A privacy-encoded caching method based on MDS codes and random permutations

Abstract

This invention discloses a privacy-encoded caching method based on MDS codes and random permutations. The implementation process includes encoding the cached content, encoding the broadcast signal, and decoding the requested file by the user. Based on MDS codes and random permutation techniques, this method is applicable to privacy-encoded caching problems where the number of users K is greater than or equal to the number of files N. When K ≥ N and the cache size is small, or when 2N - 2 ≥ K ≥ N ≥ 3 and the cache size is small, the minimum communication rate can be achieved, i.e., the broadcast signal size required to transmit a unit of file is minimized.

Description

Technical Field

[0001] This invention relates to the field of information theory, and in particular to a privacy coding caching method for the privacy coding caching problem where the number of users K is greater than or equal to the number of files N. Background Technology

[0002] In traditional coding caching solutions, participating users may leak the indexes of files requested by other users. To address this privacy leak issue, some research has focused on coding caching with demand privacy constraints, aiming to ensure that user request information is not leaked. Currently, existing research mainly provides the following types of solutions: rate-optimal privacy coding caching methods, rate-optimal methods under the condition of K=2 users, and methods for arbitrary user numbers K and arbitrary number of files N. or The optimal rate-efficiency method under given conditions. For the privacy-encoded caching problem with arbitrary numbers of users K and arbitrary numbers of files N, the precise trade-off between cache size and rate remains an unsolved problem. Summary of the Invention

[0003] Technical Problem: The technical problem this invention aims to solve is to provide a privacy-preserving coding caching method for privacy-preserving coding caching problems where the number of users K is greater than or equal to the number of files N. Coding caching techniques significantly reduce the communication rate during signal transmission; the use of MDS codes and random permutations helps generate more equivalent file segments than the number of partitions and increases the consistency of transmitted signals under different needs, thus protecting user privacy. Therefore, by combining MDS codes and random permutation strategies, a novel privacy-preserving coding caching scheme is proposed, effectively guaranteeing the privacy of user request information.

[0004] Technical solution: The technical solution adopted in this invention is as follows:

[0005] A privacy-encoded caching method based on MDS codes and random permutations, including cache size. and Two scenarios and the following steps:

[0006] Step 1: There are N files W0, W1, ... W N-1 Trusted servers will cache content Z. k Distribute the data to users k∈[K]=[0:K-1] in the communication system, where K represents the total number of users in the communication system;

[0007] Step 2: Each user k∈[K] sends a file request D to the server. k This indicates a request for a file. There are N files W0, W1, ... WN-1 Any one of the following, the server determines the outcome based on all user requests D = (D0, D1, ..., D...). K-1 ), generating broadcast signal X D And transmit the signal X through an error-free shared link channel. D Broadcast to all users in the system;

[0008] Step 3: Each user k∈[K] receives the broadcast signal X. D And the previously cached content Z k Decode the file you requested

[0009] Furthermore, cache size At that time, the cached content Z in step 1 is placed. k The encoding steps are as follows:

[0010] First, each file W n The subfiles, n∈[N]=[0:N-1], are divided into K+1 disjoint subfiles of equal size by the server, and then encoded using a (2K,K+1) MDS code. n,0 W n,1 ,…,W n,2K-1 Representing file W respectively n 2K MDS encoded segments;

[0011] Next, from all possible permutations of [2K], the server independently and uniformly selects N permutations, using... It means that, where n∈[N], Let p be the permutation vector n The 2k+mth position; the server according to the permutation p n Shuffle 2K MDS encoded segments. The shuffled segments are then used... It means that the conditions are met.

[0012]

[0013] in, For file W n The One MDS encoded segment; the cached content of user k, i.e., Z k , set as

[0014]

[0015] Where P k ~Unif([2K]), k∈[K], are K independent and identically distributed random variables uniformly distributed on the set of integers [2K], and ⊕ represents the XOR operation.

[0016] Furthermore, cache size At that time, in step 2, the broadcast signal X D The encoding steps are as follows:

[0017] The server processes all user requests, D = (D0, D1, ..., D...). K-1 ), producing X' D And auxiliary variables J0 and J1:

[0018] J1=(J 1,k ) k∈[K] ,

[0019] in,

[0020]

[0021] The server sends a broadcast signal X to user k. D By X' D It consists of two parts: the auxiliary variable (J0, J1), that is, X. D =(X′) D ,J0,J1).

[0022] Furthermore, cache size In step 3, each user decodes the requested file. The decoding steps are as follows:

[0023] First, from X D In the middle, user k directly obtains The K MDS encoded segments and their corresponding indices, i.e. and i∈[K];

[0024] Next, user k obtains the following formula: and its corresponding index

[0025]

[0026] Finally, based on the properties of (2K,K+1)MDS codes, user k can... and Obtain The indices of these K+1 MDS encoded segments are determined by... and Provided.

[0027] Furthermore, cache size At that time, the cached content Z in step 1 is placed. k The encoding steps are as follows:

[0028] First, each file W n The data, n∈[N], is divided by the server into (K+1)(N-1) disjoint subfiles of equal size. The server then uses a (2K(N-1),(K+1)(N-1)) MDS code to encode these subfiles into 2K(N-1) MDS segments. These 2K(N-1) MDS segments are represented by W. n,0 W n,1 ,…,W n,2K(N-1)-1 Indicates; the server determines the arrangement based on p n Shuffle 2K MDS encoded segments. The shuffled segments are then used... It means that the conditions are met.

[0029]

[0030] in, For file W n The One MDS encoded segment, It is a permutation that is independently and uniformly selected from all possible permutations of [2K(N-1)]. Let p be the permutation vector n The (2N-2)k+mth bit; the cached content of user k, i.e., Z k , set as

[0031]

[0032] Among them, P k,n ~Unif([2K(N-1)]), k∈[K], n∈[N], are KN independent and identically distributed random variables uniformly distributed on the integer set [2K(N-1)]. k,n ~Unif([K]), k∈[K+1], n∈[N], are (K+1)N independent and identically distributed random variables that are uniformly distributed on the set of integers [K].

[0033] Furthermore, cache size At that time, in step 2, the broadcast signal X D The encoding steps are as follows:

[0034] First, for each requested file, i.e. The server randomly selects a user, denoted as u. n These users are referred to as "leaders," and the set of leaders is defined as follows: in This represents the set of all requested files; while for Define u n It is always equal to 1, that is, u n≡1; When the total number of files N≥3, for each file index n∈[N], define an arbitrary one-to-one mapping function h. n (m), this function maps each file index m∈[N]\{n} to another file index h. n (m)∈[N]\{n,m}, such that if m1≠m2, then h n (m1)≠h n (m2);

[0035] Next, the server generates X' based on all users' requests D. D =(X D,n ) n∈[N+1] and auxiliary variable J0 = (J 0,n ) n∈[N] :

[0036]

[0037] Where, π n =(π) n,0 ,π n,1 ,…,π n,K-1 Let n∈[N] be N permutations that are independently and uniformly selected from all possible permutations of [K], where for k∈[1:K-1], n∈[N].

[0038]

[0039] For k = 0, n ∈ [N],

[0040]

[0041] For k∈[K], n∈[N],

[0042]

[0043] Then, the server generates auxiliary variables. and J3:

[0044]

[0045] Finally, the server sends a broadcast signal X to user k. D By X' D It consists of two parts: the auxiliary variable and the variable X. D =(X′) D (J0, J1, J2, J3).

[0046] Furthermore, cache size In step 3, each user decodes the requested file. The decoding steps are as follows:

[0047] First, user k decodes using the following formula:

[0048]

[0049] Among them, all those used remove Apart from that, all can be in n∈[N]\{D k} was found, and user 0 from Zhongzhidao exist The position in the middle; user k decodes using the following formula

[0050]

[0051] Among them, user k from Zhongzhidao n∈[K]\{D k}exist The position in the middle; the indices of the N MDS encoded segments obtained from the above decoding are determined by... Given, where m∈[N], these indices are known to user k;

[0052] Next, from and In the middle, user k obtains (N-1)K-1 different MDS encoded segments and their corresponding indices; specifically, user k from (N-2)K-1 different MDS encoded segments are directly obtained, and their corresponding indices are determined by... Provided by user k from Directly obtain MDS encoded segments or And user k from Zhongzhidao exist The position and index in Position in the middle; use in sequence In addition to For items other than those specified, user k decodes them using the following formula.

[0053]

[0054] The corresponding indices of the aforementioned K-1 MDS encoded segments are determined by... Given in order;

[0055] Finally, based on the properties of the (2K(N-1),(K+1)(N-1)) MDS code, user k can obtain the (K+1)(N-1) MDS encoded segments and their corresponding indices obtained from the above decoding.

[0056] Beneficial effects: This invention proposes a privacy-encoded caching method based on MDS codes and random permutations. This method, based on MDS codes and random permutations, ensures the privacy of user needs; regarding cache size... and Two scenarios are presented, each demonstrating the achievement of the cache-rate pair. and A privacy-preserving coding caching scheme is proposed. In step one, a novel coding placement method using MDS codes and random permutations is employed. In step two, a random permutation shuffling transmission signal is used, and a corresponding decoding method is designed in step three. This method features a small buffer size. This approach is applicable to any N files satisfying K ≥ N, solving the privacy coding buffer problem for K users, and achieving the minimum communication rate, i.e., minimizing the size of the broadcast signal required to transmit a unit of file; it also addresses the issue of large buffer sizes. It is applicable to the privacy encoding caching problem of N files and K users satisfying K≥N≥3, and achieves the minimum communication rate when 2N-2≥K≥N≥3. Attached Figure Description

[0057] Figure 1 A system model for the privacy encoding caching problem involving N files and K users. Detailed Implementation

[0058] The technical solution of the present invention will be described in detail below, but the scope of protection of the present invention is not limited to the embodiments described.

[0059] A privacy-encoded caching method based on MDS codes and random permutations, including cache size. and Two scenarios and the following steps:

[0060] Step 1: There are N files W0, W1, ... W N-1 Trusted servers will cache content Z. k Distribute the data to users k∈[K]=[0:K-1] in the communication system, where K represents the total number of users in the communication system;

[0061] Step 2: Each user k∈[K] sends a file request D to the server. k This indicates a request for a file. There are N files W0, W1, ... W N-1 Any one of the following, the server determines the outcome based on all user requests D = (D0, D1, ..., D...). K-1 ), generating broadcast signal X D And transmit the signal X through an error-free shared link channel. D Broadcast to all users in the system;

[0062] Step 3: Each user k∈[K] receives the broadcast signal X. D And the previously cached content Z k Decode the file you requested

[0063] Cache size At that time, the cached content Z in step 1 is placed. k The encoding steps are as follows:

[0064] First, each file W n The subfiles, n∈[N]=[0:M-1], are divided into K+1 disjoint subfiles of equal size by the server, and then encoded using a (2K,K+1) MDS code. n,0 W n,1 ,…,W n,2K-1 Representing file W respectively n 2K MDS encoded segments;

[0065] Next, from all possible permutations of [2K], the server independently and uniformly selects N permutations, using... It means that, where n∈[N], Let p be the permutation vector n The 2k+mth position; the server according to the permutation p n Shuffle 2K MDS encoded segments. The shuffled segments are then used... It means that the conditions are met.

[0066]

[0067] in, For file W n The One MDS encoded segment; the cached content of user k, i.e., Z k , set as

[0068]

[0069] Where P k ~Unif([2K]), k∈[K], are K independent and identically distributed random variables uniformly distributed on the set of integers [2K], and ⊕ represents the XOR operation.

[0070] Cache size At that time, in step 2, the broadcast signal X D The encoding steps are as follows:

[0071] The server processes all user requests, D = (D0, D1, ..., D...). K-1 ), producing X' D And auxiliary variables J0 and J1:

[0072] J1=(J 1,k ) k∈[K] ,

[0073] in,

[0074]

[0075] The server sends a broadcast signal X to user k. D By X' D It consists of two parts: the auxiliary variable (J0, J1), that is, X. D =(X′) D ,J0,J1).

[0076] Furthermore, cache size In step 3, each user decodes the requested file. The decoding steps are as follows:

[0077] First, from X D In the middle, user k directly obtains The K MDS encoded segments and their corresponding indices, i.e. and i∈[K];

[0078] Next, user k obtains the following formula: and its corresponding index

[0079]

[0080] Finally, based on the properties of (2K,K+1)MDS codes, user k can... and Obtain The indices of these K+1 MDS encoded segments are determined by... and Provided.

[0081] Cache size At that time, the cached content Z in step 1 is placed. k The encoding steps are as follows:

[0082] First, each file W n The data, n∈[N], is divided by the server into (K+1)(N-1) disjoint subfiles of equal size. The server then uses a (2K(N-1),(K+1)(N-1)) MDS code to encode these subfiles into 2K(N-1) MDS segments. These 2K(N-1) MDS segments are represented by W. n,0 W n,1 ,…,W n,2K(N-1)-1 Indicates; the server determines the arrangement based on p n Shuffle 2K MDS encoded segments. The shuffled segments are then used... It means that the conditions are met.

[0083]

[0084] in, For file W n The One MDS encoded segment, It is a permutation that is independently and uniformly selected from all possible permutations of [2K(N-1)]. Let p be the permutation vector n The (2N-2)k+mth bit; the cached content of user k, i.e., Z k , set as

[0085]

[0086] Among them, P k,n ~Unif([2K(N-1)]), k∈[K], n∈[N], are KN independent and identically distributed random variables uniformly distributed on the integer set [2K(N-1)]. k,n ~Unif([K]), k∈[K+1], n∈[N], are (K+1)N independent and identically distributed random variables that are uniformly distributed on the set of integers [K].

[0087] Cache size At that time, in step 2, the broadcast signal X D The encoding steps are as follows:

[0088] First, for each requested file, i.e. The server randomly selects a user, denoted as u. n These users are referred to as "leaders," and the set of leaders is defined as follows: in This represents the set of all requested files; while for Define u n It is always equal to 1, that is, u n≡1; When the total number of files N≥3, for each file index n∈[N], define an arbitrary one-to-one mapping function h. n (m), this function maps each file index m∈[N]\{n} to another file index h. n (m)∈[N]\{n,m}, such that if m1≠m2, then h n (m1)≠h n (m2);

[0089] Next, the server generates X' based on all users' requests D. D =(X D,n ) n∈[N+1] and auxiliary variable J0 = (J 0,n ) n∈[N] :

[0090]

[0091] Where, π n =(π) n,0 ,π n,1 ,…,π n,K-1 Let n∈[N] be N permutations that are independently and uniformly selected from all possible permutations of [K], where for k∈[1:K-1], n∈[N].

[0092]

[0093] For k = 0, n ∈ [N],

[0094]

[0095] For k∈[K], n∈[N],

[0096]

[0097] Then, the server generates auxiliary variables. and J3:

[0098]

[0099] Finally, the server sends a broadcast signal X to user k. D By X' D It consists of two parts: the auxiliary variable and the variable X. D =(X′) D (J0, J1, J2, J3).

[0100] Cache size In step 3, each user decodes the requested file. The decoding steps are as follows:

[0101] First, user k decodes using the following formula: m∈[N]\{D k}:

[0102]

[0103] Among them, all those used remove Apart from that, all can be in n∈[N]\{D k} was found, and user 0 from Zhongzhidao exist The position in the middle; user k decodes using the following formula

[0104]

[0105] Among them, user k from Zhongzhidao n∈[K]\{D k}exist The position in the middle; the indices of the N MDS encoded segments obtained from the above decoding are determined by... Given, where m∈[N], these indices are known to user k;

[0106] Next, from and In the middle, user k obtains (N-1)K-1 different MDS encoded segments and their corresponding indices; specifically, user k from (N-2)K-1 different MDS encoded segments are directly obtained, and their corresponding indices are determined by... Provided by user k from Directly obtain MDS encoded segments or And user k from Zhongzhidao exist The position and index in Position in the middle; use in sequence In addition to For items other than those specified, user k decodes them using the following formula.

[0107]

[0108] The corresponding indices of the aforementioned K-1 MDS encoded segments are determined by... Given in order;

[0109] Finally, based on the properties of the (2K(N-1),(K+1)(N-1)) MDS code, user k can obtain the (K+1)(N-1) MDS encoded segments and their corresponding indices obtained from the above decoding.

[0110] like Figure 1 As shown, this invention proposes a privacy-encoded caching method based on MDS codes and random permutations. The system model includes an accessible set of N files W0, W1, ... W N-1 A server and K users, each with a cache size of M, are connected via an error-free shared link. During the cache placement phase, the server will store Z cached content. k Distributed to each user; during the signaling phase, user k sends request D to the server. k The server processes all user requests, D = (D0, D1, ..., D...). K-1 Broadcast signal X D During the file decoding phase, user k determines the data based on the received signal X. D Local cache content Z k Decode the request file During this process, no user can deduce the reason why they requested D. k Other request information besides [other information].

[0111] The following is an example:

[0112] This embodiment considers K = 2 users and N = 2 files, corresponding to... The specific solutions for this situation are as follows:

[0113] The server divides files W0 and W1 into three non-overlapping, equally sized subfiles, and then encodes these subfiles using a (4,3) MDS code. The resulting four MDS encoded segments are respectively labeled with W... n,0 W n,1 W n,2 W n,3 This indicates that the segments are assigned according to a randomly generated [0:3] permutation. and Right now, m,k∈{0,1}, where This represents a random permutation that is independently and uniformly selected from all possible permutations of [0:3].

[0114] (1) The cached content of user k, i.e., Z k , set as

[0115]

[0116] P0 and P1 are two independent, identically distributed random variables that are uniformly distributed on the integer set [0:3].

[0117] (2) The broadcast signal X sent by the server to user k D By X' D It consists of two parts: the auxiliary variable (J0, J1), that is, X. D =(X' D ,J0,J1), where X' D The encoding methods for J0 and J1 are given in the following table:

[0118]

[0119] (3) Taking D = (D0, D1) = (0, 1) as an example. User 0 requests file W0 and directly from X D Get and and its index and Then, user 0 calculates... and get and Therefore, based on the properties of the (4,3)MDS code, user 0 can obtain... and W0 is obtained from X'. Similarly, user 1 obtains W0 directly from X'. D Get and and through decoding Through the corresponding index, i.e. and User 1 can... and Decode W1. Other cases follow a similar decoding method.

[0120] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A privacy-encoded caching method based on MDS codes and random permutations, characterized in that, Including cache size The method includes the following steps: Step 1: There are N files W0, W1, ... W N-1 Trusted servers will cache content Z. k Distribute the data to users k∈[K]=[0:K-1] in the communication system, where K represents the total number of users in the communication system; In step 1, the cached content Z is placed. k The encoding steps are as follows: First, each file W n The subfiles, n∈[N]=[0:N-1], are divided into K+1 disjoint subfiles of equal size by the server, and then encoded using a (2K,K+1) MDS code. n,0 W n,1 ,…,W n,2K-1 Representing file W respectively n 2K MDS encoded segments; Next, from all possible permutations of [2K], the server independently and uniformly selects N permutations, using... It means that, where n∈[N], Let p be the permutation vector n The 2k+mth position; The server determines the permutation p. n Shuffle 2K MDS encoded segments. The shuffled segments are then used... It means that the conditions are met. in, For file W n The One MDS encoded segment; the cached content of user k, i.e., Z k , set as WITH k =(Z′ k ,P k ), Where P k ~Unif([2K]), k∈[K], are K independent and identically distributed random variables uniformly distributed on the set of integers [2K], and ⊕ represents the XOR operation; Step 2: Each user k∈[K] sends a file request D to the server. k This indicates a request for a file. There are N files W0, W1, ... W N-1 Any one of the following, the server determines the outcome based on all user requests D = (D0, D1, ..., D...). K-1 ), generating broadcast signal X D And transmit the signal X through an error-free shared link channel. D Broadcast to all users in the system; In step 2, the broadcast signal X D The encoding steps are as follows: The server processes all user requests, D = (D0, D1, ..., D...). K-1 ), producing X' D And auxiliary variables J0 and J1: J1=(J 1,k ) k∈[K] , in, The server sends a broadcast signal X to user k. D By X' D It consists of two parts: the auxiliary variable (J0, J1), that is, X. D =(X' D ,J0,J1); Step 3: Each user k∈[K] receives the broadcast signal X. D And the previously cached content Z k Decode the file you requested 2. The privacy-encoded caching method based on MDS codes and random permutations as described in claim 1, characterized in that, Cache size In step 3, each user decodes the requested file. The decoding steps are as follows: First, from X D In the middle, user k directly obtains The K MDS encoded segments and their corresponding indices, i.e. and i∈[K]; Next, user k obtains the following formula: and its corresponding index Finally, based on the properties of (2K,K+1)MDS codes, user k from and Obtain The indices of these K+1 MDS encoded segments are determined by... and Provided.

3. A privacy-encoded caching method based on MDS codes and random permutations, characterized in that, Including cache size The method includes the following steps: Step 1: There are N files W0, W1, ... W N-1 Trusted servers will cache content Z. k Distribute the data to users k∈[K]=[0:K-1] in the communication system, where K represents the total number of users in the communication system; In step 1, the cached content Z is placed. k The encoding steps are as follows: First, each file W n The data, n∈[N], is divided by the server into (K+1)(N-1) disjoint subfiles of equal size. The server then uses a (2K(N-1),(K+1)(N-1)) MDS code to encode these subfiles into 2K(N-1) MDS segments. These 2K(N-1) MDS segments are represented by W. n,0 W n,1 ,…,W n,2K(N-1)-1 Indicates; the server according to the permutation p n Shuffle 2K MDS encoded segments. The shuffled segments are then used... It means that the conditions are met. in, For file W n The One MDS encoded segment, It is a permutation that is independently and uniformly selected from all possible permutations of [2K(N-1)]. Let p be the permutation vector n The (2N-2)k+mth bit; the cached content of user k, i.e., Z. k , set as WITH' k (WITH k，n ) n∈[N] , P k =(P k,n ) n∈[N] ,S k =(S k,n ) n∈[N] , Among them, P k,n ~Unif([2K(N-1)]), K∈[K], n∈[N], are KN independent and identically distributed random variables uniformly distributed on the integer set [2K(N-1)]. k,n ~Unif([K]), k∈[K+1], n∈[N], are (K+1)N independent and identically distributed random variables uniformly distributed on the set of integers [K]. Step 2: Each user k∈[K] sends a file request D to the server. k This indicates a request for a file. There are N files W0, W1, ... W N-1 Any one of the following, the server determines the outcome based on all user requests D = (D0, D1, ..., D...). K-1 ), generating broadcast signal X D And transmit the signal X through an error-free shared link channel. D Broadcast to all users in the system; In step 2, the broadcast signal X D The encoding steps are as follows: First, for each requested file, i.e. The server randomly selects a user, denoted as u. n These users are referred to as "leaders," and the set of leaders is defined as follows: in This represents the set of all requested files; while for Define u n It is always equal to 1, that is, u n ≡1; When the total number of files N≥3, for each file index n∈[N], define an arbitrary one-to-one mapping function h. n (m), this function maps each file index m∈[N]\{n} to another file index h. n (m)∈[N]\{n,m}, such that if m1≠m2, then h n (m1)≠h n (m2); Next, the server generates X' based on all users' requests D. D =(X D,n ) n∈[N+1] and auxiliary variable J0 = (J 0,n ) n∈[N] : Where, π n =(π) n,0 ,π n,1 ,…,π n,K-1 Let n∈[N] be N permutations that are independently and uniformly selected from all possible permutations of [K], where for k∈[1:K-1], n∈[N]. For k = 0, n ∈ [N], For k∈[K], n∈[N], Then, the server generates auxiliary variables. and J3: Finally, the server sends a broadcast signal X to user k. D By X' D It consists of two parts: the auxiliary variable and the variable X. D =(X' D (J0, J1, J2, J3); Step 3: Each user k∈[K] receives the broadcast signal X. D And the previously cached content Z k Decode the file you requested 4. The privacy-encoded caching method based on MDS codes and random permutations as described in claim 3, characterized in that, Cache size In step 3, each user decodes the requested file. The decoding steps are as follows: First, user k decodes using the following formula: Among them, all those used remove Apart from that, all can be in Found in, and user 0 from Zhongzhidao exist The position in the middle; user k decodes using the following formula Among them, user k from Zhongzhidao exist The position in the middle; the indices of the N MDS encoded segments obtained from the above decoding are determined by... Given, where m∈[N], these indices are known to user k; Next, from and In the middle, user k obtains (N-1)K-1 different MDS encoded segments and their corresponding indices; specifically, user k from (N-2)K-1 different MDS encoded segments are directly obtained, and their corresponding indices are determined by... Provided by user k from Directly obtain MDS encoded segments or And user k from Zhongzhidao exist The position and index in Position in the middle; use in sequence In addition to For items other than those specified, user k decodes them using the following formula. The corresponding indices of the aforementioned K-1 MDS encoded segments are determined by... Given in order; Finally, based on the properties of the (2K(N-1),(K+1)(N-1)) MDS code, user k obtains the (K+1)(N-1) MDS encoded segments and their corresponding indices obtained from the above decoding.

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