CN108768639A - A kind of public key order-preserving encipherment scheme - Google Patents
A kind of public key order-preserving encipherment scheme Download PDFInfo
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- CN108768639A CN108768639A CN201810573081.2A CN201810573081A CN108768639A CN 108768639 A CN108768639 A CN 108768639A CN 201810573081 A CN201810573081 A CN 201810573081A CN 108768639 A CN108768639 A CN 108768639A
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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
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
- H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
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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
- H04L9/085—Secret sharing or secret splitting, e.g. threshold 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
- H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
Abstract
The invention discloses a kind of public key order-preserving encipherment schemes, belong to cloud storage management domain.The present invention includes:Private key s is generated by CA first, and calculates corresponding public key y, open parameter param={ g, p }.Secondly, original plaintext is split, D={ D are obtained1,D2,…,Dm, using the method for mapping the data of non-uniform Distribution are mapped in equally distributed plaintext bucketTo hide the regularity of distribution of plaintext;Then data owner realizes that bucket maps the encryption of bucket using the public key y of CA distribution, each bucketCorresponding different encryption function Enci, and noise noise is added, one-to-many mapping thought is realized, to increase the uncertainty of ciphertext value.Finally, data consumer is after obtaining ciphertext c, using private key s, according to can calculate plaintext value.The present invention is suitable for database purchase, ciphertext can be made to retain the Cahn-Ingold-Prelog sequence rule of plaintext, to carry out quick searching ciphertext.
Description
Technical field
The present invention relates to cryptographies, belong to cloud storage management domain, especially design a kind of public key encryption order-preserving scheme.
Background technology
Order-preserving is encrypted to build the important tool that can search for encryption system, it allows to carry out efficient model in ciphertext
Inquiry operation is enclosed, this meets the requirement for processing safety and confidentiality in cloud environment very much.Rakesh Agrawal are proposed
OPE (Order Preserving Encryption) algorithms by by the clear data of non-uniform Distribution be mapped to uniformly point
The ciphertext section of cloth, has achieved the purpose that hiding data characteristic distributions, and remains sequence in plain text.The algorithm defines the spy of order-preserving
Property is:As plaintext x1, x2Meet x1<x2When, corresponding ciphertext Enc (x1)<Enc(x2).That is i-th of plaintext value can be reflected
It is mapped in i-th of ciphertext section.
Basic database query operations have exact numerical inquiry, range query and aggregate query, exact numerical inquiry to want
Being to determine property of encryption system, such as AES are asked, in these encryption systems, identical plaintext always will produce identical close
Text[9][10];If for the aggregate query with SUM and AVG operations, homomorphic encryption algorithm can be used for averaging
Operation[11];Based on the above-mentioned definition to order-preserving characteristic, in this paper, main inking is in looking into encryption data into line range
The operation of inquiry.
The permission of OPE algorithms is directly compared operation to ciphertext, therefore, range query and MAX, MIN, COUNT inquiry
Result can directly be obtained by encryption data, meanwhile, OPE algorithms have following characteristic[4]:
(1) inquiry operation is carried out to the ciphertext for having used order-preserving encryption (OPE) to obtain, can obtained correctly as a result, looking into
It is not in wrong report to ask result not only, but also will not miss any answer tuple.The inquiry obtained using the order-preserving characteristic of OPE algorithms
As a result, compared with some cryptogram search systems[5]Generated superset has specific improvement, these extension subsets need considerably complicated
Post-processing step filter extra data tuple.
(2) OPE algorithms can solve the problems, such as data update, and in transporting database, update and insertion data do not need to change
Become the ciphertext value of legacy data.
(3) OPE algorithms can be very good to be merged with existing Database Systems, its initial purpose of design includes energy
Enough and existing database index structure (such as B-trees) is combined.In fact, database can be made by being stored in encrypted data
For application program transparence.
Agrawal etc. proposed first complete order-preserving encryption system in 2004, they assume bright in the system
The initial distribution of text is known, realizes that encryption is calculated in fixed or randomly selected distribution by the way that known distribution to be mapped to
Method.This design seems that realizing plaintext frequency to a certain extent hides, but is not provided with formal safe-conduct in text
It is bright.The guarantor based on search tree that first formal security proving was proposed in 2009 by Boldyreva et al. is encrypted in order-preserving
It is provided in sequence encryption system.They introduce the concept of the indistinguishability (IND-OCPA) under orderly chosen -plain attact, together
When also demonstrate the stateless scheme of neither one can realize this concept, and propose be satisfied with have weaker safety
Random isotonic function encipherment scheme, this scheme it is only necessary to client store a key.Later, Boldyreva
Et al. demonstrate a kind of random isotonic function again and can realize safe window one-way, and propose one kind and can reach
The encryption system of IND-OCPA safeties, but in the system, the related content of plaintext needs to know in advance.
Wang in 2012 et al. thinks that the distribution rule of ciphertext can be expressed as correlation in deterministic encryption system
Score, and established as index and can search for system under order-preserving encryption.Author strengthens the peace of OPE algorithms in this article
Quan Xing, and " One-to-Many OPE " is proposed to response keyword search request, they establish, and one kind is possible to be added
Dense body system can hide the characteristic distributions of plaintext.
Popa RA in 2013 et al. propose mOPE (mutable Order-Preserving Encoding) algorithm, are
OPE models of currently the only idealization safety, while meeting the security requirement of IND-OCPA, ciphertext is only in the model
Show only the sequence of plaintext.One balance search tree being made of ciphertext of mOPE model creations, and require interactive
Cryptographic protocol, when new ciphertext generates, original ciphertext value can change, and user can pass through UDFs (User Define
Functions the part ciphertext) being directly changed in database.But each pair of database makes primary modification and just needs to change to have deposited
Store up the sequence of information, the strong influence performance of database.
The same year Dongxi Liu et al. proposes a kind of nonlinear order-preserving encryption system, can be promoted suitable to ciphertext database
The response of sequence searching request.The constitution can ensure being uniformly distributed for ciphertext in the case of a large amount of repetitions in plain text, and realize
The programmability of base index expression formula, therefore the distribution character of plaintext can be hidden.The encryption system that Liu is proposed can be very
The good data characteristic (such as distribution character, range etc.) that storage data are not limited to suitable for long term data library.But it is protecting
While demonstrate,proving efficiency and realize programmability, which can reveal part cleartext information.
Teranishi in 2014 et al. proposes another nonlinear OPE algorithms, they insert at random in ciphertext
The section of size, and demonstrate this method and compare for the indistinguishable random isotonic function of part plaintext with very strong
Safety.But since this algorithm is stateless, still less than IND-OCPA safeties.
Kerschbaum et al. eliminates the demand to individual server, but and is linearly stored in information different bright
In the quantity of text.It ignores in addition, the mutation probability in N number of number is reduced to by they, while reducing client and service
Frequency of interaction between device is down to Constant Grade from Logarithmic degree, and the encryption expenses of this order-preserving encryption system are permanent under normal circumstances
Fixed.
So far, order-preserving encryption system all the being to determine property proposed, Hildenbrand et al. introduces randomness
Order-preserving encipherment scheme, plaintext domain is divided into disjoint data acquisition system by them, and ensures the data order in each set
Constant, different data sets are encrypted using different keys.But since the program is also stateless, so and being unsatisfactory for
IND-OCPA safeties.Ke Li et al. people in 2015 propose one-to-many mapping OPE algorithms, are multiple by ciphertext interval division
Bucket is determined the best size of bucket using the method for minimum entropy, and realizes region estimation by relevancy labels.
Zheli Liu et al. people will be divided into disjoint multiple sections in plain text, and different mapping functions is taken in each section
It is encrypted, can only ensure to meet anti-known plain text attack under certain conditions.It is attacked so how to design and can resist only ciphertext
Hit with chosen -plain attact and reach efficient cipher text searching be the key that this programme research.
Invention content
It is an object of the invention to:It proposes a kind of concept of the order-preserving of public key encryption and realizes a kind of scheme, the program
It can not only ensure that the thought progress order-preserving encryption of public key may be used in user, but also resistance chosen -plain attact can be reached
Requirement.
Present invention comprises a kind of public key encryption order-preserving scheme, key step includes:
Secret key generates:A number s is randomly choosed as private key, calculates public key y=gsMod q, open parameter is useful
Share param in family.
Encryption:The open parameter param of input, divides plaintext bucket, for each barrel of selection random numberCalculate ciphertext
Decryption:Ciphertext c and private key s is inputted, determines the bucket i where ciphertext, is calculated in plain text.
As a result of the above-mentioned technical solution, the beneficial effects of the present invention are:
1) change original symmetrical order-preserving encryption, construct order-preserving encipherment scheme using public key thought, greatly simplified secret
Key management need not distribute a large amount of symmetrical secret key, save memory space in advance.
2) present invention employs a kind of very effective partitioning algorithms, can the data set of non-uniform Distribution be passed through mapping
Function is converted into equally distributed data set, achievees the purpose that hiding plaintext distribution rule.
3) present invention employs nonlinear mapping rulers to realize that order-preserving is encrypted, and the data after over-segmentation are divided into
Multiple buckets, each bucket correspond to an encryption function, and each in bucket data are random is mapped in corresponding ciphertext bucket, pass through this
The one-to-many mapping mode of kind increases the uncertainty of ciphertext, keeps the identical encrypted result of plaintext different, conceals close
The frequency information of text.
Description of the drawings
The present invention will be illustrated by way of specific example and attached drawing, wherein:
Fig. 1 is the cryptographic operation flow chart that the present invention is embodied;
Fig. 2 is the decryption oprerations flow chart that the present invention is embodied;
Fig. 3 is the system structure diagram of the embodiment 1 of the present invention.
Specific implementation mode
To keep the solution of the present invention technology and application clearer, with reference to specific implementation example and attached drawing, to this
Invention is described in more detail.
Embodiment 1
Referring to Fig. 3, the specific step that executes includes that CA distributes private key to each user, and calculates corresponding public key, data
Owner is decrypted by public key encryption, data consumer by private key, is described in detail below:
(1) secret key generates
(1.1) CA distributes a private key s ∈ (1, p-2) to user, and calculates corresponding public key y=gsmod q;
(1.2) param={ g, p } is as open parameter.
(2) it encrypts
(2.1) for one group of plaintext D={ D1,D2,…,Dm, it is extended to plaintext bucket set using partitioning algorithm
(2.2) two numbers are randomly choosed for each bucketIt calculatesNoise, wherein y are public keys, definitionWith
(2.3) it calculatesWithAnd it willThe data that are sent to of safety make
User.
(3) it decrypts
(3.1) after data consumer obtains ciphertext c, index (c are utilized3) determine c3The bucket i at place;
(3.2) relationship is utilizedWithDetermine (ai,bi);
(3.3) basisThe plaintext bucket value after extension is calculated, determining plaintext value is being penetrated by reflection.
The above description is merely a specific embodiment, and (including accessory claim, abstract and attached are said in this theory
Figure) disclosed in any feature, unless specifically stated, can alternative features equivalent by other or with similar purpose be subject to
It replaces, i.e., unless specifically stated, each feature is an example in a series of equivalent or similar characteristics.The present invention can expand
The new feature or any new combination what is disclosed in the present specification are taken office in exhibition, and any new method or process disclosed
Step or any new combination.
Claims (5)
1. a kind of public key order-preserving encipherment scheme, which is characterized in that include the following steps:
Secret key generates:One number s (1≤s≤p-2) of random selection is used as private key, calculates public key y=gsMod q, open parameter are
All users to share param={ g, p };
Ciphering process:Data owner will first be divided into several barrels of D={ D in plain text1,D2,…,Dm, then obtained by partitioning algorithm
To extension plaintext bucketEncryption function is used againIt is mapped to corresponding ciphertext section C={ C1,
C2,…,Cm, each bucketCorresponding different encryption function Enci, define plaintext bucketRanging from (li,hi), ciphertext section Ci
=(l 'i,h’i), for each bucket, data owner chooses two random numbersIt calculates:
Its ciphertext is
Decrypting process:Data consumer first determines the bucket i=index (c where it after receiving ciphertext c3), in conjunction with private key s andIt can be calculated:
Utilize obtained parameter (ai,bi), according toClear content is calculated.
2. the method as described in claim 1, it is characterised in that compare other symmetrical order-preserving Encryption Algorithm, realize public key and add
Close order-preserving algorithm:Use non-linear Encryption Algorithm Enc (m of the bucket to bucketi)=aimi+bi+noiseiCome under the premise of order-preserving,
Ensure the high efficiency of safety and the search of Encryption Algorithm;
For a plaintext section D, it is combined by the extension bucket Interval Set obtained after partitioning algorithm
Interval of definitionAnd there is li,hi∈ Z, any two adjacent intervalWithMeet relationship
li+1=hi;Corresponding ciphertext section is C after encryptioni=(l 'i,h’i);
Under the present circumstances, it is assumed that a plaintext x, it is index (x)=i to define its section index value, extends bucket interval range value
For range (i)=(li,hi), ciphertext interval range value is range,(i)=(li,hi), join bucket interval range value as secret
Number want safety send data consumer to;
Original plaintext produces equally distributed data interval after partitioning algorithm, which is also expressed as multiple barrels
Form defines each bucketNonlinear relation beData owner A for each bucket select two with
Machine numberIt calculatesWithValue;Use ai,biIt replaces respectivelyWithSo for
Arbitrary sectionFor, pass through Nonlinear Mapping EnciAfterwards, the interval value obtained is (lmin,hmax), it is specific to calculate such as
Under:
Meanwhile to ensure that the sequence of ciphertext is consistent with plaintext sequence, corresponding ciphertext section Ci=(l 'i,h’i) be:
Therefore for oneIts corresponding ciphertext value is as follows, wherein noise ∈ (0, ai/2):
E (x)=h 'i-1+Enci(x)=h 'i-1+(ai·x+bi+noise)
Data owner calculatesWithAnd it willSafety is sent to data use
E (x) is sent to Cloud Server storage by person.
3. such as claim 1, the method described in 2, it is characterised in that by the guarantor that symmetrical order-preserving cryptographic construction is public-key cryptosystem
Sequence is encrypted, and is simplified secret key management, is reduced the expense stored and transmitted, and the selection security parameter of randomness every time, institute
Can achieve the purpose that survey selective plaintext attack.
4. method as described in claim 2 can be by non-uniform Distribution using a kind of very effective partitioning algorithm has been crossed
Data set equally distributed data set is converted by mapping function, achieve the purpose that hiding plaintext distribution rule.
5. method as described in claim 2, nonlinear mapping ruler is used to realize that order-preserving is encrypted, it will be through over-segmentation
Data afterwards are divided into multiple buckets, and each bucket corresponds to an encryption function, and what each data were random in bucket is mapped to corresponding
In ciphertext bucket, the uncertainty of ciphertext is increased by this one-to-many mapping mode, makes the identical encrypted knot of plaintext
Fruit is different, conceals the frequency information of ciphertext.
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