CN113438085B - Efficient attribute-based server auxiliary signature verification method and system - Google Patents
Efficient attribute-based server auxiliary signature verification method and system Download PDFInfo
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- H—ELECTRICITY
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- 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
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/10—Network architectures or network communication protocols for network security for controlling access to devices or network resources
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
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Abstract
The invention relates to a signature verification method and a signature verification system assisted by a high-efficiency attribute-based server, wherein the signature verification system comprises the following steps: the attribute authorization terminal is used for generating a system master key and a public parameter; the system is also used for generating a private key and an access policy verification public key according to the system master key, the public parameter and the signature end attribute; the server verifies the public key according to the public parameters, converts the signature and calculates an intermediate signature; the signature end is used for calculating a signature according to the private key, the public parameter, the access strategy and the message; the verification terminal is used for converting the secret key, the message and the signature according to the public parameters, and calculating a conversion signature and an intermediate signature; and the method is also used for verifying the validity of the signature according to the public parameters, the intermediate signature, the access strategy, the conversion key. The invention effectively improves the access control and anonymous authentication efficiency of the resource-restricted equipment on the premise of ensuring the reliability.
Description
Technical Field
The invention relates to the technical field of use safety of resource-constrained equipment, in particular to a method and a system for verifying an auxiliary signature of a high-efficiency attribute-based server.
Background
The attribute-based signature is a new cryptographic primitive, i.e. a valid signature can be generated only when the user's attributes meet the access policy and the signature does not reveal the identity information of the user. However, there are some attribute-based signatures based on a threshold policy, where the signature algorithm is limited by a threshold, and the access policy of the threshold cannot well perform accurate access control on the attributes of the user. In addition, since a certain number of pairing operations are required in the verification stage, the calculation overhead of the verification algorithm is increased, and a heavy calculation burden is caused for the verifier. Compared with exponential operation, pairing operation is time-consuming, so that the existing ABS scheme is not suitable for devices with limited resources, such as RFID, smart cards and the like.
Disclosure of Invention
In view of this, an object of the present invention is to provide a method and a system for efficient attribute-based server-assisted signature verification, in which the server-assisted user performs a lot of computation overhead in the signature and verification algorithm, and the proposed scheme provides anonymity and non-counterfeitability. Furthermore, the proposed method reduces the computational overhead of the signer and verifier.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a signature method for a high-efficiency attribute-based server-assisted verification signature system comprises the following steps:
step S1: the attribute authorization terminal inputs a security parameter lambda and outputs a system master key MK and a public parameter params;
step S2: the attribute authorization terminal inputs MK, public parameter params and signature terminal attribute omega, and generates verification public key gpk and private key sk ω ；
Step S3: signature end input private key sk ω Public parameter params, access policy Γ, message M, output signature delta;
step S4: the verification end inputs public parameter params, conversion key tk, message M, signature delta and output conversion signature
Step S5: serviceThe device inputs public parameter params and converts signature
Verifying public key gpk, outputting an intermediate signature +.>
Step S6: the verification end inputs public parameter params and intermediate signature
The access policy Γ, the translation key tk, outputs 1 if the signature is valid, otherwise outputs 0.
Further, the step S1 specifically includes the following steps:
step S11: g 1 And G 2 For the multiplicative group of order p, G is G 1 Is a generator of (1). The attribute authorization terminal randomly selects a epsilon Z p Calculate g 1 ＝g a Wherein Z is p ＝{0,1,2,…,p-1}；
Step S12: attribute authority random selection g 2 ,u′,u 1 ,…,u n ∈G 1 And z=e (g 1 ,g 2 ) Where master key mk=a. The disclosed parameters are: params= (p, G) 1 ,G 2 ,e,g,g 1 ,g 2 ,u′,u 1 ,…,u n ,Z)；
Further, in the step S2, the method specifically includes the following steps:
step S21: attribute authority random selection
Calculation of a 2 ＝a-a 1 The method comprises the steps of carrying out a first treatment on the surface of the Then randomly select r E Z p Calculating to obtain->
Wherein->
Step S22: for each i E omega, the attribute authorization terminal randomly selects r i ∈Z p ,β i ∈Z p Calculation of
The private key of the user is sk ω ＝(d i ,{d i0 ,d i1 } i∈ω )；
Step S23: to generate the verification public key gpk for the attribute tree Γ, the attribute authority selects a d x ＝k x -polynomial q of order 1 x (. Cndot.) wherein k x Is a threshold value, q root (·)＝a 1 Is the value of the root node, the other nodes are set to q x (0)＝q parent(x) (index (x)). If a polynomial is calculated, a verification public key for the attribute tree Γ
Where i=att (x), x is the leaf node;
further, in the step S3, the method specifically includes the following steps:
step S31: the user has a private key sk about the attribute ω ω To generate a message m= {0,1} n Is chosen randomly by the user s e Z p Calculation of
Definitions->
For attributes on the attribute tree, with respect to arbitrary
The user randomly selects r' i ∈Z p Calculate->
Step S32: user output signature δ= (δ) 0 ,δ′ 0 ,{δ i0 ,δ i1 } i∈ω )；
Further, in the step S4, the calculation of the user signature specifically includes the following steps:
step S41: after the verification terminal receives the signature delta, randomly selecting t epsilon Z p As a conversion key tk, a conversion signature is calculated
Step S42: the verification end sends the conversion signature
To the server side.
Further, the step S5 specifically includes the following steps:
step S51: the attribute authority defines a recursive algorithm
To verify the signature, where x is the node about the tree. Let i=att (x), if x represents a leaf node, the server side obtains the conversion signature from the verification side
Calculation of
Step S52: if it is
Server side computing
Step S53: if it is
Server endCalculate->
Step S54: if x is a non-leaf node, then the algorithm
Is performed as follows. Calculated as +.about.node z for all>
Where all nodes z are child nodes of node x. Let S x Represented as having arbitrary k x A set of child nodes z. Let i=index (z) be the index of node z, S' x ＝{index(z):z∈S x }. server side calculation:
server-side computing
Wherein T is root Is the value of the recursive algorithm of the root node. Then output->
The server sends an intermediate signature->
To the verification end.
Step S55: the server signs the intermediate signature
And sending the data to the verification terminal.
Step S6: the verification end inputs public parameter params and intermediate signature
Access policy Γ, transform key tk, output if signature is validAnd outputting 1, otherwise outputting 0.
Further, the step S6 specifically includes the following steps:
step S61: the verification terminal obtains the intermediate signature from the server terminal
And calculate +.>
Step S62: verification terminal verifies equation
Whether or not it is. If->
The signature is valid. Otherwise, the verification end refuses the signature.
An efficient attribute-based server-assisted verification signature system, comprising:
the attribute authorization terminal is used for generating a system master key MK and a public parameter params; the method is also used for generating a verification public key gpk and a private key sk according to a system master key MK, a public parameter params, an access policy gamma and a signature end attribute omega ω ；
A signature end for receiving the private key sk ω Public parameters params, access policy Γ, message M, calculating signature delta;
a server for verifying public key gpk according to public parameter params and converting signature
Calculate intermediate signature +.>
A verification terminal for calculating conversion signature according to public parameter params, conversion key tk, message M, signature delta
And middle labelName->
Also for intermediate signature +/based on public parameter params>
The access policy Γ, the translation key tk, verifies the validity of the signature.
Compared with the prior art, the invention has the following beneficial effects:
the invention is designed based on the attribute-based signature, the private key of the user is associated with a group of attributes, the access strategy is embedded in the signature, and if the attributes meet the access strategy, the user can generate an effective signature. The verifying end is confident that a particular signature is created by a set of possible users whose attributes match the access policy so that the identity information of the signer is not revealed. Therefore, the method and the system have strong practicability and wide application prospect in data authentication and privacy protection access control.
Drawings
FIG. 1 is a schematic block diagram of a system in an embodiment of the invention;
FIG. 2 is a schematic diagram of an attribute tree in an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
Referring to fig. 1, the present invention provides a high-efficiency attribute-based server-assisted verification signature system, comprising:
the attribute authorization terminal is used for generating a system master key MK and a public parameter params; and is also used for generating a verification public key gpk and a private key sk according to the system master key MK, the public parameter params and the signature end attribute omega ω Wherein the verification public key gpk is generated in relation to a specific attribute tree Γ, the attribute tree being denoted as an access policy;
a signature end for receiving the private key sk ω Public parameters params, access policy Γ, message M, calculating signature delta;
the server is used for verifying the public according to the public parameter paramsKey gpk, conversion signature
Calculate intermediate signature +.>
A verification terminal for calculating conversion signature according to public parameter params, conversion key tk, message M, signature delta
And intermediate signature->
Also for intermediate signature +/based on public parameter params>
The access policy Γ, the translation key tk, verifies the validity of the signature.
Referring to fig. 2, in the present implementation, the attribute tree: an attribute tree Γ is set as an access policy, wherein each non-leaf node is represented by a number of children and a threshold value. num (num) x Expressed as the number of child nodes, k x Representing a threshold value, where 0 < k x ≤num x . Each node represents a threshold value for the attribute, wherein the threshold value is represented as an AND gate (k x ＝num x ) AND OR gate (k) x =1). Each child node is from 1 to num x And performing marking index. The function index (x) responds to values associated with node x, where the index value is distributed only to the nodes of the attribute tree. The function parent (x) represents the parent node index value of node x. Each leaf node of the tree is represented as an attribute and the threshold value is defined as k x =1, the function att (x) represents the index of leaf node x.
The embodiment also provides a signature verification method assisted by the high-efficiency attribute-based server, which comprises the following steps:
step S1: the attribute authority inputs the security parameter lambda and outputs the system master key MK and the public parameter params.
In this embodiment, the step S1 specifically includes the following steps:
step S11: g 1 And G 2 For the multiplicative group of order p, G is G 1 Is a generator of (1). The attribute authorization terminal randomly selects a epsilon Z p Calculate g 1 ＝g a Wherein Z is p ＝{0,1,2,…,p-1}；
Step S12: attribute authority random selection g 2 ,u′,u 1 ,…,u n ∈G 1 And z=e (g 1 ,g 2 ) Where master key mk=a. The disclosed parameters are: params= (p, G) 1 ,G 2 ,e,g,g 1 ,g 2 ,u′,u 1 ,…,u n ,Z)；
Step S2: the attribute authorization terminal inputs MK, public parameter params, access strategy gamma and signature terminal attribute omega, and generates verification public key gpk and private key sk ω ；
In this embodiment, the attribute authority generates the user's private key sk using a set of attributes ω And verifying the public key gpk, which specifically comprises the following steps:
step S21: random selection for attribute authority
Calculation of a 2 ＝a-a 1 The method comprises the steps of carrying out a first treatment on the surface of the Then randomly select r E Z p Calculating to obtain->
Wherein->
Step S22: for each i E omega, the attribute authorization terminal randomly selects r i ∈Z p ,β i ∈Z p Calculation of
The private key of the user is sk ω ＝(d i ,{d i0 ,d i1 } ω )；/>
Step S23: to generate the verification public key gpk for a particular attribute tree Γ, the authorizing terminal selects one d x ＝k x -polynomial q of order 1 x (. Cndot.) wherein k x Is a threshold value, q root (·)＝a 1 Is the value of the root node, the other nodes are set to q x (0)＝q parent(x) (index (x)). If a polynomial is calculated, a verification public key for the attribute tree Γ
Where i=att (x), x is the leaf node;
step S3: signature end input private key sk ω The public parameter params, the access policy Γ, the message M, the output signature δ.
In this embodiment, the signature end uses the private key sk ω And attribute set omega, generating signature delta of message M, comprising the following steps:
step S31: the signing end has a private key sk about an attribute omega ω To generate a message m= {0,1} n Is signed, signature end randomly selects s epsilon Z p Calculation of
Definitions->
For the attribute associated with the attribute tree, about any +.>
Signature end randomly selects r' i ∈Z p Calculate->
Step S32: signature end outputs signature delta= (delta) 0 ,δ′ 0 ,{δ i0 ,δ i1 } i∈ω )；
Step S4: the verification end inputs public parameter params, conversion key tk, message M, signature delta and output conversion signature
In this embodiment, the step S4 specifically includes the following steps:
step S41: after the verification terminal receives the signature delta, randomly selecting t epsilon Z p As a conversion key tk, a conversion signature is calculated
Step S42: the verification end sends the conversion signature
To the server.
Step S5: the server inputs public parameter params and converts signature
Outputting an intermediate signature +.>
In this embodiment, the step S5 specifically includes the following steps:
step S51: the attribute authority defines a recursive algorithm
To verify the signature, where x is the node about the tree, let i=att (x), if x represents the leaf node, the server side obtains the conversion signature from the verification side +.>
Calculate->
Step S52: if it is
Server side computing
Step S53: if it is
Server side computation +.>
/>
Step S54: if x is a non-leaf node, then the algorithm
Is performed as follows. Calculated as +.about.node z for all>
Where all nodes z are child nodes of node x. Let S x Represented as having arbitrary k x A set of child nodes z. Let i=index (z) be the index of node z, S' x ＝{index(z):z∈S x }. And (3) calculating at a server side:
server-side computing
Wherein T is root Is the value of the recursive algorithm of the root node. Then output->
The server sends an intermediate signature->
To the verification end.
Step S55: the server signs the intermediate signature
And sending the data to the verification terminal.
Step S6: verifier inputs public parameter params, intermediate signature
The access policy Γ, the translation key tk, outputs 1 if the signature is valid, otherwise outputs 0.
Step S61: the verification end obtains the intermediate signature from the server
And calculate +.>
Step S62: verification terminal verifies equation
Whether or not it is. If->
The signature is valid. Otherwise, the verification end refuses the signature.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the invention in any way, and any person skilled in the art may make modifications or alterations to the disclosed technical content to the equivalent embodiments. However, any simple modification, equivalent variation and variation of the above embodiments according to the technical substance of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims (3)
1. The high-efficiency attribute-based server assisted signature verification method is characterized by comprising the following steps of:
step S1: the attribute authorization terminal inputs a security parameter lambda and outputs a system master key MK and a public parameter params;
step S2: attribute authorization end input MK, public parameter pThe arams, the access policy Γ and the signature end attribute ω generate a verification public key gpk and a private key sk ω ；
Step S3: signature end input private key sk ω Public parameter params, access policy Γ, message M, output signature sigma; the attribute tree is represented as an access policy Γ;
step S4: the verification end inputs public parameter params, conversion key tk, message M, signature delta and output conversion signature
Step S5: the server inputs public parameter params and converts signature
Verifying public key gpk, outputting an intermediate signature +.>
Step S6: the verification end inputs public parameter params and intermediate signature
Accessing policy Γ, converting key tk, outputting 1 if signature is valid, otherwise outputting 0;
the step S1 specifically comprises the following steps:
step S11: set G 1 And G 2 For the multiplicative group of order p, G is G 1 The attribute authorization terminal randomly selects a E Z p Calculate g 1 ＝g a Wherein Z is p ＝{0,1,2,…,p-1}；
Step S12: attribute authority random selection g 2 ,u',u 1 ,…,u n ∈G 1 And z=e (g 1 ,g 2 ) Where master key mk=a, the public parameters are: params= (p, G) 1 ,G 2 ,e,g,g 1 ,g 2 ,u',u 1 ,…,u n ,Z)；
The step S2 specifically includes the following steps:
step S21: random selection for attribute authority
Calculation of a 2 ＝a-a 1 The method comprises the steps of carrying out a first treatment on the surface of the Then randomly select r E Z p Calculating to obtain->
Wherein->
Step S22: for each i E omega, the attribute authorization terminal randomly selects r i ∈Z p ，β i ∈Z p Calculation of
The private key of the user is sk ω ＝(d i ,{d i0 ,d i1 } i∈ω )；
Step S23: the attribute authorization terminal selects a d x ＝k x -polynomial q of order 1 x (. Cndot.) wherein k x Is a threshold value, q root (·)＝a 1 Is the value of the root node, the other nodes are set to q x (0)＝q parent(x) (index (x)); if a polynomial is calculated, a verification public key for the attribute tree Γ
Where i=att (x), x is the leaf node;
in the step S3, the calculation of the user signature specifically includes the following steps:
step S31: the user has a private key sk about a signature end attribute omega ω To generate a message m= {0,1} n Is chosen randomly by the user s e Z p Calculation of
δ 0 '＝g s Definitions->
For attributes related to the attribute tree, with respect to any
User randomly selects r i '∈Z p Calculate->
Step S32: user output signature δ= (δ) 0 ,δ' 0 ,{δ i0 ,δ i1 } i∈ω )；
The step S4 specifically includes the following steps:
step S41: after the verification terminal receives the signature delta, randomly selecting t epsilon Z p As a conversion key tk, a conversion signature is calculated
Step S42: the verification end sends the conversion signature
Feeding the server side;
the step S5 specifically includes the following steps:
step S51: the attribute authority defines a recursive algorithm
To verify the signature, where x is the node about the tree, let i=att (x), if x represents the leaf node, the server side obtains the conversion signature from the verification side +.>
Calculate->
Step S52: if it is
Server side computing
Step S53: if it is
Server side computation +.>
Step S54: if x is a non-leaf node, then the algorithm
Is performed as follows; calculated as +.about.node z for all>
Wherein all nodes z are child nodes of node x; let S x Represented as having arbitrary k x A sub-node z set; let i=index (z) be the index of node z, S' x ＝{index(z):z∈S x }. server side calculation:
server-side computing
Wherein T is root Is the value of the root node's recursive algorithm; then output
The server sends an intermediate signature->
To the verification end.
2. The method for assisting in verifying signatures by using a high-efficiency attribute-based server as set forth in claim 1, wherein the step S6 comprises the steps of:
step S61: the verification terminal obtains the intermediate signature from the server terminal
And calculate +.>
Step S62: verification terminal verifies equation
Whether or not to establish; if->
And if the signature is valid, the verification terminal refuses the signature.
3. A system for implementing the efficient attribute-based server-assisted signature verification method of claim 1 or 2, comprising:
the attribute authorization terminal is used for generating a system master key MK and a public parameter params; and is also used for generating a verification public key gpk and a private key sk according to the system master key MK, the public parameter params and the signature end attribute omega ω Wherein the verification public key gpk is generated based on a specific attribute tree, the attribute tree being denoted as an access policy Γ;
a signature end for receiving the private key sk ω Public parameters params, access policy Γ, message M, calculating signature delta;
a server for according to the public parametersParams, verify public key gpk, convert signature
Calculate intermediate signature +.>
A verification terminal for calculating conversion signature according to public parameter params, conversion key tk, message M, signature delta
And intermediate signature->
Also for intermediate signature +/based on public parameter params>
The access policy Γ, the translation key tk, verifies the validity of the signature. />
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| 高效的属性基远程证明方案(英文);张亦辰 等;《INFORMATION SECURITY》;全文 * |
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