CN109768857A - A kind of CVQKD multidimensional machinery of consultation using improved decoding algorithm - Google Patents
A kind of CVQKD multidimensional machinery of consultation using improved decoding algorithm Download PDFInfo
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Abstract
The present invention relates to a kind of CVQKD multidimensional machineries of consultation using improved decoding algorithm.The present invention improves decoding algorithm according to the characteristic of pseudo channel in the multidimensional negotiation step of continuous variable quantum key distribution, greatly improves accuracy and safety.The present invention is simple and effective, easily operated, effectively avoids since the characteristic of pseudo channel in multidimensional machinery of consultation and decoding algorithm mismatch brought error.
Description
Technical field
The continuous variable quantum key distribution that the present invention relates to a kind of using improved decoding algorithm (CVQKD,
Continuous-Variable Quantum Key Distribution) multidimensional machinery of consultation.
Background technique
Under the background that computer information technology rapidly develops, requirement of the information technology to information security increasingly increases.
Due to can physically guarantee the Unconditional security of quantum communications, so that quantum key distribution (QKD) is used as quantum communications
Important branch have been to be concerned by more and more people.
QKD technology can be divided into two classes on the whole: discrete variable quantum key distribution (DVQKD) and continuous variable quantum are close
Key distributes (CVQKD).For discrete variable quantum key distribution technology, CVQKD has potential high code rate and classical optical fiber
The extraordinary confluent feature of communication network, therefore CVQKD has attracted many research institutions in world wide to manage it
It is conducted in-depth research by with application technology.Continuous variable quantum key distribution becomes one of Technique on Quantum Communication at present
Important research branch.
The main bottleneck of CVQKD system is in the Data Post stage at present, firstly, negotiation efficiency determines quantum communications
Transmission range and key rate；In addition high negotiation speed is to realize the necessary condition of high code rate CVQKD system.Therefore negotiation algorithm
Performance becomes limitation CVQKD finally at the principal element of code rate and safe distance.
In CVQKD system, since the quantum signal of quantum channel transmission is very faint, in the distant feelings of transmission range
Under condition, the signal-to-noise ratio of CVQKD system is generally in very low level.In order in the extremely low environment of signal-to-noise ratio from raw information
Extract key, it is necessary to using with the algorithm in the case where signal-to-noise ratio is extremely low with high negotiation efficiency.In view of this consideration, existing
Have technology be typically employed in signal-to-noise ratio it is extremely low in the case where with very high negotiation efficiency multidimensional negotiation algorithm.
In CVQKD system, the information being modulated on quantum signal is continuous variable, in order to obtain final key,
There are the processes how one be converted to continuous variable discrete variable.Different from traditional negotiation algorithm by continuous variable
It is quantized into the way of discrete variable, but directly carries out key agreement using continuous variable.The main thought of multidimensional machinery of consultation
It is that the equally distributed variable space is become into an equally distributed variable space by mapping, prior probability is selected to be uniformly distributed
Code word space.Operation in this way, stochastic variable and code word space are all uniformly distributed, in this way when in common authentication channel
When transmitting side information, listener-in is unable to get additional amount of correlated information.Such way negotiates multidimensional can be by existing
There are the channel coding technology of conventional information field technology maturation, easily operated execution.
Summary of the invention
The object of the present invention is to provide a kind of continuous variable quantum key distribution multidimensional negotiations that security performance is greatly improved
Method.
In order to achieve the above object, the technical solution of the present invention is to provide a kind of using improved decoding algorithm
CVQKD multidimensional machinery of consultation, which comprises the following steps:
Step 1 assumes that the noise of binary system pseudo channel obeys t distribution；
Step 2 changes the primary key of transmitting terminal Alice and receiving end Bob for d dimensional vector, respectively X and Y；
Step 3 generates equally distributed codeword vector u and transmission map function M (y, u), in formula, Receiving end Bob gives transmitting terminal Alice by common authentication transmission transmission map function M (y, u):
In the case where reversed negotiate, receiving end Bob quantum True Random Number Generator d n-dimensional sphere n randomly select d tie up to
AmountAnd transmission map function M (y, u) is calculated, transmission map function M (y, u) meets M (y, u) y=u；
Step 4, transmitting terminal Alice obtain the errors of form vector v of codeword vector u, and transmitting terminal Alice calculates M (y, u) x
=v, in formula,
Step 5 is set up by the operation of step 3 with codeword vector u as input, and errors of form v is the binary system of output
Pseudo channel, the binary system pseudo channel meet t distribution, the error shape of receiving in the limited situation of dimension d that multidimensional is negotiated
Formula vector v is expressed asThe noise ε of pseudo channel is expressed as
In formula, z indicates that quantum channel noise, σ indicate that the noise criteria of quantum channel is poor, and t (d) indicates that the t that freedom degree is d is distributed；
Step 6 carries out error correction using improved decoding algorithm, comprising the following steps:
Step 601 obtains conditional probability Pr (ui=u | vi) calculation formula, i.e., in the situation known to errors of form vector v
Under, acquire the probability that position is corresponded in codeword vector u, in which:
In formula, Pr () indicates the calculating of posterior probability, viIndicate i-th of component in errors of form vector v, uiIt indicates
I-th of component in codeword vector u, n indicate errors of form vector v and the component total number of codeword vector u；
Step 602, initialization qij(0) and qij(1), in formula, qij(b) it indicates from variable node i to the letter of check-node j
Probability is ceased, b=1 or -1:
qij(0)=1-Pi=Pr (ui=+1 | vi), in formula, PiIndicate the probability calculation of variable node i；
qij(1)=Pi=Pr (ui=-1 | vi)；
The processing of step 603, check-node updates:
rji(1)=1-rji(0)
In formula, rji(b) the external information probability from check-node j to variable node i, R are indicatedj\iIt indicates to remove variable node i
Outside with the set of the check-node j variable node being connected；
The processing of step 604, variable node updates:
In formula, KijTo ensure qij(0)+qij(1)=1 normalization factor, Ci\jIndicate in addition to check-node j with variable section
The set of point i connected check-node；
Step 605, decision process:
In formula, Qi(b) posterior probability of variable node i, b=1 or -1, K are indicatediExpression makes Qi(0)+Qi(1)=1 return
One changes the factor, CiIndicate the set for all check-nodes being connected with variable node i；
Step 606, iteration control:
In formula,For the code word interpreted after decision process, ifOr reach maximum number of iterations, then operation terminates,
Otherwise, return step 603, in formula, H indicates check matrix.
The present invention is improved according to the characteristic of pseudo channel in the multidimensional negotiation step of continuous variable quantum key distribution
Decoding algorithm greatly improves accuracy and safety.The present invention it is simple and effective, it is easily operated, effectively avoid by
The characteristic of pseudo channel and decoding algorithm mismatch brought error in multidimensional machinery of consultation.
Detailed description of the invention
Fig. 1 is program flow diagram of the invention；
Fig. 2 is the improved decoding algorithm flow chart of the present invention.
Specific embodiment
Present invention will be further explained below with reference to specific examples.It should be understood that these embodiments are merely to illustrate the present invention
Rather than it limits the scope of the invention.In addition, it should also be understood that, after reading the content taught by the present invention, those skilled in the art
Member can make various changes or modifications the present invention, and such equivalent forms equally fall within the application the appended claims and limited
Range.
The present invention provides a kind of CVQKD multidimensional machineries of consultation using improved decoding algorithm to change the first of decoding algorithm
Beginning probability, the probability that the original hypothesis according to Gaussian channel is calculated are adjusted to obey the channel of t distribution according to noise
And the probability calculated after obtaining primary key, is divided into d dimensional vector by primary key by the quantum communications stage, instead
Generate binary code word u in d n-dimensional sphere n to receiving end quantum real random number generator when negotiation, in binary code word u and
M is transferred to transmitting terminal there are a mapping relations M by normalized continuous variable, will receive the form of noise v of a u,
One is set up thus with u as input, and v is the binary system pseudo channel of output, is then carried out using improved decoding algorithm
Error correction, so that communicating pair obtains the same key string, to realize continuous variable quantum key distribution under finite dimensional effect
Multidimensional machinery of consultation.The present invention specifically includes the following steps:
Step 1 assumes that the noise of binary system pseudo channel obeys t distribution；
According to original decoding algorithm, the calculation method of prior probability is adjusted, original decoding algorithm is taken with interchannel noise
Based on the hypothesis of Gaussian Profile, improved decoding algorithm then considers that the noise of pseudo channel obeys the thing of t distribution
It is adjusted to t distribution in fact and by the probability density function of interchannel noise, calculates the prior probability of decoding algorithm on this basis；
Step 2 changes the primary key of transmitting terminal Alice and receiving end Bob for d dimensional vector, respectively X and Y；
Step 3 generates equally distributed codeword vector u and transmission map function M (y, u), in formula, Receiving end Bob gives transmitting terminal Alice by common authentication transmission transmission map function M (y, u):
In the case where reversed negotiate, receiving end Bob quantum True Random Number Generator d n-dimensional sphere n randomly select d tie up to
AmountAnd transmission map function M (y, u) is calculated, transmission map function M (y, u) meets M (y, u) y=u；
Step 4, transmitting terminal Alice obtain the errors of form vector v of codeword vector u, and transmitting terminal Alice calculates M (y, u) x
=v, in formula,
Step 5 is set up by the operation of step 3 with codeword vector u as input, and errors of form v is the binary system of output
Pseudo channel, the binary system pseudo channel meet t distribution, the error shape of receiving in the limited situation of dimension d that multidimensional is negotiated
Formula vector v is expressed asTherefore the noise ε of pseudo channel isIt is obtained according to the noise representation of pseudo channelIn formula, z indicates that quantum channel is made an uproar
Sound, σ indicate that the noise criteria of quantum channel is poor, and t (d) indicates that the t that freedom degree is d is distributed；
Step 6 carries out error correction using improved decoding algorithm, comprising the following steps:
Step 601 obtains conditional probability Pr (ui=u | vi) calculation formula, i.e., in the situation known to errors of form vector v
Under, acquire the probability that position is corresponded in codeword vector u, in which:
In formula, Pr () indicates the calculating of posterior probability, viIndicate i-th of component in errors of form vector v, uiIt indicates
I-th of component in codeword vector u, n indicate errors of form vector v and the component total number of codeword vector u；
The solution procedure of above-mentioned formula are as follows:
The noise ε of pseudo channel obeys t distribution, so vi=ui+εi, εiFor i-th of component of noise ε, εiIt obeys freely
The t that degree is d is distributed, and
It is distributed, remembers T~t (n), then its probability density function assuming that T obeys the t that freedom degree is n are as follows:
In formula,Indicate second type Euler's integral.
According to the calculation formula of the available probability, that is, conditional probability of probability density function of t distribution are as follows:
Step 602, initialization qij(0) and qij(1), q in formulaij(b) it indicates from variable node i to the information of check-node j
Probability, b=1 or -1:qij(0)=1-Pi=Pr (ui=+1 | vi), in formula, PiIndicate the probability calculation of variable node i；
qij(1)=Pi=Pr (ui=-1 | vi)；
The processing of step 603, check-node updates:
rji(1)=1-rji(0)
In formula, rji(b) the external information probability from check-node j to variable node i, R are indicatedj\iIt indicates to remove variable node i
Outside with the set of the check-node j variable node being connected；
The processing of step 604, variable node updates:
In formula, KijTo ensure qij(0)+qij(1)=1 normalization factor, Ci\jIndicate in addition to check-node j with variable section
The set of point i connected check-node；
Step 605, decision process:
In formula, Qi(b) posterior probability of variable node i, b=1 or -1K are indicatediExpression makes Qi(0)+Qi(1)=1 normalizing
Change the factor, CiIndicate the set for all check-nodes being connected with variable node i；
Step 606, iteration control:
In formula,For the code word interpreted after decision process, ifOr reach maximum number of iterations, then operation terminates,
Otherwise, return step 603, in formula, H indicates check matrix.
Claims (1)
1. a kind of CVQKD multidimensional machinery of consultation using improved decoding algorithm, which comprises the following steps:
Step 1 assumes that the noise of binary system pseudo channel obeys t distribution；
Step 2 changes the primary key of transmitting terminal Alice and receiving end Bob for d dimensional vector, respectively X and Y；
Step 3 generates equally distributed codeword vector u and transmission map function M (y, u), in formula, Receiving end Bob gives transmitting terminal Alice by common authentication transmission transmission map function M (y, u):
In the case where reversed negotiate, receiving end Bob quantum True Random Number Generator randomly selects d dimensional vector in d n-dimensional sphere nAnd transmission map function M (y, u) is calculated, transmission map function M (y, u) meets M (y, u) y=u；
Step 4, transmitting terminal Alice obtain the errors of form vector v of codeword vector u, and transmitting terminal Alice calculates M (y, u) x=v,
In formula,
Step 5 is set up by the operation of step 3 with codeword vector u as input, and errors of form v is that the binary system of output is virtual
Channel, the binary system pseudo channel meet t distribution in the limited situation of dimension d that multidimensional is negotiated, the errors of form of receiving to
Amount v is expressed asThe noise ε of pseudo channel is expressed asIn formula,
Z indicates that quantum channel noise, σ indicate that the noise criteria of quantum channel is poor, and t (d) indicates that the t that freedom degree is d is distributed；
Step 6 carries out error correction using improved decoding algorithm, comprising the following steps:
Step 601 obtains conditional probability Pr (ui=u | vi) calculation formula, i.e., in the situation known to errors of form vector v,
Acquire the probability that position is corresponded in codeword vector u, in which:
In formula, Pr () indicates the calculating of posterior probability, viIndicate i-th of component in errors of form vector v, uiIndicate code word
I-th of component in vector u, n indicate errors of form vector v and the component total number of codeword vector u；
Step 602, initialization qij(0) and qij(1), in formula, qij(b) indicate general to the information of check-node j from variable node i
Rate, b=1 or -1:
qij(0)=1-Pi=Pr (ui=+1 | vi), in formula, PiIndicate the probability calculation of variable node i；
qij(1)=Pi=Pr (ui=-1 | vi)；
The processing of step 603, check-node updates:
rji(1)=1-rji(0)
In formula, rji(b) the external information probability from check-node j to variable node i, R are indicatedj\iIndicate in addition to variable node i with
The set of check-node j connected variable node；
The processing of step 604, variable node updates:
In formula, KijTo ensure qij(0)+qij(1)=1 normalization factor, Ci\jIndicate in addition to check-node j with variable node i
The set of connected check-node；
Step 605, decision process:
In formula, Qi(b) posterior probability of variable node i, b=1 or -1, K are indicatediExpression makes Qi(0)+Qi(1)=1 normalization because
Son, CiIndicate the set for all check-nodes being connected with variable node i；
Step 606, iteration control:
In formula,For the code word interpreted after decision process, ifOr reaching maximum number of iterations, then operation terminates, no
Then, return step 603, in formula, H indicates check matrix.
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| CN114629638A (en) * | 2022-03-10 | 2022-06-14 | 中国电子科技集团公司第三十研究所 | Multi-dimensional negotiation simplification method and device suitable for continuous variable quantum key distribution |
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