CN111404689A - Identity-based lightweight linear homomorphic network coding signature method - Google Patents
Identity-based lightweight linear homomorphic network coding signature method Download PDFInfo
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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
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- H04L9/008—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols involving homomorphic encryption
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- H—ELECTRICITY
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Abstract
The invention discloses a lightweight linear homomorphic network coding signature method based on identity, which comprises the steps that firstly, an identity public key system selects parameters from a public key cryptographic function library to generate a main public and private key pair of the identity public key system, and the identity public key system generates a corresponding private key for a user in the system according to system parameters; the user signs the expansion vector of the message by using a private key of the user, and then the expansion vector corresponds to the subspace label, and the expansion vector and the signature of the message are sent to other users in the system; the network intermediate node combines the verified vector and the corresponding signature to obtain a new vector signature pair which can be verified and sends the new vector signature pair to the next network node; the receiver can recover the original vector after receiving enough signatures which can pass the verification. The method has the advantages of simple implementation process and low calculation cost, and can be used for detecting the integrity of data in network coding and preventing the network from being attacked by the pollution of a third party.
Description
Technical Field
The invention belongs to the information security technology, particularly relates to a linear homomorphic signature method, and particularly relates to a lightweight linear homomorphic network coding signature method based on identity.
Background
With the rapid development of scientific technology, wireless sensor network technology is widely applied in the fields of infrastructures such as industry, agriculture, environment, traffic, logistics, security and the like. By applying the network coding technology, signals can be rapidly transmitted in a wireless channel, and the throughput of the network is greatly improved. However, using network coding techniques, wireless sensor networks are vulnerable to contamination attacks, which can present challenges to data integrity and availability.
The linear homomorphic network coding signature technology can be used for guaranteeing the integrity and authenticity of data and solving the problem of pollution attack in a wireless sensor network. The concept of linear homomorphic network coding signatures was proposed by Dan Boneh et al in 2009, where messages are expressed as vectors in vector space and the operations of the messages are linear operations in vector space. In a linear homomorphic network coding signature scheme, we first represent the message as a vector v1,...,vmThen, each vector is expanded into a vector m according to a specific rule1,...,mmSo that the node can recover the original vector after receiving enough vectors. If a public and private key pair is (pk, sk user pair vector m1,...,mmRespectively is sigma1=Signsk(m1),...,σm=Signsk(mm) Then any user is getting (m)1,σ1),...,(mm,σm) The user pair m can then be deduced1,...,mmAny linear combination of (a) results in a signature σ for the message m.
In the identity public key system, the identity of the user is the public key. Compared with the traditional public key cryptosystem, the method reduces the management cost of the user public key and the certificate, and is more suitable for being deployed in practical application. In the wireless sensor network, the unique identification code of each terminal node is used as the public key of the terminal node.
The invention provides a lightweight linear homomorphic network coding signature method based on identity. In the signature generation process, the scheme does not need the Hash to point calculation with higher calculation cost, and only needs power exponent calculation on one group, thereby greatly reducing the calculation cost of users.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problem of complex calculation of network nodes and data thereof in the identity public key system, the invention provides a lightweight linear homomorphic network coding signature method based on identity.
The technical scheme is as follows: a lightweight linear homomorphic network coding signature method based on identity comprises the following steps:
(1) generating system public and private keys
In the identity public key system, a PKG selects a set of parameters from a public key function database, including two cyclic groups with prime q in orderAndbilinear pairingsHash function According to the selected parameters, the PKG generates a system master public key mpk and a system master private key msk;
(2) generating a user private key
The user A identifies the user AASending the data to a PKG (public Key group), and generating a private key for the user A after the identity of the user A is verified by the PKG
(3) Generating signatures
User A firstly converts message m to be signed intoVector v of1,...,vmThen the vector is expandedIs identifier as VIDVector m in subspace V1,...,mm(ii) a User A computes the label τ of subspace VidAnd calculates the vector m using its own private key1,...,mmCorresponding signature σ1,...,σm(ii) a User A tags subspace τ withidVector m1,...,mmAnd its corresponding signature σ1,...,σmTo user B1,B2;
(4) Verifying signatures
Network intermediate node CiFirst according to the subspace label τidTo confirm whether V is the message sent by user A; then by signature σiVerification vector mi∈ V integrity;
(5) deriving signatures
Network intermediate node CiAnd (4) combining the received vectors to obtain a new vector m, and generating a signature sigma of the new vector m by using signatures corresponding to the vectors, wherein the vector signatures (m, sigma) can be verified in the step (4).
Further, the PKG in step (1) selects a set of parameters from a public key cryptographic function library, where the set of parameters specifically includes two cyclic groups with prime q in orderA bilinear pairA generator g of, three cryptographic hash functions
The generation steps of the system master public key mpk and the system master private key msk in the step (1) are as follows:
(12) computing and broadcasting the public key mpk ═ gs;
Further, the private key generation step of the user a in the step (2) is as follows:
Further, the signature process of the user a generating the message in step (3) is as follows:
(31) user A converts message M to be signed intoUpper vector v1,...,vmWherein v isi=(vi1,...,vin),1≤i≤m;
(32) User A expands each of the m n-dimensional vectors to have an identifier of VIDIs (n + m) -dimensional vector m in subspace V1,...,mmWherein, in the step (A),
(33) user a first starts from the prime fieldRandomly selecting two random values x, k, and calculating the commitment U-g for the two temporary variablesxAnd R ═ e (g, g)k;
(34) User A calculates the identity IDASubspace identifier VIDAnd the hash value w of the commitment U is H1(IDA,VID,U);
(35) User A computing pair (V)IDSignature of U)And setting the label tau of the subspace as (U, R, Z);
(37) and the user A sends the subspace label, the expansion vector and the corresponding signature to the next node.
Further, the verification of the signature in step (4) is performed as follows:
(41) network intermediate node CiFirst, according to public information calculationAnd w ═ H1(IDA,VIDU), then verify the equation
(42) If the above equation holds true, node CiThe received messages all come from the label tauidA subspace V; node C theniBy the equationVerifying the received vector mi。
Further, the signature derivation process described in step (5) is as follows:
(51) network intermediate node CiDiscarding vectors that fail validation;
(52) network intermediate node CiMerging the verified vectors to obtain a new vector m, i.e.Is a vector correlation coefficient;
(54) Network intermediate node CiSending the vector m and the signature sigma to a next node;
(55) when the user B1Or B2When a sufficient number of verified vectors are received, the original vector sent by user a can be decoded.
Has the advantages that: compared with the prior art, the method and the device do not need the operation of Hash to point with higher calculation cost when generating the signature, and only 1 power exponent calculation is needed when generating the signature of one vector, thereby not only reducing the calculation complexity of a user, but also improving the transmission efficiency. On the other hand, the invention enables any node in the network to integrate and verify vectors from user a with the same label. The nodes in the network may generate a new vector and signature based on the received vector and signature and the signature is indistinguishable from the signature generated by user a for this new vector with its own private key.
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FIG. 1 is a schematic diagram of network coded communications between users;
fig. 2 is a schematic diagram of the signature process of the present invention.
Detailed Description
To explain the technical solutions disclosed in the present invention in detail, the following description is further made with reference to the accompanying drawings and specific examples.
With the rapid development of scientific technology, wireless sensor network technology is widely applied in the fields of infrastructures such as industry, agriculture, environment, traffic, logistics, security and the like. By applying the network coding technology, signals can be rapidly transmitted in a wireless channel, and the throughput of the network is greatly improved. However, using network coding techniques, wireless sensor networks are vulnerable to contamination attacks, which can present challenges to data integrity and availability. The linear homomorphic network coding signature technology can be used for guaranteeing the integrity and authenticity of data and solving the problem of pollution attack in a wireless sensor network.
The invention provides an identity-based lightweight linear homomorphic network coding signature method capable of simply and efficiently realizing data integrity verification, and the specific description of the scheme is given below.
In the following description of the invention, the PKG in the identity public key system is a fully honest and trusted authority that is primarily responsible for generating system parameters, the master private key, and the private key of the user.
The symbols involved in the method of the invention and their definitions are as follows:
PKG: the 'private key generator' of the identity public key system is responsible for generating the private key of the user in the system.
A: a message sender of an identity public key system.
B1,B2: a message recipient of an identity public key system.
Ci: and the intermediate network node with the number i, such as a router, a repeater and the like.
IDA: the identity of user a.
mpk: the public key of the identity public key system.
msk: private key of the identity public key system.
a ∈ S: a is an element in the set S.
M: a message to be signed.
vi: the ith vector corresponding to the message M, where vi=(vi1,...,vin),1≤i≤m。
σi:mithe corresponding signature.
V:m1,...,mmThe subspace is the same.
VID: of the subspace VAnd identifying the identifier.
τid: and V label.
m: arbitrary vectors in the subspace V.
σ: the signature corresponding to the vector m.
mod q: and (5) performing modulo q operation. For example, 24mod 7 ═ 3.
x | | y: the concatenation of x and y, where x, y may be a string of bits or a string of bytes.
a1·a2: element a1And a2Multiplication.
The generation steps of the invention are as follows:
(1) a system public and private key generation step:
in the identity public key system, a PKG selects a set of parameters from a public key function database, including two cyclic groups with prime q in orderAndbilinear pair e:hash function H0:H1:H2:According to the selected parameters, the PKG generates a system master public key mpk and a system master private key msk;
(2) a user private key generation step:
the user A identifies the user AASending the data to a PKG (public Key group), and generating a private key for the user A after the identity of the user A is verified by the PKG
(3) A signature generation step:
user A firstly converts message M to be signed intoVector v of1,...,vmThen, the vector is expanded to have an identifier of VIDVector m in subspace V1,…,mm. User A computes the label τ of subspace VidAnd calculates the vector m using its own private key1,...,mmCorresponding signature σ1,...,σm. User A tags subspace τ withidVector m1,...,mmAnd its corresponding signature σ1,...,σmTo user B1,B2;
(4) Signature verification:
network intermediate node CiFirst according to the subspace label τidTo confirm whether V is a message sent by user a. Then, by signature σiVerification vector mi∈ V integrity;
(5) signature derivation step:
network intermediate node CiAnd (4) combining the received vectors to obtain a new vector m, and generating a signature sigma of the new vector m by using signatures corresponding to the vectors, wherein the vector signature pair (m, sigma) can pass the verification in the step (4).
More specifically, referring to fig. 1 and 2, the specific process of the present invention is as follows:
step 1, generating a public key and a private key of a system
PKG is first derived fromRandomly selecting an integer s as a system main private key msk, calculating and broadcasting a system main public key mpk ═ gs. Then, it calculates and broadcastsThe generator e (g, g).
And 2, generating a user private key.
PKG calculates user A ID firstAHash value ofThen, the private key of the user A is calculated according to the system main private key msk ═ s
And 3, generating a signature.
User A firstly converts message M to be signed intoVector v of1,...,vm. User A then expands each of the m n-dimensional vectors to have an identifier of VIDIs (n + m) -dimensional vector m in subspace V1,...,mm. And the user A calculates the signature of the group of expansion vectors according to the private key of the user A.
(31) User A first starts fromRandomly selecting two random values x, k, and calculating the commitment U-g for the two temporary variablesxAnd R ═ e (g, g)k。
(32) User A calculates the identity IDASubspace identifier VIDAnd the hash value w of the commitment U is H1(IDA,VID,U)。
(35) and the user A sends the subspace label, the expansion vector and the corresponding signature to the next node.
And 4, signature verification.
(41) Network intermediate node CiFirst, according to public information calculationAnd w ═ H1(IDA,VIDU). Then, the equation is verified
(42) If the above equation holds true, node CiThe received messages all come from the label tauidOf (3) is provided. Then, node CiBy the equationVerifying the received vector mi。
And 5, signature derivation.
Network intermediate node CiMerging vectors verified by step (4) and discarding vectors that fail verification.
(51) Network intermediate node CiMerging the verified vectors to obtain a new vector m, i.e.Are vector correlation coefficients.
(52) Network intermediate node CiComputing signatures for vector mAnd the vector signature pair (m, σ) can be verified by the signature in step (4).
(53) Network intermediate node CiThe vector m and its signature σ are sent to the next node.
When the user B1Or B2When a sufficient number of verified vectors are received, the original vector sent by user a can be decoded.
The network node of the method of the invention can be merged into a vector and a corresponding signature according to the received vector and the signature in the communication process, the signature is indistinguishable from the signature generated by the signer for the merged vector by using the own private key, and the signature can be verified by a verification algorithm. A technical method for lightweight network coding linear homomorphic signature based on an identity public key cryptosystem. The signature method can be used in network coding, so that the data can be kept complete in the transmission process, and the safety of the data is guaranteed.
Claims (7)
1. A lightweight linear homomorphic network coding signature method based on identity is characterized by comprising the following steps:
(1) generating system public and private keys
In the identity public key system, a PKG selects a set of parameters from a public key function database, including two cyclic groups with prime q in orderAndbilinear pair e:hash function H0:H1:H2:According to the selected parameters, the PKG generates a system master public key msk and a system master private key msk;
(2) generating a user private key
The user A identifies the user AASending the data to a PKG (public Key group), and generating a private key for the user A after the identity of the user A is verified by the PKG
(3) Generating signatures
User A firstly converts message M to be signed intoVector v of1,...,vmThen the vector is expanded to an identifier of VIDVector m in subspace V1,...,mm(ii) a User A computes the label τ of subspace VidAnd calculates the vector m using its own private key1,...,mmCorresponding signature σ1,...,σm(ii) a User A tags subspace τ withidVector m1,...,mmAnd its corresponding signature σ1,...,σmTo user B1,B2;
(4) Verifying signatures
Network intermediate node CiFirst according to the subspace label τidTo confirm whether V is the message sent by user A; then by signature σiVerification vector mi∈ V integrity;
(5) deriving signatures
Network intermediate node CiAnd (4) combining the received vectors to obtain a new vector m, and generating a signature sigma of the new vector m by using signatures corresponding to the vectors, wherein the vector signatures (m, sigma) can pass the verification in the step (4).
2. The identity-based lightweight linear homomorphic network coding signature method according to claim 1, wherein the PKG in step (1) selects a set of parameters from a public key cryptographic function library, the set of parameters specifically including two cyclic groups of which the order is a prime number qOne bilinear pair e: a generator g of, three cryptographic hash functions H1:H2:H3:
3. The identity-based lightweight linear homomorphic network coding signature method according to claim 1, wherein the generation steps of the system master public key mpk and the system master private key msk in the step (1) are as follows:
(12) computing and broadcasting the public key mpk ═ gs;
4. The identity-based lightweight linear homomorphic network coding signature method of claim 1, wherein the private key generation step of user A in step (2) is as follows:
5. The identity-based lightweight linear homomorphic network coding signature method according to claim 1, wherein the signature process of the user A generating the message in step (3) is as follows:
(31) user A converts message M to be signed intoUpper vector v1,...,vmWherein v isi=(vi1,…,vin),1≤i≤m;
(32) User A expands each of the m n-dimensional vectors to have an identifier of VIDIs (n + m) -dimensional vector m in subspace V1,…,mmWherein, in the step (A),
(33) user a first starts from the prime fieldRandomly selecting two random values x, k, and calculating the commitment U-g for the two temporary variablesxAnd R ═ e (g, g)k;
(34) User A calculates the identity IDASubspace identifier VIDAnd the hash value w of the commitment U is H1(IDA,VID,U);
(35) User A computing pair (V)IDSignature of U)And setting the label tau of the subspace as (U, R, Z);
(37) and the user A sends the subspace label, the expansion vector and the corresponding signature to the next node.
6. The identity-based lightweight linear homomorphic network coding signature method of claim 1, wherein the verification of the signature in the step (4) is performed as follows:
(41) network intermediate node CiFirst, according to public information calculationAnd w ═ H1(IDA,VIDU), then verify the equation
7. The identity-based lightweight linear homomorphic network coding signature method according to claim 1, wherein the signature derivation process in the step (5) is as follows:
(51) network intermediate node CiDiscarding vectors that fail validation;
(52) network intermediate node CiMerging the verified vectors to obtain a new vector m, i.e. Is a vector correlation coefficient;
(54) Network intermediate node CiSending the vector m and the signature sigma to a next node;
(55) when the user B1Or B2When a sufficient number of verified vectors are received, the original vector sent by user a is decoded.
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