embodiments are also presented below, it should be noted that not all of the possible solutions of the embodiments are presented, and if the embodiments are only combinations of the technical features listed in the examples, the embodiments still fall within the scope of the present invention.
Example 2:
the present embodiment proposes a quantum secret sharing system under an asymmetric channel, and the structure of the quantum secret sharing system is shown in fig. 3. The whole system comprises a first sending end, a second sending end and a receiving end.
The transmitting end respectively comprises a continuous laser, an intensity modulator, a signal attenuator and a phase modulator which are sequentially connected, and the functions of the transmitting end respectively correspond to the functions of the signal light transmitting module, the signal light intensity modulation module and the signal light phase modulation module.
The receiving end comprises a first beam splitter, a second beam splitter, a first detector and a second detector.
The method for realizing quantum secret sharing under the asymmetric channel by the system comprises the following specific steps:
step 1: the continuous laser at the transmitting end transmits continuous laser, and the light intensity, frequency, phase and polarization of the laser should keep consistent and continuous in time. Then the intensity modulator chops the continuous laser with certain intensity to obtain signal light pulse. Then, the weak light modulation is carried out by a signal attenuator, so that weak coherent light pulses with the average photon number less than 1 are generated. After the weak coherent light pulse reaches the signal light phase modulation module, the phase modulator randomly performs 0 (pi) phase coding on the light pulse signal with 50% (50%) possibility, wherein the phase 0 corresponds to a logic bit 0, and the phase pi corresponds to a logic bit 1, so as to obtain signal light. The signal light prepared by the first sending end is the signal light A, and the signal light prepared by the second sending end is the signal light B. The signal light B is then delayed by a time T by means of a first delay line.
Step 2: the signal light A and the signal light B enter the signal light splitting module and interfere with each other at an unequal arm Mach Zehnder interferometer formed by two beam splitters. And the receiving end adopts the first detector and the second detector to detect the interference result. When there is no detector response, no encoding is performed. When the first detector responds, the corresponding logic bit value is 0, and the relative phase difference of the two beams of signal light is 0; when the second detector responds, the corresponding logic bit value is 1, and the relative phase difference of the two signal lights is pi. When two detectors respond simultaneously, the interference result is unknown, so the receiving end randomly selects 0 or 1 for encoding with 50% (50%) probability. And obtaining the original key through the coding mode.
And step 3: the receiving end publishes the response time, and the sending end A and the sending end B can correspond to the phase coding result in the signal light phase modulation module according to the published result, so that sub-keys are respectively generated for subsequent secret sharing.
And 4, step 4: after the signal light detection module completes counting calculation, the receiving end can calculate all gains for coding based on the counting and the sending data amount of the sending end I and the sending end II. And then the receiving end randomly selects a plurality of response moments, the first sending end and the second sending end of the command signal alternately transmit the logic bit value of the sub-key corresponding to the selected response moments to the receiving end through a public channel, and the receiving end can calculate the total error rate of the system by combining the logic bits of the first sending end and the second sending end after the receiving end combines the self detection result and the coded logic bit value of the response moments recorded in the step 2.
And 5: the first sending end, the second sending end and the receiving end carry out classical error correction, error verification and privacy amplification processing on the residual original secret keys, the first sending end and the second sending end respectively extract secret keys for quantum secret sharing, and secret sharing of the receiving end can be achieved according to the respective secret keys under the condition of resisting independent attacks.
Example 3:
in this embodiment, the structural improvement of the system proposed in embodiment 2 is specifically as follows:
before the signal light A and the signal light B enter the signal light beam splitting module, a group of polarization controllers are added to form a signal light polarization modulation module, so that the polarization directions of the two weak coherent light pulses are adjusted to be consistent. As shown in fig. 4, a signal light polarization modulation module is added in the receiving end, and the function of the signal light polarization modulation module is to adjust the polarization angles of the signal light a and the signal light B which leave the signal light phase modulation module and reach the signal light polarization adjustment module to be the same, so as to ensure that the subsequent signal light interference effect is optimal, and a first polarizer and a second polarizer are used in the specific device.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (9)
1. A quantum secret sharing method under an asymmetric channel, implemented between any two transmitting ends and receiving ends participating in secret sharing, comprising the steps of:
(1) the first and second sending ends respectively use light intensity mua、μbWeak coherent light pulse signals with the period of 2T and the average photon number less than 1 are prepared, phase coding of 0/pi is carried out on the prepared light pulse signals respectively at random according to 50% of possibility to obtain signal light, the signal light prepared by the first sending end is A, and the signal light prepared by the second sending end is B;
(2) the first sending end and the second sending end send the prepared signal light to the receiving end through an unsafe quantum channel, and the time of the signal light B reaching the receiving end lags behind the time of the signal light A by a half period T;
(3) the receiving end is provided with a Mach Zehnder interferometer and two detectors; the signal light enters the Mach-Zehnder interferometer and is divided into two beams which are respectively transmitted through the upper arm and the lower arm of the Mach-Zehnder interferometer, and the signal light component transmitted through the upper arm is introduced into a delay T, so that the component of the signal light A/B transmitted through the upper arm is interfered with the component of the signal light B/A transmitted through the lower arm; the receiving end respectively detects interference results of two output ends of the Mach-Zehnder interferometer through the first detector and the second detector;
(4) the receiving end publishes the response time, and the first sending end and the second sending end respectively reserve phase coding results of the response time to obtain an original key of the local end; the receiving end encodes the response data to obtain an original key of the receiving end;
(5) the receiving end calculates all gains for code forming based on the response data and the sending data amount of the two sending ends; then the receiving end randomly selects a plurality of response moments, the first sending end and the second sending end of the command signal alternately transmit the logic bits at the corresponding moments in the original secret keys to the receiving end through the public channel, and the receiving end calculates the total error rate of the system according to the logic bits at the corresponding moments in the original secret keys of the receiving end and judges whether the preset requirements are met;
(6) and (5) on the premise that the total error rate of the system calculated in the step (5) meets the preset requirement, performing classical error correction, error verification and privacy amplification on the residual original keys by the first sending end, the second sending end and the receiving end, and extracting the keys for quantum secret sharing by the first sending end and the second sending end respectively.
2. The quantum secret sharing method under the asymmetric channel according to claim 1, wherein in the step (4), the step of encoding the response data by the receiving end specifically comprises:
in case of only one detector response:
when the occurrence time of the interference event is T-2N T, if the relative phase of the signal light A and the signal light B is 0, the first detector responds, and the logic bit of the receiving end is 0; if the relative phase of the signal light A and the signal light B is pi, the second detector responds, and the logic bit of the receiving end is 1;
when the occurrence time of the interference event is T ═ 2N +1 × T, if the relative phase of the signal light a and the signal light B is 0, the second detector responds, and the logic bit of the receiving end is 0; if the relative phase of the signal light A and the signal light B is pi, the first detector responds, and the logic bit of the receiving end is 1;
when two detectors respond simultaneously, the receiving end randomly selects 0 or 1 for encoding with a 50% probability.
3. The quantum secret sharing method under the asymmetric channel according to claim 2, wherein the gains all used for coding are:
Qμ＝Q1(1-Q2)+Q2(1-Q1)+Q1Q2＝Q1+Q2-Q1Q2
Q1and Q2The response probabilities of the two detectors at the receiving end are respectively.
4. The quantum secret sharing method under the asymmetric channel according to claim 3, wherein the calculation formula of the total error rate of the system is as follows:
wherein, muaAnd mubThe intensity of the signal light, D, respectively prepared by the first and second transmitting terminals1And D2The intensities of the interference light detected by the two detectors at the receiving end are respectively, and e is a constant; e.g. of the typedRepresenting the basis vector calibration error rate, p, of the detectordRepresenting the dark count rate, eta, of the detectoraAnd ηbRespectively indicating the channel transmission rate from the sending end one to the receiving end and the channel transmission rate from the sending end two to the receiving end.
5. The quantum secret sharing method under the asymmetric channel according to claim 2, wherein when the channel loss from the transmitting end one to the receiving end is larger than the channel loss from the transmitting end two to the receiving end, the information from the receiving end to the transmitting end two to the receiving end is transmittedExtra loss is added, so that the channel transmission efficiency from the first sending end to the receiving end is the same as the channel transmission efficiency from the second sending end to the receiving end, namely eta is obtaineda＝ηbη', the total error rate of the system is calculated as:
6. a quantum secret sharing system under an asymmetric channel is characterized by comprising any two sending ends and receiving ends which participate in secret sharing; the two sending ends and the receiving ends adopt the method of claims 1 to 5 to share quantum secret.
7. The quantum secret sharing system under the asymmetric channel of claim 6,
the transmitting end comprises a signal light transmitting module, a signal light intensity modulation module and a signal light phase modulation module; the signal light sending module is used for generating continuous laser with consistent and continuous light intensity, frequency, phase and polarization maintaining time; the signal light intensity modulation module performs chopping on continuous laser to obtain signal light pulses, and then performs weak light modulation on the signal light pulses to obtain weak coherent light pulses with the average photon number smaller than 1; the signal light phase modulation module carries out phase coding with the phase of 0 or pi on the weak coherent light pulse to obtain required signal light;
the receiving end comprises a first beam splitter, a second beam splitter, a first detector and a second detector, the first beam splitter and the second beam splitter form an unbalanced Mach Zehnder interferometer which is used for interfering two beams of signal light sent by a first sending end and a second sending end, and the first detector and the second detector are respectively used for measuring interference results.
8. The quantum secret sharing system under the asymmetric channel as claimed in claim 7, wherein the two transmitters transmit the signal lights simultaneously, and the channel from the transmitter two to the receiver has a delay line more than the path from the transmitter one to the receiver, so as to realize that the time when the signal light B reaches the receiver lags behind the signal light a by half a period T.
9. The quantum secret sharing system under the asymmetric channel according to claim 8, wherein the receiving end further includes a first polarization controller and a second polarization controller, and the first polarization controller and the second polarization controller are respectively used for adjusting the signal light a and the signal light B to the same polarization angle and then sending the signal light a and the signal light B to the first beam splitter.
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