A linear method for key sharing among five participants

Abstract

The present invention provides a linear key sharing method for five participants, comprising the following steps: Step 1: Based on the access structure, query the corresponding linear capacity domain; Step 2: Establish a corresponding integer programming model based on the polar direction vector of the linear capacity domain and the input subkey size vector, and determine the combination coefficients used in the final method based on the feasible solution of the integer programming; Step 3: Based on the optimal solution of the integer programming, combine the methods corresponding to the polar direction vectors, and the combined method becomes the final linear key sharing method. The method of the present invention is applicable to any access structure and any integer subkey size vector for the five participants, and can obtain a relatively optimal master key size.

Description

Technical Field

[0001] The present invention relates to the field of information theory technology, and in particular to a key sharing linear method for five participants with arbitrary access structures and arbitrary integer subkey size vectors. Background Art

[0002] Traditional performance metrics for key sharing are information rate and average information rate. Both focus on the ratio of the master key size to the subkey sizes; a higher ratio indicates better performance. However, in more general situations, the subkey sizes available to each participant may vary greatly. In such cases, there are relatively few results on how to achieve key sharing with optimal master key sizes. To address this issue, the concept of capacity domains is needed, specifically characterizing the relationship between the master key size and the sizes of each subkey. While there are existing results on optimal linear key sharing methods for arbitrary access structures involving five participants, no research on linear capacity domains has been reported. Summary of the Invention

[0003] Purpose of the invention: To solve the above-mentioned problems, the present invention proposes a linear key sharing method for five participants. Given any access structure, an integer programming model is constructed using the polar direction vectors of the linear capacity domain and the input sub-key size vector. After solving the model, the combination coefficients of the methods corresponding to the polar direction vectors are determined by the optimal solution, so that the final method has a better master key size.

[0004] Technical methods: To achieve the purpose of the present invention, the technical methods adopted by the present invention are:

[0005] A linear method for key sharing among five participants, comprising the following steps:

[0006] Step 1: First, query the corresponding linear capacity domain C for the access structure A A , that is, a polyhedral cone; the linear capacity domain C A Contains the polar direction vector matrix [s P], where each row corresponds to a polar direction vector, the submatrix s corresponds to the size of the master key, and the submatrix P corresponds to the size of the subkey; each polar direction vector has its corresponding linear key sharing method;

[0007] Step 2: Establish a corresponding integer programming model based on the polar direction vector [s P] of the linear capacity domain and the input subkey size vector q. The feasible solution x of the integer programming determines the combination coefficient used in the final method.

[0008] Step 3: According to the optimal solution x of integer programming ＊ , combining the methods corresponding to each polar direction vector, the combined method is the final linear key sharing method.

[0009] Furthermore, the integer programming model established in step 2 is as follows:

[0010]

[0011] such thatP T x≤q

[0012] x≥0

[0013]

[0014] Set the linear capacity domain C A There are n A polar direction vectors, then the feasible solution x contains n A non-negative integers The feasible set of this integer programming problem is not empty, using column vectors To represent an optimal solution to this integer programming problem; the optimal value is recorded as s ★ , s ★ Corresponding to the master key size of the final method; each feasible solution of this linear programming corresponds to a key sharing linear method that satisfies the access structure A and the sub-key size vector q, and the optimal solution is selected to obtain a better master key size s ★ ;

[0015] Furthermore, the specific steps of step 3 are as follows:

[0016] Step 3.1: Extension of the linear key sharing method for the i-th polar direction vector The steps are as follows:

[0017] A linear key sharing method is to distribute the linear combination of the master key and the random noise variable as a subkey to each participant; Preparation required times the master key and random noise variable, each linear combination is repeated Then distribute it to each participant as a new subkey;

[0018] Step 3.2: Merge n A The steps of the linear key sharing method are as follows:

[0019] Expand n A The master key, random noise variable and the corresponding linear combination are distributed to each participant as the subkey of the final key sharing method.

[0020] Beneficial effects:

[0021] The present invention proposes a linear key sharing method for five participants, which can be applied to any access structure and any integer sub-key size vector. An integer programming model is constructed using the polar direction vectors of the linear capacity domain and the input sub-key size vector. After solving the model, the combination coefficients of the methods corresponding to the polar direction vectors are determined by the optimal solution, so that the final method has a better master key size.

[0022] The present invention takes into account the various scenarios in which the sub-key sizes that each participant may have may be different from each other, and proposes a linear key sharing method for five participants with a better master key size. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flow chart of a linear method for key sharing for five participants according to the present invention. DETAILED DESCRIPTION

[0024] The technical method of the present invention will be further described below with reference to the accompanying drawings.

[0025] like Figure 1 As shown, the present invention provides a linear key sharing method for five participants, the method comprising the following steps:

[0026] Step 1: First, query the corresponding linear capacity domain C for the access structure A A , that is, a polyhedral cone; the linear capacity domain C A Contains the polar direction vector matrix [s P], where each row corresponds to a polar direction vector, and the sub-matrices s and P correspond to the size of the master key and the size of the sub-key respectively; each polar direction vector has its corresponding linear key sharing method;

[0027] Step 2: Establish a corresponding integer programming model based on the polar direction vector [s P] of the linear capacity domain and the input subkey size vector q. The feasible solution x of the integer programming determines the combination coefficient used in the final method.

[0028] Step 3: According to the optimal solution x of integer programming ＊ , combining the methods corresponding to the polar direction vectors, the combined method is the final linear key sharing method;

[0029] In the linear method for key sharing among five participants, the integer programming model established in step 2 is as follows:

[0030]

[0031] such thatP T x≤q

[0032] x≥0

[0033]

[0034] The column vector s is the master key size corresponding to each polar direction vector, the matrix P is the sub-key size vector corresponding to each polar direction vector, and the column vector q is the input sub-key size vector; assuming that the linear capacity domain C A There are n A polar direction vectors, then the column variable x contains n A non-negative integers The feasible set of this integer programming problem is not empty, using column vectors To represent an optimal solution to this integer programming problem; the optimal value is recorded as s ＊ , s ＊ Corresponding to the master key size of the final method; each feasible solution of this linear programming corresponds to a key sharing linear method that satisfies the access structure A and the sub-key size vector q, and the optimal solution can be selected to obtain a better master key size s ＊ ;

[0035] The specific steps of step 3 of the linear key sharing method for five participants are as follows:

[0036] Step 3.1: Extension of the linear key sharing method for the i-th polar direction vector The steps are as follows:

[0037] A linear key sharing method is to distribute the linear combination of the master key and the random noise variable as a subkey to each participant; Preparation required times the master key and random noise variable, each linear combination is repeated Then distribute it to each participant as a new subkey;

[0038] Step 3.2: Merge n A The steps of the linear key sharing method are as follows:

[0039] Expand n A The master key, random noise variable and the corresponding linear combination are distributed to each participant as the subkey of the final key sharing method.

[0040] The following data is provided for various linear capacity domains and polar direction vector methods. For five participants, after simplifying the permutation relation between the participants, there are a total of 180 possible access structures. Further simplifying by duality, only 95 access structures need to be considered. Thus, for any access structure of the five participants, the required linear capacity domain and polar direction vector method can be retrieved from these 95 access structures using the permutation relation and duality.

[0041] For ease of demonstration, let's first discuss some nomenclature. Let's say {12,13,23,14,24,15,345} is an access structure, indicating that the subkeys of the first and second participants can be used to decrypt the master key, the subkeys of the first and third participants can be used to decrypt the master key, and so on. After considering monotonicity, any other combination of subkeys cannot reveal any information about the master key.

[0042] For an extreme direction vector [121221] of the access structure, it means that the master key size is 1, the subkey size of the first participant is 2, the subkey size of the second participant is 1, and so on.

[0043] The key sharing method corresponding to the polar direction vector is recorded as:

[0044]

[0045] The first row, S, represents the column vector corresponding to the subkey. 1 represents the column vector corresponding to the first participant, and so on. This matrix has five rows. The master key size is 1, so three random noise variables need to be introduced. Let the master key be s and the random noise variables be n1, n2, and n3. From the matrix, we can derive the subkeys for the first participant as n2 and n3, the subkey for the second participant as 2s + n1, and so on.

[0046] The following formally presents the linear capacity domains of 95 access structures and the linear key sharing methods of each polar direction vector.

[0047] Accessing the structure {12, 13, 23, 14, 24, 15, 345}:

[0048] Linear key sharing method for polar direction vector [234333]:

[0049] [2 3 3 4 4 3]:

[0051] [1 1 3 2 2 2]:

[0053] [1 1 2 3 3 2]:

[0055] [1 2 2 1 1 1]:

[0057]

[0058] The data of the remaining 94 access structures can be found on GitHub, and the dataset name is SS-WN.

[0059] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed in the present invention should be included in the protection scope recorded in the claims.

Claims

1. A linear method for key sharing among five participants, characterized in that The steps include: Step 1: First, query the corresponding linear capacity domain C for the access structure A A , that is, a polyhedral cone; the linear capacity domain C A Contains the polar direction vector matrix [s P], where each row corresponds to a polar direction vector, the submatrix s corresponds to the size of the master key, and the submatrix P corresponds to the size of the subkey; each polar direction vector has its corresponding linear key sharing method; Step 2: Establish a corresponding integer programming model based on the polar direction vector [s P] of the linear capacity domain and the input subkey size vector q. The feasible solution x of the integer programming model determines the combination coefficient used in the final method. Step 3: According to the optimal solution x of the integer programming model ★ , combining the methods corresponding to the polar direction vectors, the combined method is the final linear key sharing method; The integer programming model established in step 2 is as follows: Set the linear capacity domain C A There are n A polar direction vectors, then the feasible solution x contains n A non-negative integers The feasible set of this integer programming model is not empty, using column vector To represent an optimal solution of this integer programming model; at the same time, the optimal solution is denoted as s ★ , s ★ Corresponding to the master key size of the final method; each feasible solution of the integer programming model corresponds to a key sharing linear method that satisfies the access structure A and the subkey size vector q, and the optimal solution is selected to obtain a better master key size s ★ .

2. A linear key sharing method for five participants according to claim 1, characterized in that: The specific steps of step 3 are as follows: Step 3.1: Extension of the linear key sharing method for the i-th polar direction vector The steps are as follows: Distribute the linear combination of the master key and the random noise variable as a subkey to each participant; expand Preparation required times the master key and random noise variable, each linear combination is repeated Then distribute it to each participant as a new subkey; Step 3.2: Merge n A The steps of the linear key sharing method are as follows: Expand n A The master key, random noise variable and the corresponding linear combination are distributed to each participant as the subkey of the final key sharing method.

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