A method for designing multi-user anti-interception optical coding codes

Abstract

This invention relates to the field of coding technology improvement and provides a method for designing multi-user anti-interception optical coding codewords, including: S1, selecting a prime number p and constructing a prime number sequence S in the finite field GF(p). i S2. Construct the corresponding prime number C in the finite field GF(p). i S3, based on the prime number sequence S i Hesu Digital C i S4. Construct the corresponding interfering user address code using the address code of the legitimate user; S5. Eliminate interfering user address codes that exceed the preset value based on the cross-correlation value. The system can accommodate multiple legitimate users. It only needs to ensure that the codewords of the interfering users are orthogonal to the codewords of each legitimate user, while the codewords between interfering users do not need to be orthogonal. This greatly increases the codeword capacity of the interfering users, effectively preventing eavesdroppers from cracking legitimate user information through codeword search, and increasing the physical layer security of the optical network.

Description

Technical Field

[0001] This invention belongs to the field of coding technology improvement, and in particular relates to a design method for multi-user anti-interception optical coding codewords. Background Technology

[0002] Optical Code Division Multiple Access (OCDMA) systems possess multiple protection functions, enabling secure transmission of optical information. Their main advantages include: resistance to interception, resistance to attacks, authentication, and anonymity. To prevent eavesdroppers from using codeword search methods to scan the address codes of legitimate users one by one for cracking, it is necessary to design address codes with large capacity.

[0003] Currently, many scholars both domestically and internationally have constructed various OCDMA address codes. Sharr.AA et al. constructed a prime number (PC) code, with a codeword capacity of p-1 and a code length of p. 2 The code weight is p, and the cross-correlation limit is 2. Maric.S. et al. proposed a new Extended Prime Code (EPC), which improves the cross-correlation properties of codewords by inserting p-1 "0"s after each basic prime codeword sequence. The codeword capacity of EPC is p, the code length is p(2p-1), the code weight is p, and the cross-correlation limit is 1. Sharr.AA et al. constructed optical orthogonal codes with an autocorrelation limit of 1. The cross-correlation between codewords in optical orthogonal codes is 1, and they are called equal-weight optical orthogonal codes. The upper bound of the codeword capacity is determined by the Johnson bound. There are direct construction methods, algebraic construction methods, and recursive construction methods for optical orthogonal codes. The construction methods for optical orthogonal codes proposed in domestic and foreign literature are still very limited, and most of them are proposed for some special cases.

[0004] Based on prime numbers, Tancevski et al. constructed PC / PC and EQC / PC codes. The codeword capacity of the PC / PC code is p(p-1), and the code length is p. 2 The code weight is p, the autocorrelation limit is 0, and the cross-correlation limit is 1. The codeword capacity of EQC / PC is p(p-1). 2 The codeword length is p(2p-1), the code weight is p, the autocorrelation limit is 0, and the cross-correlation limit is 2. Wan Shengpeng et al. constructed PC / OOC codes based on prime numbers and optical orthogonal codes. Its codeword capacity is mpL, the codeword length is pL, the code weight is m, the autocorrelation limit is 0, and the cross-correlation limit is 1. Li Chuanqi et al. constructed two-dimensional 2D-OOC codes and QPC codes. The codeword capacity of the 2D-OOC code is n(n+1)Φ, and the codeword length is n... 2 The code weight is n, Φ is the codeword capacity of the next dimension of OOC with the same code length and code weight, the autocorrelation limit is 0, and the cross-correlation limit is 1. Zhou Xiuli et al. constructed MPC / OOC codes based on optical orthogonal frequency hopping codes and improved prime codes, with a codeword capacity of p. 2 LΦ, code length p 2The code weight is p, the number of available wavelengths is L, the autocorrelation limit is 0, and the cross-correlation limit is 1. Yin Hongxi et al. constructed a two-dimensional OCFHC / OOC code, using OCFHC and OOC as wavelength frequency hopping and time spreading modes respectively, providing more available wavelengths. The codeword capacity theoretically reached the upper bound, with an autocorrelation limit of 0 and a cross-correlation limit of 1. Chen Zhiwen et al. constructed a two-dimensional bipolar single coincidence sequence BOCS based on the single coincidence sequence OCS. When the code length is N, the codeword capacity of BOCS is N times that of OCS. Tan Pengfei et al. constructed an ESPC / QCHC code with a codeword capacity of pq(q-1), a code length of p(2p-1), a code weight of p, an autocorrelation limit of 0, and a cross-correlation limit of 1. Guan Chenglong et al. used the modified quadratic digit MSPC as the time spreading sequence and OCS as the frequency hopping sequence. Compared with PC / OCS codes, the codeword capacity is increased while the correlation between codewords is smaller, which can reduce the bit error rate of the system. Tan Yeteng et al. constructed a high-capacity two-dimensional frequency hopping / time-spreading address code. In this system, there is only one legitimate user as the master user, and the others are interference users. The interference users only need to be orthogonal to the master user, while the interference users do not need to be orthogonal to each other, which significantly improves the codeword capacity of the legitimate user.

[0005] In multi-user OCDMA systems, the upper bound of the capacity of optical orthogonal address codes is determined by the Johnson bound. For multi-user OCDMA systems, because the address codes must satisfy orthogonality requirements, the codeword capacity of the address codes is relatively small. For example, for a PC / PC code with a code weight of 23 and a code length of 529, the codeword capacity is 506. When an eavesdropper uses a brute-force attack, they only need to search all the codewords one by one to crack the legitimate user's information. Therefore, to improve the physical layer security of multi-user two-dimensional OCDMA systems, it is necessary to design large-capacity two-dimensional address codes to effectively prevent brute-force attacks by eavesdroppers. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-user anti-interception optical coding codeword design method, which aims to solve the above-mentioned technical problems.

[0007] This invention is implemented as follows: a multi-user anti-interception optical coding codeword design method, the multi-user anti-interception optical coding codeword design method comprising the following steps:

[0008] S1. Choose a prime number p, and construct a prime number sequence S in the finite field GF(p). i ;

[0009] S2. Construct the corresponding prime number C in the finite field GF(p). i =(c i,0 ,c i,1 ,…,c i,k ,…,

[0010] c i,N-1 ), 0≤i≤p-1, N=p 2 ;

[0011] S3, based on the prime number sequence S i Hesu Digital C i Create a QR code;

[0012] S4. Construct the corresponding interference user address code using the address code of the legitimate user;

[0013] S5. Eliminate interfering user address codes that are greater than the preset value based on the cross-correlation value.

[0014] A further technical solution of the present invention is that step S1 further includes the following step:

[0015] S11. Generate a sequence of p prime numbers S i ={s i,0 ,s i,1 ,…,s i,j ,…,s i,p-1}, where s i,j =i×j(mod p), 0≤i≤p-1, 0≤j≤p-1.

[0016] A further technical solution of the present invention is that step S2 further includes the following step:

[0017] S21. Choose any sequence of prime numbers S i The corresponding elemental digit C is formed. i =(c i,0 ,c i,1 ,…,c i,k ,…,c i,N-1 ), 0≤i≤p-1, N=p 2 Where, when k = s i,j When +jp, c i,k =1, otherwise 0.

[0018] A further technical solution of the present invention is that step S3 further includes the following step:

[0019] S31. Using prime numbers as time-domain extended codes and prime number sequences as wavelength frequency hopping codes, the two are combined in a one-to-one correspondence to form a two-dimensional address code.

[0020] A further technical solution of the present invention is that step S4 further includes the following step:

[0021] S41. Perform a different cyclic right shift on each pulse in each valid user address code to construct the corresponding interference user address code.

[0022] A further technical solution of the present invention is that step S5 further includes the following step:

[0023] S51. Calculate the cross-correlation value between each interfering user address code and each legitimate user address code;

[0024] S52. Remove interfering user address codes whose calculated cross-correlation values ​​are greater than the preset value.

[0025] A further technical solution of the present invention is: in step S21, the length of the elemental digit is p. 2 The code weight is p, and the codeword capacity is p.

[0026] The beneficial effects of this invention are: the system can accommodate multiple legitimate users, only requiring that the codewords of interfering users are orthogonal to the codewords of each legitimate user, while the codewords between interfering users do not need to be orthogonal. This greatly increases the codeword capacity of interfering users, effectively preventing eavesdroppers from cracking legitimate user information through codeword search, and increasing the physical layer security of optical networks. Therefore, the multi-user anti-interception optical coding method of this application can realize a high-security, high-capacity OCDMA system, applicable to optical networks with high security requirements. Attached Figure Description

[0027] Figure 1 This is a flowchart of a multi-user anti-interception optical coding codeword design method provided in an embodiment of the present invention.

[0028] Figure 2 This is a schematic diagram illustrating the cross-correlation between the legitimate user 1 and its interfering users, provided in an embodiment of the present invention.

[0029] Figure 3 This is a schematic diagram of the cross-correlation between legitimate user 1 and legitimate user 2 and interfering users provided in an embodiment of the present invention.

[0030] Figure 4 This is a schematic diagram of the cross-correlation between legitimate user 1 and legitimate user 3 and interfering users provided in an embodiment of the present invention.

[0031] Figure 5 This is a schematic diagram of the cross-correlation between legitimate user 2 and legitimate user 1 and the interfering user provided in an embodiment of the present invention.

[0032] Figure 6 This is a schematic diagram illustrating the cross-correlation between the legitimate user 2 and its interfering users provided in an embodiment of the present invention.

[0033] Figure 7 This is a schematic diagram of the cross-correlation between legitimate user 2 and legitimate user 3 and interfering users provided in an embodiment of the present invention.

[0034] Figure 8This is a schematic diagram of the cross-correlation between legitimate user 3 and legitimate user 1, provided in an embodiment of the present invention.

[0035] Figure 9 This is a schematic diagram of the cross-correlation between legitimate user 3 and legitimate user 2 and interfering users provided in an embodiment of the present invention. Detailed Implementation

[0036] like Figure 1 The flowchart of the multi-user anti-interception optical coding codeword design method provided by the present invention is shown below in detail:

[0037] The system has multiple legitimate users. The codewords of interfering users only need to be orthogonal to the codewords of legitimate users, while the codewords of interfering users do not need to be orthogonal to each other. This greatly increases the number of interfering user codewords in the system, thereby significantly improving the system's anti-interception performance.

[0038] Step S1: Select a prime number p, and construct a prime number sequence S in the finite field GF(p). i Choose a prime number p and construct a finite field GF(p). First, generate a sequence S of p prime numbers. i ={s i,0 ,s i,1 ,…,s i,j ,…,s i,p-1}, where s i,j = i × j (mod p), 0 ≤ i ≤ p - 1, 0 ≤ j ≤ p - 1. Taking p = 5 as an example,

[0039] S0={0,0,0,0,0}, S1={0,1,2,3,4}, S2={0,2,4,1,3}, S3={0,3,1,4,2}, S4={0,4,3,2,1}.

[0040] Step S2: Construct the corresponding prime number C in the finite field GF(p). i =(c i,0 ,c i,1 ,…,c i,k ,…,c i,N-1 ), 0≤i≤p-1, N=p 2 Choose any sequence of prime numbers S i The corresponding elemental digit C is formed. i =(c i,0 ,c i,1 ,…,c i,k ,…,c i,N-1 ), 0≤i≤p-1, N=p 2 Where, when k = s i,j When +jp, c i,k =1, otherwise 0. Therefore, the length of a prime number is p. 2The code weight is p, and the codeword capacity is p. Taking p=5 as an example, C0={10000, 10000, 10000, 10000, 10000}, C1={10000, 01000, 00100, 00010, 00001}, C2={10000, 00100, 00001, 01000, 00010}, C3={10000, 00010, 01000, 00001, 00100}, C4={10000, 00001, 00010, 00100, 01000}.

[0041] Step S3, based on the prime number sequence S i Hesu Digital C i Construct a QR code; using prime numbers as the time-domain extended code and prime number sequences as the wavelength frequency-hopping code, the two are combined one-to-one to form a QR codeword. Excluding S0 and C0, a maximum of (p-1) codewords for legitimate users can be obtained. Taking p=5 as an example, C1 can choose one of S1 to S4 as the frequency hopping code. If C1 chooses S3, then C2 can only choose one of S1, S2, and S4. If C2 chooses S4, then C3 can only choose one of S1 and S2, leaving C4 as the remaining one. The legal user codewords formed are as follows: {λ0 0000, 0λ3000, 00λ100, 000λ40, 0000λ2}, {λ00000, 00λ400, 0000λ3, 0λ2000, 000λ10}, {λ00000, 000λ10, 0λ2000, 0000λ3, 00λ400}, {λ00000, 0000λ2, 000λ40, 00λ100, 0λ3000}.

[0042] Step S4: Construct corresponding interfering user address codes using the address codes of legitimate users. For each legitimate user's address code, perform a different cyclic right shift on each pulse to construct the corresponding interfering user address code. For example, for the prime number frequency hopping code {λ0 0000, 0λ3000, 00λ100, 000λ40, 0000λ2}, performing a different cyclic right shift on each pulse yields 5! = 120 possible codes, thus constructing 120 interfering user address codes. For example, the codewords corresponding to the cyclic delay (4,1,2,0,3) are {0000λ0, 00λ300, 0000λ1, 000λ40, 00λ200}; the codewords corresponding to the cyclic delay (2,1,3,4,0) are {00λ000, 00λ300, λ10000, 00λ400, 0000λ2}; and the codewords corresponding to the cyclic delay (3,4,0,1,2) are {000λ00, λ30000, 00λ100, 0000λ4, 0λ2000}. Clearly, the codewords of the legitimate user and the corresponding interfering user codewords are orthogonal, while the codewords of the interfering users are not orthogonal to each other. Similarly, for another prime frequency hopping code {λ00000, 00λ400, 0000λ3, 0λ2000, 000λ10}, performing a different cyclic right shift on each pulse yields 5! = 120 possible codes, which can also construct 120 interfering user address codes. Therefore, given any prime number p, for each legitimate user's address code, at most p! interfering user address codes can be constructed.

[0043] Step S5: Eliminate interfering user address codes that are greater than a preset value based on the cross-correlation value. For each interfering user address code, verify the cross-correlation value between the code and each legitimate user address code. If the cross-correlation value is greater than 1, then eliminate the interfering user address code. This ensures that each interfering user codeword is orthogonal to all legitimate user codewords.

[0044] Traditional prime number frequency hopping codes, given a prime number p, have a total codeword capacity of p(p-1). However, the high-capacity prime number frequency hopping code constructed in this paper allows for (p-1) legitimate users and a maximum of (p-1)p! interfering user address codes. Taking p=31, the traditional prime number frequency hopping code has a codeword capacity of 930 for both legitimate and interfering users. In contrast, the codeword capacity constructed in this paper, with a codeword capacity of 30 legitimate users, results in a maximum interfering user codeword capacity of 2.5E+35. Therefore, the number of interfering codewords corresponding to each legitimate user is significantly larger than the codeword capacity of the traditional prime number frequency hopping code. In other words, the multi-user anti-interception code constructed in this paper, by greatly increasing the codeword capacity for interfering users, can effectively prevent brute-force search attacks and improve the physical layer security of the OCDMA system.

[0045] For the case of p=5, some anti-interception codewords are shown in Table 1.

[0046] Table 1 shows some anti-interception codewords when p=5.

[0047]

[0048]

[0049] Based on the codewords in Table 1, verify the cross-correlation value between the codewords of legitimate users and those of interfering users. The cross-correlation value between legitimate user 1 and interfering users is as follows: Figure 2-4 As shown

[0050] The cross-correlation values ​​between legitimate user 2 and all interfering users, such as Figure 5-7 As shown.

[0051] The cross-correlation values ​​between legitimate user 3 and all interfering users, such as Figure 8-9 As shown.

[0052] The system can accommodate multiple legitimate users. It only requires ensuring that the codewords of interfering users are orthogonal to the codewords of each legitimate user, while the codewords between interfering users do not need to be orthogonal. This significantly increases the codeword capacity of interfering users, effectively preventing eavesdroppers from cracking legitimate user information through codeword search, thus enhancing the physical layer security of the optical network. Therefore, the multi-user anti-interception optical coding method of this invention can realize a high-security, high-capacity OCDMA system, applicable to optical networks with high security requirements.

[0053] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for designing multi-user anti-interception optical coded codewords, characterized in that, The multi-user anti-interception optical coding codeword design method includes the following steps: S1. Choose a prime number p, and construct a prime number sequence S in the finite field GF(p). i ={s i,0 , s i,1 , … , s i,j , … ,s i,p-1 }, where s i,j =i×j (mod p), 0≤i≤p-1, 0≤j≤p-1; S2. Construct the corresponding prime number C in the finite field GF(p). i =(c i,0 , c i,1 ,…, c i,k ,…, c i,N-1 ), 0≤i≤p-1,N=p 2 Where, when k = s i,j When +jp, c i,k =1, otherwise 0; S3, based on the prime number sequence S i Hesu Digital C i Create a QR code; S4. Construct the corresponding interference user address code using the address code of the legitimate user; S5. Eliminate interfering user address codes that are greater than the preset value based on the cross-correlation value; Step S3 also includes the following steps: S31. Using prime numbers as time-domain extended codes and prime number sequences as wavelength frequency hopping codes, the two are combined in a one-to-one correspondence to form a two-dimensional address code.

2. The multi-user anti-interception optical coding codeword design method according to claim 1, characterized in that, Step S4 also includes the following steps: S41. Perform a different cyclic right shift on each pulse in each valid user address code to construct the corresponding interference user address code.

3. The multi-user anti-interception optical coding codeword design method according to claim 2, characterized in that, Step S5 also includes the following steps: S51. Calculate the cross-correlation value between each interfering user address code and each legitimate user address code; S52. Remove interfering user address codes whose calculated cross-correlation values ​​are greater than the preset value.

4. The multi-user anti-interception optical coding codeword design method according to claim 3, characterized in that, In step S2, the length of the prime number is p. 2 The code weight is p, and the codeword capacity is p.

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