CN107425955A - A kind of identity base graded encryption method on lattice that can efficiently fix the derivation of dimension trapdoor - Google Patents
A kind of identity base graded encryption method on lattice that can efficiently fix the derivation of dimension trapdoor Download PDFInfo
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- 238000004422 calculation algorithm Methods 0.000 claims abstract description 66
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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
- H04L9/002—Countermeasures against attacks on cryptographic mechanisms
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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
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/0838—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these
- H04L9/0847—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these involving identity based encryption [IBE] schemes
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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
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/0852—Quantum cryptography
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Abstract
The invention discloses a kind of identity base graded encryption (HIBE) method on lattice that can efficiently fix the derivation of dimension trapdoor.This method is implemented according to following steps：A kind of optimization is proposed first with the characteristic of MP12 trapdoor functionsInvertible matrix extraction algorithm, then trapdoor derivation algorithm and the foundation of MP12 trapdoor function Method Of Accomplishments and the trapdoor derivation stage for fixing dimension are combined based on the optimized algorithm, then it is combined the construction of completion HIBE methods with antithesis Regev algorithms.The trapdoor of the method disclosed in the present, which derives from complexity, to be significantly reduced, and the parameter such as the dimension of lattice, trapdoor size and ciphertext rate of spread has reduced, and computational efficiency substantially optimizes；The security of scheme is based on difficult problem on lattice, possesses the characteristics of anti-quantum attack.In summary, the present invention has higher practical application feasibility.
Description
Technical field
The present invention relates to field of information security technology, and in particular to a kind of lattice upper body that can efficiently fix the derivation of dimension trapdoor
Part base graded encryption (HIBE) method, this method possess the characteristics of anti-quantum calculation analysis, and relatively low trapdoor derives from complexity, can
For mitigating the burden of key generation centre in large scale network.
Background technology
In recent years, novel cipher system based on case theory construction because have preferable progressive efficiency, computing simply, can be simultaneously
The advantages that rowization, anti-quantum are attacked and deposit random example in the worst cases, turn into the study hotspot in rear quantum cryptography epoch,
And obtain a series of achievement in research.
Graded encryption (HIBE) system of identity-based is a kind of popularization of Identity-based encryption (IBE) system.In HIBE
In system, multiple KGC entities according to directed tree structure distribution.HIBE can preferably apply the applied field in large scale network
Jing Zhong, it can not be that each user completes effective checking of identity information simultaneously in the case where substantial amounts of user asks effectively to solve IBE systems
The problem of securely transmitting private key for it.The characteristics of HIBE systems is that every sub- KGC trapdoor is specified by its father KGC in system,
The process is referred to as trapdoor derivation.
The efficiency of the graded encryption system of identity-based and the complexity that trapdoor derives from are closely related on lattice, are that one kind is based on
The HIBE systems of case theory construction.The dimension of lattice correspondingly expands with the growth of system level depth in the system, and body
The dimension of the parameter of the system such as dative such as the public and private key size of trapdoor size, user and plaintext-ciphertext rate of spread is closely related.Based on solid
The dimension that determining the HIBE systems of dimension trapdoor derivation technology has the lattice before and after trapdoor derivation is kept for the advantages of constant, but the system
Trapdoor derive from algorithm and need to rely on a kind of extractThe SampleR algorithms of invertible matrix.Therefore SampleR calculations how are optimized
Method, and it is that the present invention will solve the problems, such as to construct efficient HIBE methods based on this.
The content of the invention
The purpose of the present invention is overcome the deficiencies in the prior art, there is provided a kind of efficiently to fix on the lattice of dimension trapdoor derivation
Identity base graded encryption method, a kind of SampleR algorithms of optimization are constructed first with the characteristic of MP12 trapdoor functions；Then
The trapdoor that SampleR algorithms based on optimization combine fixed dimension derives from algorithm and efficient MP12 trapdoors generating algorithm completion HIBE
The trapdoor generation of scheme and trapdoor derive from the stage, and the construction of Method Of Accomplishment is then organically combined with antithesis Regev algorithms.
To reach above-mentioned purpose, the present invention constructs a kind of optimization first with the characteristic of MP12 trapdoor functions
SampleR algorithms.The construction of algorithm relies primarily on following two algorithms：
MP12 trapdoor generating algorithmsInput the homogeneous matrix randomly selectedAnd list
Bit matrix H, output random matrix A0With its trapdoor matrix
MP12 preimage sampling algorithmsInput the output of MP12 trapdoors generating algorithm
Random matrix A0With its trapdoor matrixThe matrix M and vectorial u randomly selected, Gaussian parameter σ, export uniformly vectorial e.
The trapdoor that SampleR algorithms after optimizing based on more than combine fixed dimension derives from algorithm and the life of efficient MP12 trapdoors
Into algorithm complete HIBE schemes trapdoor generation and trapdoor derive from the stage, then with antithesis Regev algorithms organically combine complete with
Scheme construction under machine oracle model, the model of building method are as follows：
System establishes algorithm HIBE-Setup → (MPK, MSK)：Algorithm inputs security parameter, modulus and the maximum classification of system
Depth, export a pair of Your Majesty's keys (MPK) and main private key (MSK).
User key extraction algorithmInput Your Majesty's key MPK；InputRepresent system level
Client public key matrix when depth is lCorresponding trapdoor matrix, output user identity id|lUser key
AES HIBE-Encrypt → CT：It is using Your Majesty's key MPK, hierarchy depthRecipient's user identity id
With message b ∈ { 0,1 } to be encrypted, output and identityRelated ciphertext CT.
Decipherment algorithm HIBE-Decrypt → b：Utilize Your Majesty's key MPK, trapdoor matrix SKidWith ciphertext CT, calculate and export
Plaintext b.
Indistinguishability (IND-aID- under the safe sexual satisfaction adaptability selection identity chosen -plain attact of method
CPA).The experiment of security verification is as follows：
Define attackerAnd mimic
Establish：MimicHIBE-Setup algorithms are run, Your Majesty's key MPK is exported and is sent to attacker
Stage 1：AttackerAdaptively inquire sequence of user identity.For inquiring mimic each timeOperation
MP12Sample algorithms are responded；
Challenge：In attackerA challenge bit is exported after the inquiry of ending phase 1.MimicChoose one at random
Bit r ∈ { 0,1 }, call HIBE-Encrypt algorithms that challenge bit is encrypted if r=0, it is random if r=1
Choose ciphertext.MimicFinal ciphertext is sent to attacker
Stage 2：AttackerThe targeted customer's identity to be attacked is exported, on condition that the target identities were ask in the stage 1
Any prefix identity asked.AttackerAnd mimicThe inquiry and response with the same nature of stage 1 are carried out again；
Conjecture：AttackerOne conjecture result r ' of the output returned to mimic, attacker wins if r '=r.
Above attackerThe advantage of triumph and the Dominant Facies for solving LWE problem are same, then HIBE methods are provable IND-
AID-CPA safety.
The present invention has the advantages that：
1) present invention derives from technical construction based on fixed dimension trapdoor, it means that the dimension of lattice is before and after trapdoor derivation
Keep constant, then the dimension of dative related efficiency parameters such as trapdoor size, public and private key length and plaintext-ciphertext rate of spread etc.
Also keep constant, this causes the efficiency of the present invention to possess not the advantages of by system level effect of depth, and the SampleR after optimization
Algorithm make it that the complexity that trapdoor derives from is lower；
2) present invention is a kind of MP12 trapdoors generation based on highly effective and safe, the encryption side that is constructed of preimage sampling algorithm
Method, there is relatively low complexity in trapdoor generation and preimage sample phase, and the dimension of the lattice generated is lower, so that user
The extraction complexity of key is lower；
3) present invention is that one kind is added based on what fault-tolerant study (LWE, learning with errors) problem on lattice constructed
Decryption method, to this method crack can in polynomial time reduction to difficult problem under worst case on plaid matching solution, because
This possesses the advantages of anti-quantum attack.
Brief description of the drawings
Fig. 1 is identity base graded encryption flow chart on a kind of lattice that can efficiently fix the derivation of dimension trapdoor.
Embodiment
The invention will be further described with accompanying drawing with reference to embodiments.
The basic parameter of the present invention includes：Uniformly random matrixWith its trapdoorWherein n is safety
Parameter, d be system support maximum hierarchy depth, q=poly (n), m=O (n logq),W=nk,User identity id=(id1||...||idl)∈({0,1}*)l, wherein l ∈ [d].Order
WhereinMatrix disclosed in one constructionWherein InIt is n × n unit matrixs,SHA1 hash algorithms：
The designed SampleR algorithm flows optimized using MP12 trapdoor function characteristics are specific as follows：
Algorithm
Input：Integer m=O (n logq), in coset Λ⊥(G) algorithm of Gauss samplingIts Gaussian parameter is
σG。
Output：Invertible matrix
1) setUniformly choose at randomMatrix, G are matrix disclosed in a construction,
Wherein InIt is n × n unit matrixs, TGIt is matrix G open trapdoor；
2) For i=1 ..., m do:
A) Gauss sampling algorithm is calledJudgeWithWhether statistics approaches,
If not, generate again；
B) calculate
C) calculate
D) makeAnd export
3) by riAs matrix R column vector, detection R whether beIt is reversible, it is to export R, otherwise re-starts step
2)；
SampleR algorithms after optimizing based on more than combine the trapdoor derivation algorithm for fixing dimension and MP12 trapdoor functions are complete
The stage is derived from foundation and trapdoor into method, is then combined the construction of completion HIBE methods with antithesis Regev algorithms.
HIBE-Setup(1n,1d)：Security parameter n and system maximum hierarchy depth d is inputted, operation MP12 trapdoor generations are calculated
MethodExport uniformly random matrixAnd A0Trapdoor matrixChoose n and tie up uniformly random vectorExport Your Majesty key MPK=(A0,u0) and main private key
Input Your Majesty's key MPK；InputRepresent that user is public when system level depth is l
Key matrixCorresponding trapdoor matrix, whereinFather's user identity id|l=(id1||,...,||idl), can
Inverse matrixInput child user identity
WhereinCalculateAnd makeCall the trapdoor group of fixed dimension
Raw algorithmExport trapdoor matrixIn addition, by parameterIt is set to A0,It is set toHIBE-Derive algorithms are equivalent to the user key extraction algorithm IBE-Extract in IBE schemes.
HIBE-Encrypt(MPK,id,b)：Your Majesty key MPK is inputted, hierarchy depth isRecipient's user identity id and to be added
Close message b ∈ { 0,1 }.Calculate invertible matrixCalculate client public key matrix
Message b is encrypted using antithesis Regev algorithms：Uniformly random vector is chosen firstThen fault-tolerant value is chosenWith
Fault-tolerant vectorCalculate and export ciphertext
HIBE-Decrypt(MPK,SKid,CT)：Input Your Majesty's key MPK；Input trapdoor matrix SKid, wherein user identity
Id hierarchy depth isInput ciphertext CT.Make Gaussian parameterCalculate such as HIBE-
Matrix in EncryptRun MP12 preimage sampling algorithmsIt is full
Sufficient Aideid=u0.CalculateBy b ' withIt is considered asIn integer and compare, ifOutput 1, otherwise exports 0.
Examine correctness：The output of scheme decipherment algorithm is：
Error-term on the right of equation is fault-tolerant value.To ensure the correctness of decryption, we carry out defined below to parameter：
M >=2n logq,As b=1, then
Export b=b '=1；As b=0, thenExport b=b '=0.Decryption is correct, it was demonstrated that finishes.
The present invention proposes a kind of identity base graded encryption method on lattice that can efficiently fix the derivation of dimension trapdoor, institute's extracting method
The advantages of be that constructed trapdoor algorithm complex is relatively low and be based on MP12 trapdoors generating algorithm and MP12 preimages sampling
Algorithm has relatively low complexity.In security, the present invention has the characteristic that anti-quantum is attacked based on difficult problem on lattice.
Embodiment described herein and accompanying drawing be intended for demonstrate purpose, with help reader understand this method principle and
Inventor should be understood to be not limited to this specific example for the thinking for promoting full homomorphic cryptography to apply and contributing
And condition.In addition, all equivalents done according to spirit of the invention or extension, should all cover in protection scope of the present invention
It is interior.
Claims (1)
1. a kind of identity base graded encryption (HIBE) method on lattice that can efficiently fix the derivation of dimension trapdoor, it is characterised in that：It is first
A kind of optimization is proposed first with the characteristic of MP12 trapdoor functionsInvertible matrix extraction algorithm, then based on the optimized algorithm knot
The trapdoor for closing fixed dimension derives from algorithm and the foundation of MP12 trapdoor function Method Of Accomplishments and trapdoor derives from the stage, then with antithesis
Regev algorithms are combined the construction for completing HIBE methods.The graded encryption method tool of identity-based on a kind of described new lattice
Body implementation steps are：
A kind of optimization is constructed first with the characteristic of MP12 trapdoor functions(SampleR is calculated invertible matrix extraction algorithm
Method)：
Basic parameter includes：Uniformly random matrixWith its trapdoorWherein n is security parameter, and d is system
The maximum hierarchy depth of support, q=poly (n), m=O (nlogq),W=nk,User identity
Id=(id1||...||idl)∈({0,1}*)l, wherein l ∈ [d].OrderWhereinOne structure
Make disclosed matrixWherein InIt is n × n unit matrixs,SHA1
Hash algorithm：
The designed SampleR algorithm flows optimized using MP12 trapdoor function characteristics are specific as follows：
Algorithm
Input：Integer m=O (nlogq), in coset Λ⊥(G) algorithm of Gauss samplingIts Gaussian parameter is σG。
Output：Invertible matrix
1) setUniformly choose at randomMatrix, G are matrix disclosed in a construction,Wherein
InIt is n × n unit matrixs, TGIt is matrix G open trapdoor；
2) For i=1 ..., m do:
A) Gauss sampling algorithm is called JudgeWithWhether statistics approaches, if not
It is then to generate again；
B) calculate
C) calculate
D) makeAnd export
3) by riAs matrix R column vector, detection R whether beIt is reversible, it is to export R, otherwise re-starts step 2)；
The trapdoor that SampleR algorithms after optimizing based on more than combine fixed dimension derives from algorithm and MP12 trapdoor functions completion side
The foundation of method and trapdoor derive from the stage, are then combined the construction of completion HIBE methods with antithesis Regev algorithms.
HIBE-Setup(1n,1d)：Security parameter n and system maximum hierarchy depth d is inputted, runs MP12 trapdoor generating algorithmsExport uniformly random matrixAnd A0Trapdoor matrixChoose n and tie up uniformly random vectorExport Your Majesty key MPK=(A0,u0) and main private key
Input Your Majesty's key MPK；InputRepresent client public key when system level depth is l
MatrixCorresponding trapdoor matrix, whereinFather's user identity id|l=(id1||,...,||idl), can
Inverse matrixInput child user identity
WhereinCalculateAnd makeCall the trapdoor group of fixed dimension
Raw algorithmExport trapdoor matrixIn addition, by parameterIt is set to A0,It is set toHIBE-Derive algorithms are equivalent to the user key extraction algorithm IBE-Extract in IBE schemes.
HIBE-Encrypt(MPK,id,b)：Your Majesty key MPK is inputted, hierarchy depth isRecipient's user identity id and message b to be encrypted
∈{0,1}.Calculate invertible matrixCalculate client public key matrix
Message b is encrypted using antithesis Regev algorithms：Uniformly random vector is chosen firstThen fault-tolerant value is chosen
With fault-tolerant vectorCalculate and export ciphertext
HIBE-Decrypt(MPK,SKid,CT)：Input Your Majesty's key MPK；Input trapdoor matrix SKid, wherein user identity id point
Level depth beInput ciphertext CT.Make Gaussian parameterCalculate as in HIBE-Encrypt
MatrixRun MP12 preimage sampling algorithmsMeet Aideid=
u0.CalculateBy b ' withIt is considered asIn integer and compare, ifIt is defeated
Go out 1, otherwise export 0.
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| CN109040041A (en) * | 2018-07-23 | 2018-12-18 | 深圳职业技术学院 | Data hierarchy encryption device and related electronic device, storage medium |
| CN109739892A (en) * | 2018-12-27 | 2019-05-10 | 王梅 | The method and system of grading extension are carried out to the data acquisition request in internet |
| CN113347211A (en) * | 2021-08-04 | 2021-09-03 | 北京微芯感知科技有限公司 | Identity hierarchical encryption method, device, system, computer equipment and storage medium |
| CN115952551A (en) * | 2023-03-15 | 2023-04-11 | 山东知方源科技信息有限公司 | Data processing method for building BIM model |
| CN117254897A (en) * | 2023-11-20 | 2023-12-19 | 暨南大学 | Identity base matrix homomorphic encryption method based on fault-tolerant learning |
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Cited By (9)
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| CN109040041A (en) * | 2018-07-23 | 2018-12-18 | 深圳职业技术学院 | Data hierarchy encryption device and related electronic device, storage medium |
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| CN113347211A (en) * | 2021-08-04 | 2021-09-03 | 北京微芯感知科技有限公司 | Identity hierarchical encryption method, device, system, computer equipment and storage medium |
| CN113347211B (en) * | 2021-08-04 | 2021-11-23 | 北京微芯感知科技有限公司 | Identity hierarchical encryption method, device, system, computer equipment and storage medium |
| CN115952551A (en) * | 2023-03-15 | 2023-04-11 | 山东知方源科技信息有限公司 | Data processing method for building BIM model |
| CN117254897A (en) * | 2023-11-20 | 2023-12-19 | 暨南大学 | Identity base matrix homomorphic encryption method based on fault-tolerant learning |
| CN117254897B (en) * | 2023-11-20 | 2024-02-02 | 暨南大学 | Identity base matrix homomorphic encryption method based on fault-tolerant learning |
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