CN110798312A - Secret negotiation method of continuous variable quantum key distribution system - Google Patents

Secret negotiation method of continuous variable quantum key distribution system Download PDF

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CN110798312A
CN110798312A CN201911031115.6A CN201911031115A CN110798312A CN 110798312 A CN110798312 A CN 110798312A CN 201911031115 A CN201911031115 A CN 201911031115A CN 110798312 A CN110798312 A CN 110798312A
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decoding
negotiation
check
secret
distribution system
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黄端
李伯鹏
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Central South 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
    • H04L9/0852—Quantum cryptography
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1105—Decoding
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0061—Error detection codes
    • 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

Abstract

The invention discloses a secret negotiation method of a continuous variable quantum key distribution system, which comprises a local decoder negotiation step and a global decoder negotiation step. The secret negotiation method of the continuous variable quantum key distribution system provided by the invention completes the simultaneous decoding of a plurality of data blocks by utilizing the structural characteristics of the global coupling low-density parity check code, so that the decoding speed can be greatly improved, and the high-speed decoding can meet the technical requirements of the high-speed continuous variable quantum key distribution system; meanwhile, a local decoder and a global decoder exist in the whole decoding process, the frame error rate and the bit error rate of the system can be greatly reduced by carrying out secondary decoding on the data block with the decoding error, and the negotiation efficiency of the continuous variable quantum key distribution system can be improved; therefore, the method has high reliability, good accuracy and high decoding speed.

Description

Secret negotiation method of continuous variable quantum key distribution system
Technical Field
The invention belongs to the technical field of information security, and particularly relates to a secret negotiation method of a continuous variable quantum key distribution system.
Background
With the background of rapid development of communication technology, society has increasingly high requirements for security of information communication. In recent years, quantum key distribution, which is a new communication method for information transfer using the quantum entanglement effect, has attracted increasing attention. Quantum key distribution can guarantee unconditional security of communication by using quantum characteristics. Quantum key distribution is divided into continuous variable quantum key distribution and discrete variable quantum key distribution, and compared with discrete variable quantum key distribution, the continuous variable quantum key distribution can realize that a single pulse encodes multiple bits, so that higher communication rate and efficiency can be realized. The continuous variable quantum key distribution system comprises signal preparation, signal transmission and signal reception. The secret negotiation takes an important position in signal reception, and erroneous symbols can be removed through the secret negotiation. Secret negotiation can be divided into two types, namely forward negotiation and reverse negotiation: the forward negotiation is that the receiving end performs error correction processing according to the data of the transmitting end, and the reverse negotiation is that the transmitting end performs error correction processing according to the data of the receiving end. Since the forward negotiation cannot break through the theoretical limit of 3dB, it becomes a common technical solution to use the low density parity check code in the reverse negotiation.
In the continuous variable quantum key distribution technique, one typically completes the secret negotiation process using a conventional low density parity check code. However, due to the sparsity of the check matrix of the low density parity check code, the complexity in the negotiation process is greatly increased, and the complexity of calculation and the negotiation time are also greatly increased.
Disclosure of Invention
The invention aims to provide a secret negotiation method of a continuous variable quantum key distribution system, which has high reliability, good accuracy and high decoding speed.
The secret negotiation method of the continuous variable quantum key distribution system provided by the invention comprises the following steps:
s1, negotiating a local decoder;
and S2, global decoder negotiation.
The local decoder negotiation in step S1, specifically, the global coupled low density parity check code structure characteristic is used to complete the first-level decoding.
The local decoder negotiation in step S1 specifically includes the following steps:
A. the sender sends the sending data to the receiving end through a Gaussian channel;
B. the receiving end compiles the data and the random secret key and then sends the compiled information to the sending end;
C. dividing the compiled data into sub-data blocks with the same number as that of the local decoders by the receiving end and the sending end, and decoding each sub-data block by the local decoders;
D. the receiving end and the transmitting end use the local check node of the check matrix in the local decoder to check the decoding result:
if the verification result is correct, the decoding result is a secret key sequence, and the secret negotiation is completed;
and if the check result is wrong, carrying out global decoder negotiation.
The global decoder negotiation described in step S2 is to complete secondary decoding by using the structural characteristics of the global coupled low-density parity-check code.
The global decoder negotiation in step S2 specifically includes the following steps:
a. c, performing secondary decoding on the data block with the decoding error in the step C by adopting a global decoder;
b. b, adopting a global check node in the check matrix to check the decoding result in the step a:
if the verification result is correct, the decoding result is a secret key sequence, and the secret negotiation is completed;
if the detection result is wrong, sending error information to a sending end; this secret negotiation fails.
And (4) completing decoding and checking of the data block by adopting a belief propagation algorithm.
The global coupling low-density parity check code in the decoding process is constructed by adopting the following method: firstly, expanding the basic matrix into a check matrix by a circulation method according to the structural characteristics of the basic matrix; the circulating method comprises the following steps: by consulting elements in the basic matrix, when the elements are zero, replacing the elements by a zero matrix of (q-1) × (q-1); when the elements are not zero, replacing by a cyclic permutation matrix with the dimension of (q-1) × (q-1); q is the power of a prime number of the non-binary domain.
And (3) checking the decoding result, specifically, checking by adopting the following steps:
(1) initialization is performed using the following equation:
Figure BDA0002250175980000031
Figure BDA0002250175980000032
in the formula xl0 denotes the x-th of the received datalThe prior probability of a bit is 0;
Figure BDA0002250175980000033
represents that the probability of initialization to 0 is P;
Figure BDA0002250175980000034
representing a probability of 1-P for initialization to 1;
(2) respectively storing the row position and the column position of a non-zero element in the check matrix by using two one-dimensional matrixes;
(3) performing horizontal iteration: the message L (r) passed by each check node to the variable node is calculated by the following formulan)：
Figure BDA0002250175980000035
Wherein tan h-1() Is the inverse of the function of tanh (); n 'is the nth' variable node;is composed ofFrom which position N is removed(n)Set of post-rest positions；L(qn') Is qn'Checking the information of the nodes; m(n)Is a one-dimensional matrix of rows in which non-zero elements of the check matrix are located, N(n)A one-dimensional matrix of the columns of the non-zero elements in the check matrix;
(4) performing vertical iteration: the message L (q) transmitted to the check node by each variable node is calculated by the following formulan)：
Figure BDA0002250175980000041
In the formula
Figure BDA0002250175980000042
To initialize the decoding probability;
Figure BDA0002250175980000043
is rn'The value of the message of the variable node in the log domain;
(5) decoding is performed by adopting the following formula:
L(Pi)＝L(pi)+L(rn)
Figure BDA0002250175980000044
wherein L (P)i) Is PiTotal information of nodes; l (p)i) Is piThe initial information of (1); l (r)n) Is rnThe amount of information of the node; p is a radical ofiIs the p thiA bit;
if under the set conditionsIf yes, the verification is determined to be successful;
if under the set conditions
Figure BDA0002250175980000046
If not, determining that the test fails, turning to the step (3) to perform loop iteration calculation again until a set condition is met or the maximum iteration number is reached, and jumping out of loop iteration.
The secret negotiation method of the continuous variable quantum key distribution system provided by the invention completes the simultaneous decoding of a plurality of data blocks by utilizing the structural characteristics of the global coupling low-density parity check code, so that the decoding speed can be greatly improved, and the high-speed decoding can meet the technical requirements of the high-speed continuous variable quantum key distribution system; meanwhile, a local decoder and a global decoder exist in the whole decoding process, the frame error rate and the bit error rate of the system can be greatly reduced by carrying out secondary decoding on the data block with the decoding error, and the negotiation efficiency of the continuous variable quantum key distribution system can be improved; therefore, the method has high reliability, good accuracy and high decoding speed.
Drawings
FIG. 1 is a schematic process flow diagram of the process of the present invention.
FIG. 2 is a schematic diagram of the basic matrix structure of the global coupling LDPC code according to the present invention.
Fig. 3 is a schematic diagram of a check matrix structure of a global coupling low density parity check code according to the method of the present invention.
Fig. 4 is a diagram illustrating negotiation rate of the quantum key distribution system according to the method of the present invention.
Fig. 5 is a schematic diagram of the frame error rate of the quantum key distribution system according to the method of the present invention.
Detailed Description
In a continuous variable quantum key distribution system, Alice (sender) corrects classical information M on an optical fiber using a belief propagation algorithm, whereAiming at the structural characteristics of the low-density parity-check code based on global coupling, the decoding process is divided into a local decoding part and a global decoding part. The received data M is divided into t sequences, and the t sequences are decoded by a t independent decoder; if the decoding of the t sequence is successful; the locally decoded code word U satisfies the check matrix H of the globally coupled parity check codeqc,gcI.e. U satisfiesThe code word U can be used to eliminate channel noise in the information received by Bob (receiving end); check matrix
Figure BDA0002250175980000053
Is a check matrix Hqc,gcThe transposed matrix of (2); if the local decoder has errors during decoding, i.e. if the local decoder has errors
Figure BDA0002250175980000054
Switching decoding from the local part to the global part by the global check node; in general, a global decoder is only needed when the amount of errors in local decoding is large.
FIG. 1 is a schematic flow chart of the method of the present invention: the secret negotiation method of the continuous variable quantum key distribution system provided by the invention comprises the following steps:
s1, negotiating a local decoder; in particular, a first-level decoding is completed by utilizing the structural characteristics of the global coupling low-density parity-check code;
in the specific implementation, the following steps are adopted for negotiation:
A. the sender sends the sending data to the receiving end through a Gaussian channel;
B. the receiving end compiles the data and the random secret key and then sends the compiled information to the sending end;
C. dividing the compiled data into sub-data blocks with the same number as that of the local decoders by the receiving end and the sending end, and decoding each sub-data block by the local decoders;
D. the receiving end and the transmitting end use the local check node of the check matrix in the local decoder to check the decoding result:
if the verification result is correct, the decoding result is a secret key sequence, and the secret negotiation is completed;
if the check result is wrong, carrying out global decoder negotiation;
s2, global decoder negotiation; the method specifically comprises the steps of completing secondary decoding by utilizing the structural characteristics of a global coupling low-density parity check code;
in the specific implementation, the following steps are adopted for negotiation:
a. c, performing secondary decoding on the data block with the decoding error in the step C by adopting a global decoder;
b. b, adopting a global check node in the check matrix to check the decoding result in the step a:
if the verification result is correct, the decoding result is a secret key sequence, and the secret negotiation is completed;
if the detection result is wrong, sending error information to a sending end; this secret negotiation fails.
In the decoding and checking process, a belief propagation algorithm is adopted to finish the decoding and checking of the data block; meanwhile, the global coupling low-density parity check code in the decoding process is constructed by the following method: firstly, expanding the basic matrix into a check matrix through a circulation method according to the structural characteristics of the basic matrix (the structure of the basic matrix is shown in figure 2) (the result of the check matrix is shown in figure 3); the circulating method comprises the following steps: by consulting elements in the basic matrix, when the elements are zero, replacing the elements by a zero matrix of (q-1) × (q-1); when the elements are not zero, replacing by a cyclic permutation matrix with the dimension of (q-1) × (q-1); q is the power of a prime number of a non-binary field;
in addition, in the above steps, the decoding result is checked, specifically, the following steps are adopted for checking:
(1) initialization is performed using the following equation:
Figure BDA0002250175980000071
Figure BDA0002250175980000072
in the formula xl0 denotes the x-th of the received datalThe prior probability of a bit is 0;
Figure BDA0002250175980000073
represents that the probability of initialization to 0 is P;
Figure BDA0002250175980000074
the probability of initialization to 1 is 1-P;
(2) respectively storing the row position and the column position of a non-zero element in the check matrix by using two one-dimensional matrixes;
for example,
Figure BDA0002250175980000075
then, using matrix M to represent the row of the non-zero element in matrix H, and using N to represent the column of the non-zero element in matrix H, the following matrices M and N are obtained:
M＝[1 1 1 2 2 2 3 3 3 4 4 4]
N＝[1 2 3 4 5 6 1 4 7 2 5 8]
(3) performing horizontal iteration: the message L (r) passed by each check node to the variable node is calculated by the following formulan) (ii) a The step is used for updating the information of the check node;
Figure BDA0002250175980000076
wherein tan h-1() Is the inverse of the function of tanh (); n 'is the nth' variable node;is composed of
Figure BDA0002250175980000078
From which position N is removed(n)A set of post-rest positions; l (q)n') Is qn'Checking the information of the nodes; m(n)Is a one-dimensional matrix of rows in which non-zero elements of the check matrix are located, N(n)A one-dimensional matrix of the columns of the non-zero elements in the check matrix;
(4) performing vertical iteration: the message L (q) transmitted to the check node by each variable node is calculated by the following formulan) (ii) a The step is used for updating the information of the variable node;
in the formula
Figure BDA0002250175980000082
To initialize the decoding probability; l (r)n') Is rn'The value of the message of the variable node in the log domain;
(5) decoding is performed by adopting the following formula:
L(Pi)＝L(pi)+L(rn)
Figure BDA0002250175980000083
wherein L (P)i) Is PiTotal information of nodes; l (p)i) Is piThe initial information of (1); l (r)n) Is rnThe amount of information of the node; p is a radical ofiIs the p thiA bit;
if under the set conditions
Figure BDA0002250175980000084
If yes, the verification is determined to be successful;
if under the set conditions
Figure BDA0002250175980000085
If not, determining that the test fails, turning to the step (3) to perform loop iteration calculation again until a set condition is met or the maximum iteration number is reached, and jumping out of loop iteration.
As can be seen from fig. 4 and 5: the method of the invention can reduce the error frame rate of the system and improve the decoding speed.

Claims (8)

1. A secret negotiation method of a continuous variable quantum key distribution system comprises the following steps:
s1, negotiating a local decoder;
and S2, global decoder negotiation.
2. The secret negotiation method of the continuous variable quantum key distribution system according to claim 1, wherein the local decoder negotiation in step S1, specifically, the one-level decoding is completed by using the structural characteristics of the globally coupled low-density parity-check code.
3. The secret negotiation method of the continuous variable quantum key distribution system according to claim 2, wherein the local decoder negotiation in step S1 is specifically performed by adopting the following steps:
A. the sender sends the sending data to the receiving end through a Gaussian channel;
B. the receiving end compiles the data and the random secret key and then sends the compiled information to the sending end;
C. dividing the compiled data into sub-data blocks with the same number as that of the local decoders by the receiving end and the sending end, and decoding each sub-data block by the local decoders;
D. the receiving end and the transmitting end use the local check node of the check matrix in the local decoder to check the decoding result:
if the verification result is correct, the decoding result is a secret key sequence, and the secret negotiation is completed;
and if the check result is wrong, carrying out global decoder negotiation.
4. The secret negotiation method of the continuous variable quantum key distribution system according to claim 2 or 3, wherein the global decoder negotiation in step S2, in particular, the secondary decoding is performed by using the structural characteristics of the globally coupled low density parity check code.
5. The secret negotiation method of the continuous variable quantum key distribution system according to claim 4, wherein the global decoder negotiation in step S2 is specifically performed by adopting the following steps:
a. c, performing secondary decoding on the data block with the decoding error in the step C by adopting a global decoder;
b. b, adopting a global check node in the check matrix to check the decoding result in the step a:
if the verification result is correct, the decoding result is a secret key sequence, and the secret negotiation is completed;
if the detection result is wrong, sending error information to a sending end; this secret negotiation fails.
6. The secret negotiation method of a continuous variable quantum key distribution system according to claim 5, characterized in that the decoding and checking of the data blocks is done using a belief propagation algorithm.
7. The secret negotiation method of the continuous variable quantum key distribution system according to claim 6, characterized in that the global coupling low density parity check code in the decoding process is constructed by adopting the following method: firstly, expanding the basic matrix into a check matrix by a circulation method according to the structural characteristics of the basic matrix; the circulating method comprises the following steps: by consulting elements in the basic matrix, when the elements are zero, replacing the elements by a zero matrix of (q-1) × (q-1); when the elements are not zero, replacing by a cyclic permutation matrix with the dimension of (q-1) × (q-1); q is the power of a prime number of the non-binary domain.
8. The secret negotiation method of a continuous variable quantum key distribution system according to claim 7, characterized by performing a check on the decoding result, specifically performing a check by using the following steps:
(1) initialization is performed using the following equation:
xl＝0
Figure FDA0002250175970000022
in the formula xl0 denotes the x-th of the received datalThe prior probability of a bit is 0;
Figure FDA0002250175970000023
represents that the probability of initialization to 0 is P;
Figure FDA0002250175970000024
the probability of initialization to 1 is 1-P;
(2) respectively storing the row position and the column position of a non-zero element in the check matrix by using two one-dimensional matrixes;
(3) performing horizontal iteration: the message L (r) passed by each check node to the variable node is calculated by the following formulan)：
Figure FDA0002250175970000031
Wherein tan h-1() Is the inverse of the function of tanh (); n 'is the nth' variable node;
Figure FDA0002250175970000032
is composed ofFrom which position N is removed(n)A set of post-rest positions; l (q)n') Is qn'Checking the information of the nodes; m(n)Is a one-dimensional matrix of rows in which non-zero elements of the check matrix are located, N(n)A one-dimensional matrix of the columns of the non-zero elements in the check matrix;
(4) performing vertical iteration: the message L (q) transmitted to the check node by each variable node is calculated by the following formulan)：
Figure FDA0002250175970000034
In the formula
Figure FDA0002250175970000035
To initialize the decoding probability; l (r)n') Is rn'The value of the message of the variable node in the log domain;
(5) decoding is performed by adopting the following formula:
L(Pi)＝L(pi)+L(rn)
Figure FDA0002250175970000036
wherein L (P)i) Is PiTotal information of nodes; l (p)i) Is piThe initial information of (1); l (r)n) Is rnThe amount of information of the node; p is a radical ofiIs the p thiA bit;
if under the set conditionsIf yes, the verification is determined to be successful;
if under the set conditionsIf not, determining that the test fails, turning to the step (3) to perform loop iteration calculation again until a set condition is met or the maximum iteration number is reached, and jumping out of loop iteration.
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Publication number Priority date Publication date Assignee Title
CN111786787A (en) * 2020-07-29 2020-10-16 中南大学 Quantum key distribution post-processing method and system based on verifiable secret sharing
CN115348010A (en) * 2022-07-20 2022-11-15 中国电子科技集团公司第三十研究所 Method and system suitable for eliminating residual error code in continuous variable quantum key distribution
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