CN115603991A - Improved anonymous identity authentication implementation method based on secret sharing - Google Patents
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Abstract
The invention discloses an improved anonymous identity authentication implementation method based on secret sharing. On the basis of the existing interactive anonymous identity authentication model and algorithm, the invention redesigns the coding scheme based on secret sharing, randomly and uniformly generates nonrepeated user keys and Verifier auxiliary data by removing a linear space formed by stretching a specific column vector in a Galois field, and meets the requirements of integrity, robustness and anonymity of the anonymous authentication problem. The improved scheme reduces the probability of external attack in the anonymous authentication system on the basis of the original scheme, and improves the system capacity.
Description
Technical Field
The invention relates to the technical field of information theory, in particular to an improved anonymous identity authentication implementation method capable of achieving smaller attacked probability and larger system capacity.
Background
Anonymous identity authentication means that a user enters a system to use resources or services on the premise of not revealing identity, and the problem is widely applied to the fields of wireless body area networks, cloud computing, encryption currency, electronic voting and the like. Most of researches on anonymous identity authentication problems are based on relevant technologies in the field of cryptography such as RSA algorithm and ECC algorithm, and the computational security is realized. The invention concerns the information theory security of the anonymous identity authentication problem based on an interactive information theory anonymous identity authentication model and an achievable algorithm under a single authenticator and limited long key scene proposed by Kazempour et al in 2019, improves the original model, reduces the probability of attack of the inside and the outside and improves the system capacity by redesigning an encoding scheme.
Disclosure of Invention
The technical problem is as follows: the technical problem to be solved by the invention is to design a coding scheme, randomly generate auxiliary data for a Verifier and generate a key for a legal user, and achieve smaller attacked probability and larger system capacity on performance on the basis of meeting the requirements of integrity, robustness, anonymity and the like required by the anonymous identity authentication problem.
The technical scheme is as follows: the technical scheme adopted by the invention is as follows:
(1) And a data distribution stage. This phase CA randomly and uniformly generates a secret S = a over GF (q) 0 And for protecting a 0 Random noise a of 1 ,…,a k-1 Obtaining a vector a = [ a ] 0 ,a 1 ,…,a k-1 ]. The CA then sends a over the secure channel to the Verifier. Next, the CA generates auxiliary data V for the Verifier, generates keys C different from each other for the user, and transmits them to the Verifier and the user, respectively.
(2) And (5) an authentication phase. The interaction process between the Verifier and the user in this stage is as follows. Firstly, a user sends an authentication request to a Verifier, and sends a secret key of the user to a CA. After receiving the authentication request, the Verifier will send S = a 0 Keeps secret and sends the auxiliary information V to the user. User recovery of secrets by means of an auxiliary information V and a secret key C
And sends it to the Verifier. Verifier test
And if so, the user passes the identity authentication, otherwise, the user is rejected.
(3) And (5) a checking stage. The CA generates a white list of user keys during the data distribution phase and clears out users not on the list on the fly. If a user maliciously attacks the system, the CA can trace the identity of the user through the key and execute corresponding punishment measures such as forbidding the key.
The method comprises the following steps of generating auxiliary data V for a Verifier in a data distribution stage CA:
first, generating N v A k-dimensional column vector, wherein N v <k. First from k-dimensional space (GF (q)) k Medium removal vector [1,0, \ 8230;, 0] 1×k T A stretched linear space, and randomly and uniformly selecting V from the residual vector 1 . Next, from k-dimensional space (GF (q)) k Medium removal vector [1,0, \ 8230;, 0] 1×k T And V 1 After the linear space is formed, V is randomly and uniformly selected from residual vectors 2 . Continuing to generate according to the steps
The column vectors are linearly independent of each other.
Second, separately calculating
And vector a = [ a = 0 ,a 1 ,…,a k-1 ]Is internally accumulated to obtain
And finally, the CA sends the auxiliary data to the Verifier
The length of the transmitted data is l V ＝N v (k+1)。
The data distribution phase CA generates keys C different from each other for the user as follows:
firstly, generating M k-dimensional column vectors, wherein M is the number of users in the system. Finding all k-dimensional column vectors that simultaneously satisfy the following condition:
wherein, span { v } 1 ,v 2 ,…,v n Represents v 1 ,v 2 ,…,v n A linear space spanned by the vectors. The column vectors apparently satisfying the above conditions total
And (4) respectively. The CA randomly, uniformly and non-repeatedly selects M vectors which are respectively U 1 ,U 2 ,…,U M 。
Second, calculate U separately 1 ,U 2 ,…,U M And vector a = [ a = 0 ,a 1 ,…,a k-1 ]Inner product of (2) to obtain a.U 1 ,a·U 2 ,…,a·U M . Finally, CA sends key C = { (U) to user 1 ,a·U 1 ),(U 2 ,a·U 2 ),…,(U M ,a·U M ) }. The transmitted data has a length of l C ＝M(k+1)。
User recovery of secrets by means of auxiliary information V and a secret key C during an authentication phase
(with user i, i ∈ [ M ]]For example) the procedure was as follows:
first, the Verifier first begins with the auxiliary data
And sending the information to the user i. The user holds the key C from the CA at the same time i ＝(U i ,a·U i )。
Second, user i calculates (N) v + 1) dimension row vector V coe To satisfy the following equation:
can prove that V coe Are present and unique.
Third, user i calculates
If user i is a legitimate user (i.e. holds a key issued by the CA),
and (4) passing the authentication.
Has the advantages that: the invention provides an improved anonymous identity authentication implementation scheme based on secret sharing, which redesigns an encoding matrix on the basis of the original scheme, reduces redundancy by randomly generating elements in the matrix, and realizes smaller attacked probability and larger system capacity than the original scheme on the basis of meeting the requirements of integrity, robustness and anonymity of the anonymous identity authentication problem.
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FIG. 1 is a schematic diagram of an anonymous identity authentication model of an interactive information theory.
Detailed Description
The technical solution of the present invention is described in detail below, but the scope of the present invention is not limited to the embodiment.
The invention provides an improved anonymous identity authentication implementation scheme based on secret sharing.
An example is given below: the first step, data distribution stage: the stage comprises three steps of generating a vector a by a CA, generating auxiliary data V for a Verifier by the CA and generating a key C for a user by the CA, and the detailed description is as follows:
(1) CA generates a vector a. CA first generates a secret S = a uniformly and randomly over GF (7) 0 And (5). And (3) selecting the dimension k =4 of the vector, paying attention to the k value to determine indexes such as system capacity, attack probability and the like of the anonymous identity authentication system, and determining the value of k according to actual requirements in application. Generating to protect a 0 Random noise a of 1 ,a 2 ,a 3 Composition vector a = [5,4,1,6 ]]。
(2) CA generates auxiliary data V for Verifier. First, determine N v ＝3(N v <k) In that respect From (GF (7)) 4 Vector of middle removal [1,0] T A stretched linear space, and randomly and uniformly selecting V from the residual vector 1 Suppose V 1 ＝[0,2,0,0] T (ii) a Next, from (GF (7)) 4 Vector of middle removal [1,0] T And V 1 ＝[0,2,0,0] T A linear space is formed by stretching, and V is randomly and uniformly selected from the residual vector 2 Suppose V 2 ＝[1,2,3,0] T (ii) a Final slave (GF (7)) 4 Middle removal vector [1,0] T 、V 1 ＝[0,2,0,0] T And V 2 ＝[1,2,3,0] T A stretched linear space, and randomly and uniformly selecting V from the residual vector 3 Suppose V 3 ＝[1,2,3,4] T . The set of column vectors is linearly independent.
CA calculates V separately 1 ,V 2 ,V 3 Inner product with vector a: to obtain a.V 1 ＝8,a·V 2 ＝16,a·V 3 =40.CA compares the auxiliary data V = { (V) 1 ＝[0,2,0,0] T ,8),(V 2 ＝[1,2,3,0] T ,16),(V 3 ＝[1,2,3,4] T 40) to the Verifier. The transmitted data has a length of l V ＝N v (k+1)＝15。
(3) The CA generates a key C for the user. For ease of understanding and calculation, it is assumed that there is a common denominator in the system
And (4) a user. The CA finds all four-dimensional column vectors that meet the following condition simultaneously:
the CA randomly, uniformly, and non-repeatedly selects two vectors from all the vectors satisfying the above conditions, which are:
U 1 ＝[1,0,6,4] T ,U 2 ＝[1,2,0,4] T 。
CA calculates U separately 1 ,U 2 Inner product with vector a to obtain a.U 1 ＝35,a·U 2 ＝37.CA sends key C to users 1, 2 in turn 1 ＝(U 1 ＝[1,0,6,4] T ,35),C 2 ＝(U 2 ＝[1,2,0,4] T ,37). Total length of data transmitted is l C ＝M(k+1)＝10。
Step two, authentication stage: the stage comprises that a Verifier sends auxiliary data to a user and the user calculates
Two steps, detailed as follows: (take users 1, 2 as examples)
(1) Verifier firstly puts auxiliary data V = { (V) 1 ＝[0,2,0,0] T ,8),(V 2 ＝[1,2,3,0] T ,16),(V 3 ＝[1,2,3,4] T 40) to the user requesting authentication, i.e. user 1, 2.
(2) User-based key and helper data computation
As follows.
User 1: calculating a four-dimensional row vector V coe1 So as to satisfy: v coe1 ·[V 1 ,V 2 ,V 3 ,U 1 ]＝[1,0,0,0]To obtain V coe1 ＝[-2,1,1,-1]. User 1 computing
And (4) passing the authentication.
And (4) a user 2: calculating a four-dimensional row vector V coe2 So as to satisfy: v coe2 ·[V 1 ,V 2 ,V 3 ,U 2 ]＝[1,0,0,0]To obtain V coe2 ＝[-1,1,-1,1]. User 2 computing
And (4) passing the authentication.
The third step, the inspection stage: the CA generates a white list of user keys during the data distribution phase and clears out users not on the list when idle. If a user maliciously attacks the system, the CA can trace the identity of the user through the key and execute corresponding punishment measures such as forbidding the key.
It is worth noting that there must be a valid user
Therefore, the legal user is authenticated by the Verifier certainly, and the correctness of the anonymous identity authentication problem is ensured. If an attacker (illegal user) sends an authentication request to the Verifier, he probably cannot recover S = a correctly due to lack of key issued by CA 0 Therefore, the authentication can not be passed, and the robustness of the anonymous identity authentication problem is ensured. In addition, since all legitimate users have calculated
Similarly, the Verifier can not identify the difference between users, so that the anonymity of the anonymous identity authentication problem is ensured.
Claims (4)
1. An improved anonymous identity authentication implementation method based on secret sharing is characterized by comprising the following steps:
(1) A data distribution stage; this phase CA randomly and uniformly generates a secret S = a over GF (q) 0 And for protecting a 0 Random noise a of 1 ，...，a k-1 Form a k-dimensional vector a = [ a ] 0 ，a 1 ，...，a k-1 ]Then the CA sends a to a Verifier through a secure channel; the CA generates auxiliary data V for the Verifier, generates different keys C for the user and respectively sends the keys C to the Verifier and the user;
(2) An authentication stage; the interaction process between the Verifier and the user in the stage is as follows: firstly, a user sends an authentication request to a Verifier and sends a secret key of the user to a Certificate Authority (CA); after receiving the authentication request, the Verifier sends S = a 0 Keeping secret and sending auxiliary information V to the user; user based on auxiliary information V and passwordKey C recovery secret
And send it to the Verifier; verifier test
If yes, the user passes the identity authentication, otherwise, the user is rejected;
(3) A checking stage; the CA generates a white list of user keys in a data distribution stage, and clears out users not on the list in a free state; if a user maliciously attacks the system, the CA traces back the identity of the user through the key and executes corresponding punishment measures such as forbidding the key.
2. The method for implementing the improved anonymous identity authentication based on the secret sharing as claimed in claim 1, wherein the step of generating the auxiliary data V for the Verifier by the CA is as follows:
(11) Generating N v A k-dimensional column vector, wherein N v K is less than; first from k-dimensional space (GF (q)) k Removing vector [1, 0., 0] 1×k T A stretched linear space, and randomly and uniformly selecting V from the residual vector 1 (ii) a Next, from k-dimensional space (GF (q)) k Removing vector [1, 0., 0 ] from] 1×k T And V 1 After the linear space is formed by stretching, V is randomly and uniformly selected from the residual vector 2 (ii) a Continuing to generate according to the steps
The set of column vectors is linearly independent;
(12) Respectively calculate
And vector a = [ a = 0 ，a 1 ，...，a k-1 ]Inner product of (1) to obtain
And finally, the CA sends the auxiliary data to the Verifier
The length of the transmitted data is l V ＝N v (k+1)。
3. The improved secret sharing based anonymous identity authentication implementation method of claim 1, wherein the step of the CA generating mutually different keys C for the user is as follows:
(21) Firstly, generating M k-dimensional column vectors, wherein M is the number of users in the system; finding all k-dimensional column vectors that simultaneously satisfy the following condition:
wherein, span { v } 1 ，v 2 ，...，v n Represents v 1 ，v 2 ，...，v n A linear space spanned by the equal vectors; CA never satisfies the above conditions
Randomly, uniformly and non-repeatedly selecting M vectors from the column vectors, wherein the M vectors are respectively U 1 ，U 2 ，...，U M ；
(22) Respectively calculate U 1 ，U 2 ，...，U M And vector a = [ a = 0 ，a 1 ，...，a k-1 ]Inner product of (b) to obtain a. U 1 ，a·U 2 ，...，a·U M (ii) a Finally, CA sends key C = { (U) to user 1 ，a·U 1 )，(U 2 ，a·U 2 )，...，(U M ，a·U M ) }; the length of the transmitted data is l C ＝M(k+1)。
4. Such asThe improved secret sharing based anonymous identity authentication implementation method of claim 1, wherein the user recovers the secret based on the auxiliary information V and the key C
The method comprises the following specific steps:
(31) The Verifier firstly begins to carry out auxiliary data
Sending to user i, i ∈ [ M ]]The user simultaneously holds a key C i ＝(U i ，a·U i )；
(32) User i calculates (N) v + 1) dimension row vector V coe To satisfy the following equation:
(33) User i calculation
If the user i is a legitimate user,
and (6) passing the authentication.
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| WO2020143246A1 (en) * | 2019-01-07 | 2020-07-16 | 苏宁云计算有限公司 | Method and system for de-anonymization by combining blockchain and secret sharing |
| CN112953727A (en) * | 2021-03-02 | 2021-06-11 | 西安电子科技大学 | Internet of things-oriented equipment anonymous identity authentication method and system |
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| CN107231230A (en) * | 2017-05-31 | 2017-10-03 | 福州大学 | Cross-domain dynamic anonymity authentication group key management method and system based on illness |
| WO2020143246A1 (en) * | 2019-01-07 | 2020-07-16 | 苏宁云计算有限公司 | Method and system for de-anonymization by combining blockchain and secret sharing |
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