CN108632043B - Optimized ring signature method and system - Google Patents
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- CN108632043B CN108632043B CN201810354020.7A CN201810354020A CN108632043B CN 108632043 B CN108632043 B CN 108632043B CN 201810354020 A CN201810354020 A CN 201810354020A CN 108632043 B CN108632043 B CN 108632043B
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
- H04L9/3255—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using group based signatures, e.g. ring or threshold signatures
Abstract
The invention discloses an optimized ring signature method and system. The ring signature method comprises the following steps: acquiring each user identity and a message to be signed; randomly selecting parameters according to each user identity to generate system parameters and a master key; determining a private key corresponding to the user identity according to the system parameter, the master key and the user identity; obtaining a corresponding ring signature according to the message to be signed, the user identity and the private key corresponding to the user identity; and judging whether the ring signature is a valid signature. By adopting the optimized ring signature method, the communication efficiency of the ring signature can be improved.
Description
Technical Field
The present invention relates to the field of communications, and in particular, to an optimized ring signature method and system.
Background
The ring signature scheme under the traditional Public Key Infrastructure (PKI) framework faces two major problems: firstly, the management of a user public key certificate is carried out, under a PKI system, the identity of a user and the public key of the user are bound through a digital certificate, and when the number of the users is large, the management and verification of the certificate occupy a large amount of system resources and become the bottleneck of the application of the whole system. In a ring signature system, the problem is particularly obvious, a verifier needs to verify not only a public key certificate of a signer but also public key certificates of other users in a ring, and the signer needs to verify the certificates of the other users in the ring before signing to ensure the anonymity of the signer, and when the number of users in the ring is large, the signing and verifying efficiency is seriously influenced. Under the architecture, identity information of a user is a public key of the user, and a corresponding private key is calculated by a Key Generation Center (KGC) according to the user identity and a private key of a system. The identity-based ring signature system is formed by fusing an identity-based cryptographic technology and a ring signature technology, and is slightly different from the original ring signature system in that the identity-based ring signature system has a trusted central KGC which is responsible for generating corresponding public and private keys for users in the system, but the existence of the KGC should not influence the anonymity of the ring signature, namely the KGC cannot know which user in the ring carries out the signature. So far, although there are a series of grid ring signature schemes and grid identity-based signature schemes, in the existing ring signature schemes, the main problems are focused on the aspects of calculation, communication efficiency and security of the system, which still need to be improved.
Disclosure of Invention
The invention aims to provide an optimized ring signature method and system, which can improve the communication efficiency of ring signatures.
In order to achieve the purpose, the invention provides the following scheme:
an optimized ring signature method, the ring signature method comprising:
acquiring each user identity and a message to be signed;
randomly selecting parameters according to each user identity to generate system parameters and a master key;
determining a private key corresponding to the user identity according to the system parameter, the master key and the user identity;
obtaining a corresponding ring signature according to the message to be signed, the user identity and the private key corresponding to the user identity;
and judging whether the ring signature is a valid signature.
Optionally, the acquiring each user identity and the message to be signed specifically includes:
and acquiring a plurality of user identity IDs and the message m to be signed according to the two hash functions.
Optionally, the randomly selecting a parameter according to each user identity, and generating a system parameter and a corresponding master key specifically includes:
selecting a parameter n according to each user identity, and operating a trap generation function TrapGen (1) according to the parameter n and KGCn) Generating a matrix
And ^ a┴(A0) Corresponding to a short base S0And then, calculating the average value of the average value,
and order S0Is a master secretKey, order (A)0T) is a primary public key;
among them, TrapGen (1)n) Is a trap generation function that is run to output a pair of information (A, T), where A is statistically close to
One is uniformly distributed, T is ^┴(A) A good group of0Is a matrix of nxm dimensions, ID1Identity ID, indicating the first user in the ring2ID representing the second user in the ring, and so on, H0Representing hash functions, formulas
Representing the calculation of the sum of the public keys of the respective users.
Optionally, the determining, according to the system parameter, the master key, and the user identity, a private key corresponding to the user identity specifically includes:
calling the BasisDel function (A)0,H0(IDi),S0Sigma) algorithm gets
Wherein
Is a┴(A0(H0(IDi))-1) And
any one of the groups of (1);
wherein BasisDel is a base deletion function, sigma represents a normal distribution standard deviation parameter, and the function output is ^┴(A0(H0(IDi))-1) A random base of (1), and satisfy
Wherein A is0(H0(IDi))-1Represents a transpose of a matrix;
for j is more than or equal to 1 and less than or equal to m, a non-uniform small integer de-sampling function is called
To generate SijWherein t isjIs the jth column of T and
order to
Is IDiThe secret key of (a), and therefore,
and A is0(H0(IDi))-1Si＝T。
Optionally, the obtaining a corresponding ring signature according to the message to be signed, the user identity, and the private key corresponding to the user identity specifically includes:
(a)
wherein the content of the first and second substances,
is a discrete normal distribution over Zm with standard deviation σ, y1,y2,…ylA feature vector for each user ID;
(b) computing
Wherein, y1,y2,…ylA syndrome (i.e., a feature vector) representing each user ID on the ring R, μ represents information of a signature of the ring R, and c represents information according to an algorithm formula
The calculated signature information;
(c) if j is i, then z is setj＝Sic+yjZj represents the feature vector of the jth user ID on ring R, otherwise, set zj＝yjOutput signature (. mu., z)1，z2，...zlC, the probability of R) is
R denotes a ring composed of respective user IDs,
where M represents a constant calculated, whose value is related to T,
expressed as a discrete normal distribution over Zm with standard deviation sigma,
denotes the value v ∈ ZmA discrete normal distribution on a vector Zm centered at and standard deviation σ, and l represents the number of users in the ring R.
Optionally, the determining whether the ring signature is a valid signature specifically includes:
sign the ring (μ, z)1，z2，...zlC, R) the following formula is input:
H(A0H0(ID1)-1z1+A0H0(ID2)-1z2...+A0H0(IDl)-1zl-Tc，μ)＝c
judging whether the equation is established or not;
if the above equation is true, the ring signature is a valid signature;
if the above equation does not hold, the ring signature is an invalid signature.
In order to achieve the purpose, the invention provides the following scheme:
an optimized ring signature system, the ring signature system comprising:
the user identity acquisition module is used for acquiring each user identity;
the message to be signed acquisition module is used for acquiring the message to be signed;
the system parameter and master key acquisition module is used for randomly selecting parameters according to each user identity to generate system parameters and master keys;
the private key acquisition module is used for determining a private key corresponding to the user identity according to the system parameter, the master key and the user identity;
the ring signature acquisition module is used for acquiring a corresponding ring signature according to the message to be signed, the user identity and the private key corresponding to the user identity;
and the judging module is used for judging whether the ring signature is a valid signature.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses an optimized ring signature method and system. The ring signature method comprises the following steps: acquiring each user identity and a message to be signed; randomly selecting parameters according to each user identity to generate system parameters and a master key; determining a private key corresponding to the user identity according to the system parameter, the master key and the user identity; obtaining a corresponding ring signature according to the message to be signed, the user identity and the private key corresponding to the user identity; and judging whether the ring signature is a valid signature. By adopting the optimized ring signature method, the communication efficiency of the ring signature can be improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of an optimized ring signature method according to an embodiment of the present invention;
fig. 2 is a diagram of an optimized ring signature system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an optimized ring signature method and system, which can improve the communication efficiency of ring signatures.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of an optimized ring signature method according to an embodiment of the present invention. As shown in fig. 1, an optimized ring signature method includes:
step 101: acquiring each user identity and a message to be signed, specifically comprising: and acquiring a plurality of user identity IDs and the message m to be signed according to the two hash functions.
Step 102: randomly selecting parameters according to each user identity to generate system parameters and a master key;
step 103: determining a private key corresponding to the user identity according to the system parameter, the master key and the user identity;
step 104: obtaining a corresponding ring signature according to the message to be signed, the user identity and the private key corresponding to the user identity;
step 105: and judging whether the ring signature is a valid signature.
In step 102, the randomly selecting a parameter according to each user identity to generate a system parameter and a corresponding master key specifically includes:
according to eachSelecting a parameter n for each user identity, and operating a trap generation function TrapGen (1) according to the parameter n and KGCn) Generating a matrix
And ^ a┴(A0) Corresponding to a short base S0And then, calculating the average value of the average value,
and order S0Is a master private key, order (A)0T) is a primary public key;
among them, TrapGen (1)n) Is a trap generation function that is run to output a pair of information (A, T), where A is statistically close to
One is uniformly distributed, T is ^┴(A) A good group of0Is a matrix of nxm dimensions, ID1Identity ID, indicating the first user in the ring2ID representing the second user in the ring, and so on, H0Representing hash functions, formulas
Representing the calculation of the sum of the public keys of the respective users.
In step 103, the determining a private key corresponding to the user identity according to the system parameter, the master key, and the user identity specifically includes:
calling the BasisDel function (A)0,H0(IDi),S0Sigma) algorithm gets
Wherein
Is a┴(A0(H0(IDi))-1) And
any one of the groups of (1);
wherein BasisDel is a base deletion function, sigma represents a normal distribution standard deviation parameter, and the function output is ^┴(A0(H0(IDi))-1) A random base of (1), and satisfy
Wherein A is0(H0(IDi))-1Represents a transpose of a matrix;
for j is more than or equal to 1 and less than or equal to m, a non-uniform small integer de-sampling function is called
To generate SijWherein t isjIs the jth column of T and
order to
Is IDiThe secret key of (a), and therefore,
and A is0(H0(IDi))-1Si＝T。
In step 104, obtaining a corresponding ring signature according to the message to be signed, the user identity, and the private key corresponding to the user identity specifically includes:
(a)
wherein the content of the first and second substances,
is a discrete normal distribution over Zm with standard deviation σ, y1,y2,…ylA feature vector for each user ID;
(b) computing
Wherein, y1,y2,…ylA syndrome (i.e., a feature vector) representing each user ID on the ring R, μ represents information of a signature of the ring R, and c represents information according to an algorithm formula
The calculated signature information;
(c) if j is i, then z is setj＝Sic+yjZj represents the feature vector of the jth user ID on ring R, otherwise, set zj＝yjOutput signature (. mu., z)1，z2，...zlC, the probability of R) is
R denotes a ring composed of respective user IDs,
where M represents a constant calculated, whose value is related to T,
expressed as a discrete normal distribution over Zm with standard deviation sigma,
denotes the value v ∈ ZmA discrete normal distribution on a vector Zm centered at and standard deviation σ, and l represents the number of users in the ring R.
In step 105, the method specifically includes:
sign the ring (μ, z)1，z2，...zlC, R) the following formula is input:
H(A0H0(ID1)-1z1+A0H0(ID2)-1z2...+A0H0(IDl)-1zl-Tc，μ)＝c
judging whether the equation is established or not;
if the above equation is true, the ring signature is a valid signature;
if the above equation does not hold, the ring signature is an invalid signature.
Fig. 2 is a diagram of an optimized ring signature system according to an embodiment of the present invention. As shown in fig. 2, an optimized ring signature system includes:
a user identity obtaining module 201, configured to obtain each user identity;
a message to be signed acquisition module 202, configured to acquire a message to be signed;
a system parameter and master key obtaining module 203, configured to randomly select a parameter according to each user identity, and generate a system parameter and a master key;
a private key obtaining module 204, configured to determine, according to the system parameter, the master key, and the user identity, a private key corresponding to the user identity;
a ring signature obtaining module 205, configured to obtain a corresponding ring signature according to the message to be signed, the user identity, and the private key corresponding to the user identity;
a determining module 206, configured to determine whether the ring signature is a valid signature.
First, most ring signature schemes so far rely on the hard-theoretic problem, discrete logarithm, and bilinear peer-to-peer support techniques, but unfortunately, the above-described number-theoretic-based cryptographic problem can be easily broken in the latter quantum era. Because of its simplicity and high security, lattice-based cryptography is receiving great attention. The scheme provided by the invention only uses linear operations such as modular multiplication, modular addition and the like, so that the signature scheme provided by the invention has more advantages in efficiency compared with the traditional ring signature scheme based on number theory. Secondly, the efficiency of the lattice-based signature scheme is mainly determined by factors such as the length of a public key, a private key and a signature, lattice dimension, and the computation time in an extraction and signature algorithm, the scheme of the invention can realize the signature algorithm only by a few matrix vectors, and in order to embody the advantages of the scheme of the invention in the aspect of efficiency, two lattice-based ring signature schemes which have public impact on the generated public key length, the private key length and the signature length are selected as comparison.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (3)
1. An optimized ring signature method, the ring signature method comprising:
acquiring each user identity and a message to be signed;
randomly selecting parameters according to each user identity to generate system parameters and a master key;
determining a private key corresponding to the user identity according to the system parameter, the master key and the user identity;
obtaining a corresponding ring signature according to the message to be signed, the user identity and the private key corresponding to the user identity;
judging whether the ring signature is a valid signature;
the randomly selecting parameters according to each user identity to generate system parameters and corresponding master keys specifically includes:
selecting a parameter n according to each user identity, and operating a trap generation function TrapGen (1) according to the parameter n and KGCn) Generating a matrix
And ^ a┴(A0) Corresponding to a short base S0And then, calculating the average value of the average value,
and order S0Is a master private key, order (A)0T) is a primary public key;
among them, TrapGen (1)n) Is a trap generation function that is run to output a pair of information (A, T), where A is statistically close to
One is uniformly distributed, T is ^┴(A) A good group of0Is a matrix of nxm dimensions, ID1Identity ID, indicating the first user in the ring2ID representing the second user in the ring, and so on, H0Representing hash functions, formulas
Representing calculating the sum of public keys of each user;
the determining, according to the system parameter, the master key, and the user identity, a private key corresponding to the user identity specifically includes:
calling the BasisDel function (A)0,H0(IDi),S0Sigma) algorithm gets
Wherein
Is a┴(A0(H0(IDi))-1) And
any one of the groups of (1);
wherein BasisDel is a base deletion function, sigma represents a normal distribution standard deviation parameter, and the function output is ^┴(A0(H0(IDi))-1) A random base of (1), and satisfy
Wherein A is0(H0(IDi))-1Represents a transpose of a matrix;
for j is more than or equal to 1 and less than or equal to m, a non-uniform small integer de-sampling function is called
To generate SijWherein t isjIs the jth column of T and
order to
Is IDiThe secret key of (a), and therefore,
and A is0(H0(IDi))-1Si＝T；
The obtaining of the corresponding ring signature according to the message to be signed, the user identity and the private key corresponding to the user identity specifically includes:
(a)
wherein the content of the first and second substances,
z with standard deviation of sigmamDiscrete normal distribution of (a), y1,y2,…ylA feature vector for each user ID;
(b) computing
Wherein, y1,y2,…ylA syndrome representing each user ID on the ring R, i.e., a feature vector,. mu.represents information of the ring R signature, and c represents a formula according to an algorithm
The calculated signature information;
(c) if j is i, then z is setj＝Sic+yj，zjA feature vector representing the jth user ID on ring R, otherwise, set zj＝yjOutput signature (. mu., z)1，z2，...zlC, the probability of R) is
R denotes a ring composed of respective user IDs,
where M represents a constant calculated, whose value is related to T,
z expressed as standard deviation sigmamThe discrete normal distribution of (a) above,
denotes the value v ∈ ZmVector Z centered and having standard deviation σmAbove the discrete normal distribution, l denotes the users in the ring RThe number of (2);
the determining whether the ring signature is a valid signature specifically includes:
sign the ring (μ, z)1，z2，...zlC, R) the following formula is input:
H(A0H0(ID1)-1z1+A0H0(ID2)-1z2...+A0H0(IDl)-1zl-Tc,μ)＝c
judging whether the formula is established or not;
if the formula is established, the ring signature is a valid signature;
and if the formula is not satisfied, the ring signature is an invalid signature.
2. The optimized ring signature method according to claim 1, wherein the obtaining of each user identity and the message to be signed specifically comprises:
and acquiring a plurality of user identity IDs and the message m to be signed according to the two hash functions.
3. An optimized ring signature system, the ring signature system comprising:
the user identity acquisition module is used for acquiring each user identity;
the message to be signed acquisition module is used for acquiring the message to be signed;
a system parameter and master key obtaining module for randomly selecting parameters according to each user identity to generate system parameters and master keys, specifically for selecting a parameter n according to each user identity and operating a trap generation function TrApgen (1) according to the parameter n and KGCn) Generating a matrix
And ^ a┴(A0) Corresponding to a short base S0And then, calculating the average value of the average value,
and order S0Is a master private key, order (A)0T) is a primary public key;
among them, TrapGen (1)n) Is a trap generation function that is run to output a pair of information (A, T), where A is statistically close to
One is uniformly distributed, T is ^┴(A) A good group of0Is a matrix of nxm dimensions, ID1Identity ID, indicating the first user in the ring2ID representing the second user in the ring, and so on, H0Representing hash functions, formulas
Representing calculating the sum of public keys of each user;
a private key obtaining module, configured to determine, according to the system parameter, the master key, and the user identity, a private key corresponding to the user identity, specifically,
for calling the BasisDel function (A)0,H0(IDi),S0Sigma) algorithm gets
Wherein
Is a┴(A0(H0(IDi))-1) And
any one of the groups of (1);
wherein BasisDel is a base deletion function, sigma represents a normal distribution standard deviation parameter, and the function output is ^┴(A0(H0(IDi))-1) A random base ofAnd satisfy
Wherein A is0(H0(IDi))-1Represents a transpose of a matrix;
for j is more than or equal to 1 and less than or equal to m, a non-uniform small integer de-sampling function is called
To generate SijWherein t isjIs the jth column of T and
order to
Is IDiThe secret key of (a), and therefore,
and A is0(H0(IDi))-1Si＝T；
A ring signature obtaining module, configured to obtain a corresponding ring signature according to the message to be signed, the user identity, and the private key corresponding to the user identity, which is specifically used in (a)
Wherein the content of the first and second substances,
z with standard deviation of sigmamDiscrete normal distribution of (a), y1,y2,…ylA feature vector for each user ID;
(b) computing
Wherein, y1,y2,…ylA syndrome representing each user ID on the ring R, i.e., a feature vector,. mu.represents information of the ring R signature, and c represents a formula according to an algorithm
The calculated signature information;
(c) if j is i, then z is setj＝Sic+yjZj represents the feature vector of the jth user ID on ring R, otherwise, set zj＝yjOutput signature (. mu., z)1，z2，...zlC, the probability of R) is
R denotes a ring composed of respective user IDs,
where M represents a constant calculated, whose value is related to T,
z expressed as standard deviation sigmamThe discrete normal distribution of (a) above,
denotes the value v ∈ ZmVector Z centered and having standard deviation σmThe above discrete normal distribution, l represents the number of users in ring R;
a judging module for judging whether the ring signature is a valid signature, specifically for judging whether the ring signature (μ, z) is a valid signature1，z2，...zlC, R) the following formula is input:
H(A0H0(ID1)-1z1+A0H0(ID2)-1z2...+A0H0(IDl)-1zl-Tc，μ)＝c
judging whether the formula is established or not;
if the formula is established, the ring signature is a valid signature;
and if the formula is not satisfied, the ring signature is an invalid signature.
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