QKD system-oriented PAC-AIR hybrid information negotiation method and system, and storage medium
By combining convolutional precoding and polar code encoding, the PAC-AIR hybrid information negotiation method solves the problems of insufficient negotiation efficiency and large decoding delay of Polar codes under medium code length, realizing efficient and low-latency key negotiation, which is suitable for a variety of QKD application scenarios.
Patent Information
- Application Number
- CN202511205099.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-26
- Publication Date
- 2025-11-07
AI Technical Summary
Existing information negotiation methods based on Polar codes suffer from insufficient negotiation efficiency, large decoding delay, and poor system flexibility under medium code lengths, making it difficult to meet the needs of real-time and resource-constrained scenarios.
The PAC-AIR hybrid information negotiation method is adopted, which involves convolutional precoding and polar code encoding of the key bit sequence, combined with classical channel public frozen bit information, and repair through a multi-round interactive additional information negotiation mechanism after the initial negotiation fails. Error correction is performed using the recursive structure of Polar codes and the SCL decoding algorithm.
It improves negotiation efficiency under medium code length, reduces decoding latency, enhances system flexibility and adaptability, and is suitable for various QKD application scenarios, including resource-constrained scenarios such as satellite terminals and portable devices, meeting the requirements of real-time key distribution.
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Figure CN120915446A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application relates to the technical field of secret communication, in particular to a PAC-AIR hybrid information negotiation method and system for a QKD system and a storage medium. BACKGROUND
[0002] Quantum Key Distribution (QKD) as an important technology for realizing unconditional secure transmission of information has been widely concerned in recent years. Information reconciliation (IR) is a key step in a QKD system for correcting the key difference between the two communication parties, and its performance directly affects the final key generation rate and system stability. At present, the information reconciliation scheme based on Polar code is widely studied because it can theoretically approach the Shannon limit under infinite code length. In order to improve its performance, structures such as SCL decoding, CRC assistance and LDPC hybrid scheme are introduced in the prior art to improve the error correction capability and reconciliation efficiency.
[0003] At present, such a scheme has strong dependence on code length. Its efficiency decreases significantly under medium code length. In addition, although some schemes try to introduce techniques such as LDPC code auxiliary decoding and SCL decoding to improve performance, the problem of poor reconciliation efficiency and poor flexibility of Polar code under medium and short block length has not been effectively solved, and the decoding delay overhead is introduced. On the other hand, although the existing interactive information reconciliation method (such as Cascade) has certain advantages in efficiency, it relies on multiple rounds of interaction, has high overall delay, slow system response speed, and is difficult to meet the actual needs in some real-time or resource-limited scenarios.
[0004] Therefore, in view of the strong dependence of the existing information reconciliation method based on Polar code on code length, the problems of insufficient reconciliation efficiency, large decoding delay and poor system flexibility under medium code length, a new information reconciliation mechanism is needed, which can balance high efficiency and low delay under medium block length and be suitable for more extensive actual QKD application scenarios. SUMMARY
[0005] The technical scheme adopted by the application to solve the above technical problems is as follows:
[0006] The application provides a PAC-AIR hybrid information negotiation method for a QKD system, comprising the following steps:
[0007] S100, performing PAC encoding processing on the key bit sequence with a length of n held by the Alice end: first, performing convolution pre-encoding on the bit sequence, then performing Polar code encoding to obtain a codeword with a length of n, and calculating the checksum of the codeword;
[0008] S200, Alice calculates the position of the frozen bit according to the channel error rate, and discloses the information of the frozen bit through the classical channel, and sends the checksum to Bob;
[0009] S300, Bob decodes the key bit sequence with a length of n held by him by using the PAC decoding algorithm, calculates the checksum after the decoding is completed, and if the checksum is passed, the information negotiation process is ended, and if the checksum is not passed, S400 is executed;
[0010] S400, Bob sends the decoding failure information to Alice, and Alice obtains additional check information according to the bit information of the disclosed part of the channel position according to the channel error rate, and sends the additional check information to Bob;
[0011] S500, Bob redecodes according to the received additional decoding information, checks the checksum, and if the decoding is successful, the information negotiation process is ended, and if the decoding is not successful, steps S400-S500 are repeatedly executed until the key is consistent or the maximum interaction round number is reached.
[0012] Further, the convolution encoding polynomial in S100 is g(D) = 1 + D + D 3 +D 7 +D 10 .
[0013] Further, the block length n of the code word obtained by performing the polar code encoding in S100 is 2 10 -2 14 bits.
[0014] Further, the SCL decoding algorithm is used for decoding in S300.
[0015] Further, the metric function of the SCL decoding in S300 is:
[0016]
[0017] wherein
[0018]
[0019] PM (i) represents the path metric value of the i-th decoding, L i represents the log-likelihood ratio of i bits, u i represents the candidate value of the i-th bit, and y represents the sequence obtained by the receiving end.
[0020] Further, the checksum for checking the success and failure of the decoding in S300 is the number of 1s in the bit sequence.
[0021] Further, the list size L of the SCL decoding algorithm is 16.
[0022] The application further provides a PAC-AIR hybrid information reconciliation system for a QKD system, which has program modules corresponding to the steps of the method according to any one of the above technical solutions, and executes the steps in the PAC-AIR hybrid information reconciliation method for a QKD system.
[0023] The application further provides a computer readable storage medium, which stores a computer program configured to implement the steps in the PAC-AIR hybrid information reconciliation method for a QKD system according to any one of the above technical solutions when called by a processor.
[0024] Compared with the prior art, the application has the following beneficial effects:
[0025] The application provides an information reconciliation scheme based on polarization-adjusted convolutional (PAC) code, which sends the bits after convolutional encoding into a Polar encoding module, performs polarization transformation by using the recursive structure of the Polar code, and forms the final encoded bits. This way not only retains the low-complexity encoding characteristics of the Polar code, but also significantly enhances the polarization effect, thereby improving the channel capacity utilization rate and effectively alleviating the dependence of the information reconciliation scheme based on the Polar code on the code length. Meanwhile, to further improve the reconciliation efficiency under a medium code length, the application combines an appending information reconciliation (AIR) scheme, constructs a reconciliation strategy supporting multiple rounds of interaction, and after the initial reconciliation is completed, if it is found that the reconciliation fails, the system sends part of the frozen bits, auxiliary bits or check bits by appending to complete the reconciliation repair process, thereby effectively improving the reconciliation efficiency under a medium code length. BRIEF DESCRIPTION OF DRAWINGS
[0026] Figure 1 FIG. 1 is a PAC code encoding and decoding architecture diagram in the embodiments of the application;
[0027] Figure 2 FIG. 2 is a PAC-AIR information reconciliation method schematic diagram in the embodiments of the application. DETAILED DESCRIPTION
[0028] In order to make the person skilled in the art better understand the present application, the exemplary embodiments or examples of the present application will be described in the following with reference to the accompanying drawings. Obviously, the described embodiments or examples are only a part of the embodiments or examples of the present application, but not all. Based on the embodiments or examples in the present application, all other embodiments or examples obtained by those skilled in the art without creative work should belong to the scope of protection of the present application.
[0029] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the accompanying drawings.
[0030] Specific embodiment one: the present application provides a PAC-AIR hybrid information negotiation method for QKD system, comprising the following steps:
[0031] S100, the key bit sequence held by Alice end with a length of n is subjected to PAC encoding processing: different from the information negotiation scheme based on polar code, the bit sequence is first subjected to convolution precoding, then polar code encoding is performed to obtain a codeword with a length of n, and the checksum of the codeword is calculated;
[0032] S200, Alice end calculates the position of the frozen bit according to the channel error rate, discloses the information of the frozen bit through the classical channel, and sends the checksum to Bob end. The formula of the channel error rate is as follows, which is obtained by simulation;
[0033]
[0034] Wherein, P e represents the error probability, u i represents the i-th channel, represents the i-th to i-1-th channel.
[0035] S300, Bob end subjects the key bit sequence held by the end with a length of n to PAC decoding, calculates the checksum after decoding, and if the checksum is passed, the information negotiation process is ended, and if the checksum is not passed, S400 is executed;
[0036] S400, Bob end sends the decoding failure information 5 to Alice end, Alice end obtains additional check information according to the bit information of the disclosed part of the channel position according to the channel error rate, and sends it to Bob end;
[0037] S500, Bob end redecodes according to the received additional decoding information, checks the checksum, and if the decoding is successful, the information negotiation process is ended, and if the decoding is not successful, steps S400-S500 are repeated, until the key is consistent or the maximum interaction round number is reached.
[0038] Specific implementation two: the convolutional encoding polynomial in S100 is g(D) = 1 + D + D 3 +D 7 +D 10 The encoding module is the inverse operation of the classical channel transmission encoding module. Since the inverse matrix of the Polar encoding matrix is itself, only the inverse of the convolutional encoding is required to complete the encoding operation of the information negotiation process. The other aspects of this embodiment are the same as those of specific implementation one.
[0039] Specific implementation three: the block length n of the code word obtained by performing Polar code encoding in S100 is 2 10 -2 14 bits. The other aspects of this embodiment are the same as those of specific implementation two.
[0040] Specific implementation four: the SCL decoding algorithm is used for decoding in S300. The other aspects of this embodiment are the same as those of specific implementation three.
[0041] Specific implementation five: the metric function of SCL decoding in S300 is:
[0042]
[0043] wherein
[0044]
[0045] pM (i) represents the path metric value of the i-th decoding, L i represents the log-likelihood ratio of i bits, u i represents the candidate value of the i-th bit, and y represents the sequence obtained at the receiving end. The other aspects of this embodiment are the same as those of specific implementation four.
[0046] Specific implementation six: the checksum used to check whether the decoding is successful or not in S300 is the number of 1s in the bit sequence. The other aspects of this embodiment are the same as those of specific implementation five.
[0047] Specific implementation seven: in each round of interaction in the additional information negotiation process, the additional check information contains the code word bit value selected according to the pre-agreed frozen bit position, and Bob uses the additional check information to treat the bit at the corresponding frozen bit position as a known value to participate in decoding. The other aspects of this embodiment are the same as those of specific implementation six.
[0048] Specific implementation eight: the list size L of the SCL decoding algorithm is 16. The other aspects of this embodiment are the same as those of specific implementation seven.
[0049] Specific implementation nine: the system adopts discrete variable QKD protocol BB84 or BBM92, and is used for correcting the difference between the key sequences at Alice side and Bob side in the key post-processing stage. The other aspects of this implementation are the same as specific implementation eight.
[0050] The method of the present application mainly includes three parts of encoding stage, decoding stage and interaction stage. As shown in Figure 2 the sending party (taking Alice in the QKD system as an example) first performs PAC encoding processing on the original key bit sequence, sends the encoded information to the receiving party (Bob), the receiving party performs PAC decoding on the received information and checks the key consistency, in the case that the initial decoding fails to correct errors, the two parties enter the additional information interaction stage, and finally realize the consistency of the key through multiple rounds of small-capacity information exchange.
[0051] I. Encoding stage
[0052] In the encoding process in the classical channel, the original information bits are first subjected to convolutional encoding processing, a fixed generator polynomial is used to construct a linear shift register structure to constrain and expand the information sequence, and the structural property of the sequence is enhanced. Convolution operation can effectively utilize the information wasted by setting the frozen bit part of the classical Polar code as a channel for auxiliary decoding.
[0053] The sending party of the present embodiment performs polar adjustment convolutional encoding (PAC encoding) on the original key data. Specifically, the original information bit sequence (length n) is first input into the Polar encoding module, and then input into the inverse convolutional encoding module. Convolutional encoding uses a pre-set generator polynomial to constrain and expand the information bits through a linear shift register, and outputs a convolutionally pre-processed bit sequence. The role of convolutional preprocessing is to enhance the structural property of the information sequence: on the one hand, convolutional operation expands and mixes the original bit stream, so that the subsequent Polar encoding stage can utilize the bit channel information that was originally unused as frozen bits in the classical Polar code; on the other hand, the constraints introduced by convolution are equivalent to giving some of the original frozen bits check relations, and these dynamic check bits participate in error correction, improving the overall reliability of the encoding. The PAC code encoding and decoding process of the classical channel is as shown in Figure 1 Since the QKD channel is different from the classical communication process, Alice and Bob have the keys screened by both parties, and the information negotiation process is to correct the inconsistency of the screened keys, so the screened keys can be regarded as the sequence transmitted in the classical channel, and therefore the encoding process of the information negotiation process is actually the inverse encoding process. At the same time, the inverse matrix of the Polar encoding matrix is itself, so only the inverse of the convolution operation is taken.
[0054] After completing the convolution and polarization transformation, Alice obtains a PAC code encoding sequence of length n. She then calculates the frozen bits using the channel error probability and transmits the PAC code sequence information containing the frozen bits to Bob via a classical channel. Because PAC coding introduces convolutional precoding on top of Polar codes, it significantly enhances channel polarization and improves channel capacity utilization compared to traditional Polar codes. Therefore, under medium code length conditions, it can reduce the number of redundant parity bits required to achieve the target error correction performance, thereby improving negotiation efficiency from the source.
[0055] II. Decoding Stage
[0056] After receiving the PAC-encoded sequence, Bob performs PAC decoding to recover the original key bits. Bob uses an improved Successive Elimination List (SCL) decoding algorithm to process the PAC code. The PAC decoding process is similar to traditional Polar code decoding, also having a complexity of O(L·N log N) (where L is the list size), but the path metric adds convolution state tracking to ensure that convolution constraints are satisfied. Specifically, during decoding, Bob uses the pre-agreed Polar code freeze bit positions and convolution generator polynomial to perform polarization decoding on the received sequence and combines it with convolution constraints to determine the possible values of the information bits. Relying only on the initial redundant bits, if the channel error rate is low, Bob can often directly and successfully correct the discrepancies, matching the key bit sequence with Alice's. At this point, no further interaction is needed, and information negotiation is completed directly. If the initial decoding fails to completely correct the errors (using a checksum, where the checksum is the length of the 1s in the sequence), Bob notifies Alice via the feedback channel that the negotiation failed, and the process enters the third stage of additional information exchange.
[0057] III. Interaction Phase
[0058] Upon detecting an initial negotiation failure, an Additional Information Negotiation (AIR) mechanism is initiated for multiple rounds of interactive error correction. This phase, as follows... Figure 2 As shown, the process includes the following steps: First, the receiver, Bob, informs the sender, Alice, of the decoding failure via a feedback message. Then, Alice decides to send additional checksum bits to assist Bob in error correction based on the feedback. The additional information is calculated based on the channel error rate. Preferably, only the "minimum necessary" redundant information is sent in each round of interaction. After receiving the additional information for that round, Bob updates the decoding constraints and then re-attempts PAC decoding. When Bob re-decodes and obtains a result that satisfies the checksum constraints, it indicates that the negotiation was successful, the key bits of both parties are consistent, and the process terminates. If it is still unsuccessful and the maximum number of interaction rounds has not been reached, Bob can again send feedback to request more information and enter the next round of additional information transmission. The above interaction process can be executed for a maximum of 1 to N rounds, but in practice, only a few rounds are generally required.
[0059] The AIR mechanism of the present application adopts a decreasing information addition strategy: with the increase of rounds, the number of bits sent in each round tends to decrease, that is, the minimum necessary information is added in a decreasing manner to balance the communication overhead and negotiation efficiency. By receiving real-time feedback from the receiver, the present application adds redundant bits in a targeted manner, effectively reducing the risk of excessive information leakage and significantly reducing the negotiation failure rate. Through the processing of the above three stages, the receiver Bob can finally successfully restore the same key information as the sender Alice and complete the information negotiation. In the entire negotiation process, the present application scheme fully combines the advantages of forward error correction and interactive error correction: the initial PAC encoding provides strong single-round error correction capability, and the AIR interactive mechanism further provides remedial measures in error conditions, thus combining high efficiency and high reliability. Compared with the traditional fixed forward error correction (FEC) scheme based on Polar code, the number of redundant bits is dynamically adjusted according to the feedback of the receiving end, and in addition, the mechanism does not need to restart the entire negotiation process, has high fault tolerance, and is suitable for restricted channels, fluctuating environments or real-time systems.
[0060] The PAC-AIR hybrid information negotiation method (algorithm) for the QKD system proposed by the present application is the underlying technical core of the present application, and various products can be derived based on the algorithm.
[0061] Based on the method proposed by the present application, a PAC-AIR hybrid information negotiation system for the QKD system is developed using a program language, which has program modules corresponding to the steps of the above technical solution, and executes the steps in the PAC-AIR hybrid information negotiation method for the QKD system described above when running.
[0062] The computer program of the developed system (software) is stored on a computer readable storage medium, and the computer program is configured to realize the steps of the PAC-AIR hybrid information negotiation method for the QKD system described above when called by a processor. That is, the present application is materialized on a carrier to become a computer program product.
[0063] The various embodiments of the systems and techniques described here can be implemented in digital electronic circuitry, integrated circuitry, specially designed ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include implementation in one or more computer programs that are executable and / or interpretable on a programmable system including at least one programmable processor, which can be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device.
[0064] The computing procedures (also called programs, software, software applications, or code) in the present application include machine instructions of programmable processors, and can be implemented using high-level process and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, apparatus, and / or device (e.g., magnetic discs, optical discs, memories, programmable logic devices (PLDs)) used to provide machine instructions and / or data to programmable processors, including a machine-readable medium that receives the machine instructions as a machine-readable signal. The term "machine-readable signal" refers to any signal used to provide machine instructions and / or data to programmable processors.
[0065] Embodiments
[0066] Under typical quantum channel error rate conditions (e.g., QBER is about 2%), when the code length N = 1024 (2 10 The conventional Polar code scheme often needs a negotiation efficiency of about 1.7 to ensure a low failure rate, while the PAC encoding reduces the negotiation efficiency to about 1.2 at a similar code length, greatly reducing the proportion of redundant information. In the medium block length range of N = 16384 (2^14), it can also maintain a high negotiation efficiency of about 1.1-1.2, achieving an error correction performance close to the Shannon limit. Since there is no need to use a super-long code word, the present application effectively avoids the high delay and high memory overhead caused by long code decoding, greatly reduces the decoding delay of information negotiation, and improves the response speed of the system.
[0067] The PAC-AIR hybrid information negotiation scheme of the present application has good system adaptability and engineering usability. On the one hand, the method of the present application has the three characteristics of high efficiency, low delay, and interactivity, and is very suitable for deployment in various QKD application scenarios. Including: for scenarios such as satellite terminals and portable devices where computing and storage resources are limited; for scenarios such as high-speed optical fiber links that are sensitive to time delay, without the need for a large number of interactive rounds and with low single-round decoding delay, it can meet the requirements of real-time key distribution. On the other hand, the implementation architecture of the method of the present application is simple and clear, and each module is improved based on the existing Polar code encoding / decoding process, and is easy to integrate into existing Polar code information negotiation hardware or software systems.
[0068] Although the present application discloses as above, the protection scope of the present application is not limited to this. The person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present application, and these changes and modifications will fall within the protection scope of the present application.
Claims
1. A PAC-AIR hybrid information negotiation method for a QKD system, characterized in that: The method comprises the following steps: S100, PAC encoding processing is performed on a key bit sequence with a length of n held by Alice, i.e., first, convolution pre-encoding is performed on the bit sequence, then, polar code encoding is performed to obtain a codeword with a length of n, and a check sum of the codeword is calculated; S200, Alice calculates the position of a frozen bit according to a channel error rate, discloses the information of the frozen bit through a classical channel, and sends the check sum to Bob; S300, Bob performs PAC decoding on a key bit sequence with a length of n held by Bob, calculates a check sum after decoding, and if the check is passed, the information negotiation process ends, and if the check is not passed, S400 is performed; S400, Bob sends decoding failure information to Alice, Alice obtains additional check information according to the bit information of the disclosed part of the channel position according to the channel error rate, and sends the additional check information to Bob; S500, Bob re-decodes according to the received additional decoding information, checks the check sum, and if the decoding is successful, the information negotiation process ends, and if the decoding is not successful, steps S400-S500 are repeatedly performed until the key is consistent or the maximum interaction round number is reached.
2. The PAC-AIR hybrid information negotiation method for a QKD system according to claim 1, characterized in that: The convolutional encoding generating polynomial in S100 is g(D) = 1 + D + D 3 +D 7 +D 10 .
3. The PAC-AIR hybrid information negotiation method for a QKD system according to claim 2, characterized in that: The block length n of the codeword obtained by performing the polar code encoding in S100 is 2 10 -2 14 bits.
4. The PAC-AIR hybrid information negotiation method for a QKD system according to claim 3, characterized in that: In S300, SCL decoding algorithm is used for decoding.
5. The PAC-AIR hybrid information negotiation method for a QKD system according to claim 4, characterized in that: In S300, the metric function of SCL decoding is: wherein PM (i) L represents the path metric value of the i-th decoding i u represents the log-likelihood ratio of i bits i y represents the sequence obtained at the receiving end 6. The PAC-AIR hybrid information negotiation method for a QKD system according to claim 5, characterized in that: In S300, the check sum for checking decoding success and failure is the number of 1s in the bit sequence.
7. The PAC-AIR hybrid information negotiation method for a QKD system according to claim 6, characterized in that: The list size L of the SCL decoding algorithm is 16. 8.A PAC-AIR hybrid information negotiation system for a QKD system, characterized in that: The system has program modules corresponding to the steps of the method according to any one of claims 1-7, and when running, the steps in the PAC-AIR hybrid information negotiation method for a QKD system are executed.
9. A computer-readable storage medium, characterized in that: The computer readable storage medium stores a computer program, and the computer program is configured to realize the steps in the PAC-AIR hybrid information negotiation method for a QKD system according to any one of claims 1-7 when called by the processor.