High-speed quantum key distribution privacy amplification method based on SQH hash function

Abstract

The invention discloses a high-speed quantum key distribution privacy amplification method based on an SQH hash function, and belongs to the technical field of quantum communication and information security. The SQH hash function is adopted, and square operation is introduced to replace traditional multiplication operation, so that the calculation complexity is remarkably reduced, the security of a key is ensured, and the security of the key is improved. The processing efficiency of privacy amplification is improved, and the method is particularly suitable for application scenes needing efficient privacy enhancement in a quantum key distribution system; through the technical scheme of the invention, the security in the privacy amplification process can be ensured, the calculation efficiency is remarkably improved, the consumption of hardware resources is reduced, and noise interference in a quantum communication environment can be effectively coped with, so that the requirements of a quantum key distribution system for efficient and rapid privacy enhancement in the future are met.

Description

Technical Field

[0001] The present invention belongs to the technical fields of quantum communication and information security, and particularly relates to a high-speed quantum key distribution privacy amplification method based on the SQH hash function. Background Art

[0002] Quantum key distribution (QKD) is an important application of quantum communication, which can securely distribute keys through the basic principles of quantum mechanics in an untrusted channel. QKD technology mainly relies on the unclonability of quantum bits (qubits) and the unpredictability of quantum states, thus ensuring a high level of security in the key distribution process.

[0003] In practical applications, although QKD can ensure the secure distribution of keys, due to the influence of noise and interference during the transmission of quantum signals, the generated keys may contain a certain number of error bits, affecting the security of the keys. Therefore, after quantum key distribution, it is often necessary to use privacy amplification technology to eliminate these potential errors and enhance the security of the keys.

[0004] The goal of privacy amplification algorithms is to minimize potential error bits and information leakage through post-processing of shared keys, thereby improving the security of the final keys. Existing privacy amplification methods include various algorithms based on hash functions, such as classical hash methods based on Boolean functions, scalable hash functions, etc. These methods effectively correct noise and potential attacks, but still have problems such as high computational complexity and low efficiency. Therefore, high-speed privacy amplification algorithms have become the focus of research. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a high-speed quantum key distribution privacy amplification method based on the SQH hash function for the quantum key distribution QKD system in view of the deficiencies of the background art, so as to solve the problems of high computational complexity, low efficiency, and performance degradation in the case of long key processing and large noise interference in existing privacy amplification algorithms.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] A high-speed quantum key distribution privacy amplification method based on the SQH hash function, which adopts the SQH hash function and applies the SQH hash function family to quantum key distribution privacy amplification by introducing a square operation to replace the traditional multiplication operation, specifically including the following steps;

[0008] Step 1, input the original key x of j×k bits, and divide it into k blocks, denoted as (x1, x2, x3,..., x k ), where each xi is a j-bit binary bit, where i ∈ k;

[0009] Step 2: Randomly generate a j×k-bit random number M and divide it into k blocks, denoted as (m1, m2, m3,..., m k ), where each m i is a j-bit binary bit;

[0010] Step 3: Calculate the prime number p and select a Mersenne prime;

[0011] Step 4: Calculate (m i +x i ) and NTT(m i +x i ) in parallel, where NTT is the number-theoretic transform;

[0012] Step 5: Use accelerated square to calculate NTT(m i +x i )*NTT(m i +x i ) in parallel;

[0013] Step 6: Calculate INTT(NTT(m i +x i )*NTT(m i +x i )) in parallel and denote it as t i , where INTT is the inverse number-theoretic transform;

[0014] Step 7: After summing t i and performing a modulo operation, obtain the final r-bit secure key R.

[0015] As a further preferred solution of the high-speed quantum key distribution privacy amplification method based on the SQH hash function of the present invention, the expression of the SQH hash function is:

[0016]

[0017] where h(M,X) is the SQH hash function.

[0018] As a further preferred solution of the high-speed quantum key distribution privacy amplification method based on the SQH hash function of the present invention, in Step 3, the specific calculation of p is as follows: p = 2 r -1, where r > j.

[0019] As a further preferred solution of the high-speed quantum key distribution privacy amplification method based on the SQH hash function of the present invention, in Step 4, denote x in NTT(x) as (x1, x2,... x N ); the formula for the NTT transform is: Among them, W N is a primitive root modulo p, and {W N 1 , W N 2 ,..., W N N} are all distinct, and W N N = 1 mod p.

[0020] Compared with the prior art, the present invention adopting the above technical solutions has the following technical effects:

[0021] 1. The present invention realizes the privacy amplification method in the quantum key distribution system based on the SQH hash algorithm, and solves the problems of high computational complexity, low efficiency and performance degradation when processing long keys in the prior art (such as HMAC, MMH, etc.); by introducing square operations to replace traditional multiplication operations, the computational efficiency of privacy amplification is significantly improved, and the consumption of hardware resources is reduced;

[0022] 2. The present invention improves the computational efficiency: the privacy amplification method of the present invention uses the SQH hash algorithm, which reduces the computational complexity by replacing traditional multiplication operations with square operations; compared with the commonly used MMH in the prior art, the present invention significantly improves the computational speed under the same key length and the same security requirements;

[0023] 3. The present invention reduces the consumption of hardware resources: when processing quantum keys, the present invention uses square operations to reduce the need for multiplication operations, reducing the occupation of computational resources and storage space;

[0024] 4. The present invention enhances the security of quantum keys: based on the design of universal hash functions, the present invention significantly improves the computational efficiency while ensuring security. Through the privacy amplification process, potential error bits and information leakage in quantum keys can be effectively reduced, enhancing the confidentiality and anti-attack ability of the keys; compared with the prior art, the present invention can better cope with common noise interference in quantum communication and improve the security of the quantum key distribution system in complex environments;

[0025] 5. The present invention has strong adaptability and is applicable to different quantum key distribution scenarios: the privacy amplification method of the present invention can flexibly adjust the parameters of the hash function according to actual needs to adapt to different quantum key distribution systems and application scenarios; by introducing randomized parameters in the hash calculation process, the flexibility and scalability of the method are increased, meeting the application requirements of different security levels and computational needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1It is a flowchart of a high-speed quantum key distribution privacy amplification method based on the SQH hash function of the present invention. Detailed implementation manners

[0027] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0028] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention. The present invention will be described in detail below according to the accompanying drawings and preferred embodiments, and the purpose and effect of the present invention will become more obvious. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0029] The purpose of the present invention is to provide a privacy amplification method based on the SQH hash algorithm for use in a quantum key distribution (QKD) system to solve the problems of high computational complexity, low efficiency, and performance degradation in the case of long key processing and large noise interference in existing privacy amplification algorithms.

[0030] In traditional privacy amplification schemes, common hash methods (such as MMH) can effectively improve the security of keys, but they usually rely on complex multiplication and addition operations, resulting in excessive consumption of computing resources and slow processing speed when dealing with long quantum keys. This problem is more obvious especially in quantum key distribution environments with high noise or requiring fast real-time processing. Therefore, the privacy amplification methods in the prior art cannot meet the requirements for efficient, fast, and low computational complexity privacy enhancement.

[0031] To solve this problem, the present invention proposes a new privacy amplification algorithm that uses the SQH hash function and significantly reduces the computational complexity by introducing a squaring operation to replace the traditional multiplication operation. This innovative design not only ensures the security of the key but also improves the processing efficiency of privacy amplification, especially suitable for application scenarios in quantum key distribution systems that require efficient privacy enhancement.

[0032] Through the technical solution of the present invention, it is possible to significantly improve the computational efficiency while ensuring the security during the privacy amplification process, reduce the consumption of hardware resources, and effectively cope with noise interference in the quantum communication environment, thereby meeting the requirements for efficient and fast privacy enhancement in future quantum key distribution systems.

[0033] A high-speed quantum key distribution privacy amplification method based on the SQH hash function. The SQH hash function is adopted, and by introducing a squaring operation to replace the traditional multiplication operation, the SQH hash function family is applied to quantum key distribution privacy amplification. The specific steps are as follows;

[0034] Step 1: Input the j×k-bit original key x, and divide it into k blocks, denoted as (x1, x2, x3,..., x k ), where each x i is a j-bit binary bit, and i ∈ k;

[0035] Step 2: Randomly generate a j×k-bit random number m, and divide it into k blocks, denoted as (m1, m2, m3,..., m k ), where each m i is a j-bit binary bit;

[0036] Step 3: Calculate the prime number p, and select a Mersenne prime number. The specific calculation of p is as follows: p = 2 r -1, where r > j;

[0037] Step 4: Calculate (m i +x i ) and NTT(m i +x i ) in parallel, where NTT is the number-theoretic transform;

[0038] Denote x in NTT(x) as (x1, x2,...x N ). The formula for the NTT transform is: where W N is the unit root of mod p, and {W N 1 , W N 2 ,..., W N N} are distinct from each other, and W N N = 1 mod p.

[0039] Step 5: Use accelerated squaring to calculate NTT(m i +x i )*NTT(m i +x i ) in parallel;

[0040] Step 6: Calculate INTT(NTT(m i +x i )*NTT(m i +x i )) in parallel, denoted as t i , where INTT is the inverse number-theoretic transform;

[0041] Step 7, take t i After summation, perform a modulo operation to obtain the final r-bit secure key R.

[0042] The expression of the SQH hash function is:

[0043]

[0044] where h(M,X) is the SQH hash function.

[0045] Example 1: Apply the SQH hash function family to quantum key distribution privacy amplification using the following steps:

[0046] Step 1, input the 112130000-bit raw key x, and divide it into 10 blocks, denoted as (x1,x2,x3,...,x 10 ), where each x i is 11213000-bit binary bits.

[0047] Step 2, randomly generate a 112130000-bit random number m, and divide it into 10 blocks, denoted as (m1,m2,m3,...,m 10 ), where each m i is 11213000-bit binary bits.

[0048] Step 3, calculate p, select a Mersenne prime number in the form of p = 2 r -1, where r is 42643801.

[0049] Step 4, calculate (m i +x i ) in parallel, and calculate NTT(m i +x i ) in parallel; the formula for the NTT transform is

[0050] Step 5, use accelerated squaring to calculate NTT(m i +x i )*NTT(m i +x i ) in parallel.

[0051] Step 6, calculate INTT(NTT(m i +x i )*NTT(m i +x i )) in parallel, denoted as t i .

[0052] Step 7, take t iAfter summation, a modulo operation is performed to obtain the final 42643801-bit secure key R.

[0053] The present invention implements a privacy amplification method in a quantum key distribution system based on the SQH hash algorithm, solving the problems of high computational complexity, low efficiency, and performance degradation when processing long keys in the prior art (such as HMAC, MMH, etc.). By introducing a squaring operation to replace the traditional multiplication operation, the computational efficiency of privacy amplification is significantly improved, and the consumption of hardware resources is reduced.

[0054] The privacy amplification method of the present invention uses the SQH hash algorithm, which reduces the computational complexity by replacing the traditional multiplication operation with a squaring operation. Compared with the commonly used MMH in the prior art, the present invention significantly improves the computational speed under the same key length and the same security requirements. In the experiment, tests using an Apple M1 processor show that when processing long keys using the SQH hash algorithm of the present invention, the computational speed is increased by approximately 43% compared to the traditional MMH scheme. This acceleration effect is particularly suitable for quantum key distribution systems that require real-time performance and efficient computation.

[0055] When processing quantum keys, the present invention reduces the need for multiplication operations by using a squaring operation, reducing the occupation of computational resources and storage space. Experimental results show that when the privacy amplification method of the present invention is run on an ARM7 processor, the memory consumption is reduced by approximately 42% compared to the MMH and HMAC-SHA1 schemes. This makes the method very suitable for hardware platforms with limited computational resources, such as embedded devices and smart cards.

[0056] Based on the design of a universal hash function, the present invention significantly improves the computational efficiency while ensuring security. Through the privacy amplification process, potential error bits and information leakage in the quantum key can be effectively reduced, enhancing the confidentiality and anti-attack ability of the key. Compared with the prior art, the present invention can better cope with common noise interference in quantum communication and improve the security of the quantum key distribution system in complex environments.

[0057] The privacy amplification method of the present invention can flexibly adjust the parameters of the hash function according to actual needs to adapt to different quantum key distribution systems and application scenarios. By introducing randomized parameters in the hash calculation process, the flexibility and scalability of the method are increased, meeting the application requirements of different security levels and computational needs.

[0058] Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not used to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, for those skilled in the art, they can still modify the technical solutions described in the foregoing examples or perform equivalent replacements on some of the technical features. Any modifications, equivalent replacements, etc. made within the spirit and principle of the invention shall be included within the protection scope of the invention. All technical features in this embodiment can be freely combined according to actual needs.

Claims

1. A high-speed quantum key distribution privacy amplification method based on the SQH hash function, characterized by: The SQH hash function is used to replace the traditional multiplication operation by introducing the square operation, and the SQH hash function family is applied to the privacy amplification of quantum key distribution, which specifically includes the following steps; Step 1: Input the j×k bit original key x and divide it into k blocks, represented as (x1, x2, x3, ..., x k ), where each x i is a j-bit binary bit, i∈k; Step 2: randomly generate a j×k bit random number M and divide it into k blocks, represented as (m1,m2,m3,...,m k ), where each m i is a j-bit binary bit, i∈k; Step 3, calculate the prime number p and select the Mersenne prime number; Step 4, parallel computing (m i +x i ) and NTT(m i +x i ), where NTT is a number theoretic transformation; Step 5: Use the square of the acceleration to parallelize the calculation of NTT(m i +x i )*NTT(m i +x i ); Step 6: Parallel calculation of INTT(NTT(m i +x i )*NTT(m i +x i )), denoted as t i , INTT is the inverse number theory transformation; Step 7: i After the summation, a modular operation is performed to obtain the final r-bit security key R.

2. The privacy amplification method for high-speed quantum key distribution based on the SQH hash function according to claim 1 is characterized in that: The expression of the SQH hash function is: Among them, h(M,X) is the SQH hash function.

3. The privacy amplification method for high-speed quantum key distribution based on the SQH hash function according to claim 1, characterized in that: In step 3, the specific calculation of p is as follows: p = 2 r -1, where r>j.

4. The privacy amplification method for high-speed quantum key distribution based on the SQH hash function according to claim 1, characterized in that: In step 4, let x in NTT(x) be (x1, x2, … x N ); the formula for NTT transformation is: Among them, W N is the unit root of modp, and {W N 1 ,W N 2 ,...,W N N } are different from each other, and W N N =1mod p.

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