An improved anonymous identity authentication method based on secret sharing

Abstract

The present invention discloses an improved anonymous identity authentication implementation method based on secret sharing. Based on the existing interactive anonymous identity authentication model and algorithm, the present invention redesigns the encoding scheme based on secret sharing, and randomly and uniformly generates non-repeating user keys and Verifier auxiliary data by removing the linear space spanned by specific column vectors in the Galois field, thereby meeting the integrity, robustness and anonymity requirements of the anonymous authentication problem. This improved scheme reduces the probability of attacks inside and outside the anonymous authentication system on the basis of the original scheme, and improves the system capacity.

Description

Technical Field

[0001] The invention relates to the technical field of information theory, and in particular to an improved anonymous identity authentication implementation method which achieves a lower attack probability and a larger system capacity. Background Art

[0002] Anonymous identity authentication refers to the user entering the system to use resources or services without revealing his or her identity. This problem is widely used in wireless body area networks, cloud computing, cryptocurrency, electronic voting and other fields. Most of the research on anonymous identity authentication is based on cryptography-related technologies such as RSA algorithm and ECC algorithm to achieve computational security. The present invention is based on the interactive information theory anonymous identity authentication model proposed by Kazempour et al. in 2019 and the achievable algorithm under the scenario of single authenticator and finite-length key. It focuses on the information theory security of anonymous identity authentication problem, improves the original model, and reduces the probability of internal and external attacks and improves the system capacity by redesigning the coding scheme. Summary of the invention

[0003] Technical problem: The technical problem to be solved by the present invention is to design a coding scheme to randomly generate auxiliary data for the Verifier and keys for legitimate users, while meeting the requirements of integrity, robustness, anonymity, etc. required by the anonymous identity authentication problem, while achieving a lower probability of attack and a larger system capacity in terms of performance.

[0004] Technical solution: The technical solution adopted by the present invention is as follows:

[0005] (1) Data distribution phase. In this phase, CA randomly and uniformly generates the secret S = a0 and the random noise a1, ..., a1 used to protect a0 on GF(q). k-1 , we get the vector a=[a0,a1,…,a k-1 ]. The CA then sends a to the Verifier through a secure channel. Next, the CA generates auxiliary data V for the Verifier and a key C that is different from each other for the user, and sends them to the Verifier and the user respectively.

[0006] (2) Authentication phase. The interaction between the Verifier and the user in this phase is as follows. First, the user sends an authentication request to the Verifier and sends his or her key to the CA. After receiving the authentication request, the Verifier keeps S=a0 confidential and sends auxiliary information V to the user. The user uses the auxiliary information V and the key C to recover the secret key. And send it to Verifier. Verifier checks Is it true? If so, the user passes the identity authentication, otherwise it is rejected.

[0007] (3) Verification stage. The CA generates a whitelist of user keys during the data distribution stage and removes users not on the list during idle time. If a user maliciously attacks the system, the CA can trace the user's identity through the key and implement corresponding punishment measures such as disabling the key.

[0008] Among them, the steps for the CA to generate the auxiliary data V for the Verifier during the data distribution stage are as follows:

[0009] The first step is to generate N v k-dimensional column vectors, where N v < k. First, remove the linear space spanned by the vector [1, 0, …, 0] k from the k-dimensional space (GF(q)) 1×k T , and randomly and uniformly select V1 from the remaining vectors. Next, remove the linear space spanned by the vector [1, 0, …, 0] k and V1 from the k-dimensional space (GF(q)) 1×k T , and then randomly and uniformly select V2 from the remaining vectors. Continue to generate the above column vectors in the above steps, and these column vectors are linearly independent of each other. The above column vectors are linearly independent of each other.

[0010] The second step is to calculate the inner product of with the vector a = [a0, a1, …, a k-1 respectively to obtain Finally, the CA sends the auxiliary data The length of the data sent is l V = N v (k + 1).

[0011] The steps for the CA to generate different keys C for users during the data distribution stage are as follows:

[0012] The first step is to generate M k-dimensional column vectors, where M is the number of users in the system. Find all k-dimensional column vectors that meet the following conditions simultaneously:

[0013]

[0014] Among them, span{v1, v2, …, v n} represents the linear space spanned by vectors such as v1, v2, …, v n . Obviously, the total number of column vectors that meet the above conditions is . The CA randomly, uniformly and without repetition selects M vectors from them, which are U1, U2, …, U M .

[0015] The second step is to calculate U1, U2, ..., U respectively. M With the vector a=[a0,a1,…,a k-1 ], we get a·U1,a·U2,…,a·U M Finally, the CA sends the key C = {(U1, a·U1), (U2, a·U2), …, (U M ,a·U M )}. The length of the data sent is l C =M(k+1).

[0016] During the authentication phase, the user recovers the secret with the help of auxiliary information V and key C (Take user i, i∈[M] as an example) the steps are as follows:

[0017] In the first step, Verifier first converts the auxiliary data Sent to user i. The user also holds the key C from CA i =(U i ,a·U i ).

[0018] The second step is to calculate (N v +1)-dimensional row vector V coe To satisfy the following equation:

[0019]

[0020] It can be proved that V coe Exists and is unique.

[0021] Step 3: User i calculates If user i is a legitimate user (i.e., holds a key issued by the CA), Passed certification.

[0022] Beneficial effects: The present invention proposes an improved anonymous identity authentication implementation scheme based on secret sharing. The coding matrix is ​​redesigned on the basis of the original scheme. The elements in the matrix are randomly generated to reduce redundancy. On the basis of meeting the integrity, robustness and anonymity requirements of the anonymous identity authentication problem, a smaller probability of attack and a larger system capacity are achieved than the original scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Schematic diagram of the interactive information theory anonymous identity authentication model. DETAILED DESCRIPTION

[0024] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the implementation examples.

[0025] The present invention proposes an improved implementation scheme for anonymous identity authentication based on secret sharing.

[0026] The following is an embodiment: The first step, the data distribution phase: This phase includes three steps: the CA generates the vector a, the CA generates the auxiliary data V for the Verifier, and the CA generates the key C for the user, which are described in detail as follows:

[0027] (1) The CA generates the vector a. The CA first uniformly and randomly generates the secret S = a0 = 5 on GF(7). Select the dimension k of the vector = 4. Note that the k value determines indicators such as the system capacity and the probability of being attacked of the anonymous identity authentication system. In applications, the value of k should be determined according to actual requirements. Generate the random noises a1, a2, a3 used to protect a0, and form the vector a = [5, 4, 1, 6].

[0028] (2) The CA generates the auxiliary data V for the Verifier. First, determine N v = 3 (N v < k). Remove the linear space spanned by the vector [1, 0, 0, 0] 4 from (GF(7)) T , and randomly and uniformly select V1 from the remaining vectors. Assume V1 = [0, 2, 0, 0] T ; Next, remove the linear space spanned by the vector [1, 0, 0, 0] 4 and V1 = [0, 2, 0, 0] T from (GF(7)) T , and randomly and uniformly select V2 from the remaining vectors. Assume V2 = [1, 2, 3, 0] T ; Finally, remove the linear space spanned by the vector [1, 0, 0, 0] 4 , V1 = [0, 2, 0, 0] T , and V2 = [1, 2, 3, 0] T from (GF(7)) T , and randomly and uniformly select V3 from the remaining vectors. Assume V3 = [1, 2, 3, 4] T . The above column vector group is linearly independent.

[0029] The CA calculates the inner products of V1, V2, V3 with the vector a respectively: Obtain a·V1 = 8, a·V2 = 16, a·V3 = 40. The CA sends the auxiliary data V = {(V1 = [0, 2, 0, 0] T , 8), (V2 = [1, 2, 3, 0] T , 16), (V3 = [1, 2, 3, 4] T , 40)} to the Verifier. The length of the data sent is l V = N v(k+1)=15.

[0030] (3) CA generates a key C for the user. For ease of understanding and calculation, assume that there are a total of users. CA finds all four-dimensional column vectors that satisfy the following conditions simultaneously:

[0031]

[0032] CA randomly, uniformly and non-repeatedly selects two vectors from all the vectors that meet the above conditions, which are:

[0033] U1=[1,0,6,4] T ,U2=[1,2,0,4] T .

[0034] CA calculates the inner product of U1, U2 and vector a respectively, and obtains a·U1=35, a·U2=37. CA sends the key C1=(U1=[1,0,6,4] T ,35),C2=(U2=[1,2,0,4] T ,37). The total length of the data sent is l C =M(k+1)=10.

[0035] Step 2: Authentication phase: This phase includes the Verifier sending auxiliary data to the user, the user calculating The two steps are detailed as follows: (taking users 1 and 2 as examples)

[0036] (1) Verifier first converts the auxiliary data V = {(V1 = [0,2,0,0] T ,8),(V2=[1,2,3,0] T ,16),(V3=[1,2,3,4] T ,40)} is sent to the users requesting authentication, i.e., users 1 and 2.

[0037] (2) The user calculates based on his own key and auxiliary data as follows.

[0038] User 1: Calculate the 4D row vector V coe1 To meet: V coe1 [V1, V2, V3, U1] = [1, 0, 0, 0], we get V coe1 =[-2,1,1,-1]. User 1 calculates Passed certification.

[0039] User 2: Calculate the four-dimensional row vector V coe2To meet: V coe2 [V1, V2, V3, U2] = [1, 0, 0, 0], we get V coe2 =[-1,1,-1,1]. User 2 calculates Passed certification.

[0040] Step 3, verification phase: CA generates a whitelist of user keys during the data distribution phase and removes users not on the list during idle time. If a user maliciously attacks the system, CA can trace his identity through the key and take corresponding punishment measures such as disabling the key.

[0041] It is worth noting that there must be Therefore, legitimate users must pass the Verifier's authentication, ensuring the correctness of the anonymous identity authentication problem. If an attacker (illegal user) sends an authentication request to the Verifier, due to the lack of the key issued by the CA, he is unlikely to be able to correctly restore S=a0, so he cannot pass the authentication, ensuring the robustness of the anonymous identity authentication problem. In addition, because all legitimate users calculate Similarly, Verifier cannot identify differences between users, ensuring the anonymity of anonymous identity authentication issues.

Claims

1. An improved anonymous identity authentication implementation method based on secret sharing, characterized in that: The steps include: (1) Data distribution phase; in this phase, CA randomly and uniformly generates the secret S = a0 and the random noise a1, ..., a1 used to protect a0 on GF(q). k-1 , forming a k-dimensional vector a=[a0,a1,...,a k-1 ], then CA sends a to Verifier through a secure channel; CA generates auxiliary data V for Verifier and generates a key C different from each other for the user, and sends them to Verifier and user respectively; (2) Authentication phase: The interaction between the Verifier and the user is as follows: First, the user sends an authentication request to the Verifier and sends his or her key to the CA. After receiving the authentication request, the Verifier keeps S=a0 confidential and sends auxiliary information V to the user. The user recovers the secret key based on the auxiliary information V and the key C. And send it to Verifier; Verifier checks Is it true? If so, the user passes the identity authentication, otherwise it is rejected; (3) Inspection stage; CA generates a whitelist of user keys during the data distribution phase and removes users not on the list during idle time. If a user maliciously attacks the system, CA traces his identity through the key and implements corresponding punishment measures. The steps for CA to generate auxiliary data V for Verifier are as follows: (11) Generate N v k-dimensional column vector, where N v <k; first from the k-dimensional space (GF(q)) k Remove the vector [1, 0, ..., 0] 1×k T Zhang Cheng's linear space, randomly and uniformly select V1 from the remaining vectors; next, from the k-dimensional space (GF(q)) k Remove the vector [1, 0, ..., 0] 1×k T After the linear space formed by and V1 is formed, V2 is randomly and uniformly selected from the remaining vectors; continue to generate according to the above steps N v The k-dimensional column vectors are linearly independent; (12) Calculate separately With the vector a = [a0, a1, ..., a k-1 ], we get Finally, CA sends auxiliary data to Verifier The length of the data sent is l V =N v (k+1); The steps for CA to generate a key C that is different from the user are as follows: (21) First, generate M k-dimensional column vectors, where M is the number of users in the system; find all k-dimensional column vectors that meet the following conditions at the same time: Where span{v1, v2, ..., v n } represents v1, v2, ..., v n The linear space spanned by equal vectors; CA is derived from the linear space that satisfies the above conditions. Select M vectors randomly, uniformly and without duplication from the column vectors, namely U1, U2, ..., U M ; (22) Calculate U1, U2, ..., U respectively M With the vector a = [a0, a1, ..., a k-1 ], we get a·U1, a·U2, ..., a·U M ; Finally, CA sends the key C = {(U1, a·U1), (U2, a·U2), ..., (U M , a.U M )}; The length of the data sent is l C =M(k+1); The user recovers the secret based on the auxiliary information V and the key C The specific steps are as follows: (31) Verifier first converts the auxiliary data Sent to user i, i∈[M], who also holds the key C i =(U i , a.U i ); (32) User i calculates (N v +1)-dimensional row vector V coe To satisfy the following equation: (33) User i calculation If user i is a legitimate user, Passed certification.

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