CN110011782A - A kind of full homomorphic encryption algorithm of many-one - Google Patents
A kind of full homomorphic encryption algorithm of many-one Download PDFInfo
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- CN110011782A CN110011782A CN201910180640.8A CN201910180640A CN110011782A CN 110011782 A CN110011782 A CN 110011782A CN 201910180640 A CN201910180640 A CN 201910180640A CN 110011782 A CN110011782 A CN 110011782A
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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
- H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
- H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
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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
- H04L9/008—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols involving homomorphic encryption
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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
- H04L9/0863—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving passwords or one-time passwords
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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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Abstract
The present invention relates to a kind of full homomorphic encryption algorithms of many-one, the full homomorphic cryptography of one side of multi-way encryption decryption is proposed in this algorithm, wherein, encryption side encrypts the message for needing to upload to Cloud Server with the private key of oneself, so encryption side can carry out the verifying in later period to the data of encryption, decryption side can carry out the message of all uploads decrypting again after full homomorphism operation, it had not only saved operation time in this way but also had improved the efficiency of operation, in this method, the number of encryption side is controlled in the range of capable of being decrypted correctly, and it is experimentally confirmed, the method has feasibility in integer range, meets the needs of user response.In addition, the full homomorphic encryption algorithm of many-one of the invention increases the transmission quantity of information, transmission speed is improved, more meets the demand of existing big data society.
Description
Technical field
The present invention relates to full homomorphic cryptography security technology areas, and in particular to a kind of full homomorphic encryption algorithm of many-one.
Background technique
Based on the multiplicative homomorphic of RSA public encryption system, Rivest et al. proposes the concept of homomorphic cryptography, that is, is not understanding
In the case where ciphertext, the operation to plaintext is realized by executing operation to ciphertext, and its result is consistent.Homomorphic cryptography mentions
Out, the extensive concern of domestic and foreign scholars is received, but the program is not realizing full homomorphism completely, it can not arbitrary number of times
Operate and handle ciphertext.Gentry proposes first based on the full homomorphic encryption scheme of ideal lattice, and constructing one can be achieved
The SomeWhat scheme that time homomorphism calculates is limited, the update of ciphertext is realized by homomorphic decryption, to realize full homomorphic cryptography.
Research based on Gentry, domestic and foreign scholars propose many improvement projects.Dijk et al. is proposed based on integer
Full homomorphic encryption scheme, referred to as DGHV scheme is first full homomorphic encryption scheme based on integer, and proposing can be same
The multiple bit datas of Shi Jiami it is assumed that but the disadvantage is that calculating speed is slow, computation complexity is high, to the dependence of security parameter compared with
It is high.In recent years, with the development of big data and cloud computing, full homomorphic cryptography computation complexity is high, the data volume that single can encrypt
The disadvantages of less, causes the performance of existing full homomorphic encryption scheme to need to be improved and enhanced.
Summary of the invention
Based on defect in the prior art and deficiency, the main purpose of the present invention is to provide a kind of full homomorphisms of many-one to add
Close algorithm.
Based on above-mentioned purpose, the present invention is at least provided the following technical solutions:
A kind of full homomorphic encryption algorithm of many-one comprising following steps:
System initialization step, the step generate the public affairs of Cloud Server P by approximate greatest common factor (G.C.F.) difficult problem first
Then private key pair converts to obtain multiple user P by public keyiPublic private key pair；
Ciphertext generation step, user choose the clear-text message to be encrypted, and encryption obtains ciphertext；
Decryption step is decrypted using public key, obtains clear-text message；
Full homomorphism appraisal procedure, inputs multiple ciphertexts of the same user or different user, solves after carrying out full homomorphism operation
It is close.
Further, the Cloud Server P is decryption side, the user PiFor encryption side.
Further, in the system initialization step, it includes following sub-step that the public and private key of the Cloud Server, which generates:
Choose one η odd-integral numbersAs private key sk, i.e. sk=p；
SelectionWherein q0It is maximum and be odd number, enable x0=pq0
+r0,0≤i≤τ；Public key pk=< x0,x1,…,xτ>。
Further, in the system initialization step, it includes following sub-step that the public and private key of the user, which obtains:
User Pi(i=0,1 ..., τ) one integer of random selectionAs oneself
Private key, i.e. ski=pi；
PiVector transformation is carried out to the public key pk of Cloud Server P, randomly selects vectorAnd vectorMake
Obtain xi,0←x0ki,0+2li,0, xi,j←xiki,j+2li,j, j ∈ { 0,1,2 ..., τi}；Assuming that xi,0Maximum then takesThat is PiPublic key pki=< xi,0,xi,1,…,xi,τ>。
Further, in the ciphertext generation step, the cipher mode that is related to are as follows:
Wherein, miFor the plaintext to be encrypted,For the integer set randomly selected,The integer randomly selected.
Further, in the decryption step, the manner of decryption that is related to are as follows:
User PiWith the private key sk of oneselfi=piDecrypt ciphertext, the formula being related to are as follows:
Cloud Server P decrypts ciphertext, the formula being related to the private key sk=p of oneself are as follows:
Wherein, ciIt indicates the ciphertext for needing to decrypt, is obtained in plain text by modular arithmetic.
Further, in the full homomorphism appraisal procedure, the user's number or ciphertext number of full homomorphism operation are participated in
Formula it is as follows:
Wherein, u indicates the number of user or the number of ciphertext, and η indicates private key length, ρ ' expression noise, and f expression passes through
The multinomial of gate circuit.
Further, in the full homomorphism appraisal procedure, meet the full homomorphism operation of multiple users and can correctly solve
It is close, it is expressed as follows:
ci+cj=p (ai+aj)+2(bi+bj)+(mi+mj)；
ci·ci=p (ai(paj+2bj+mj)+aj(2bi+mi))+2(2bibj+bimj+mibj)+mimj；
Wherein ci,cjIndicate user i, the ciphertext of j, mi,mjIndicate that user i, the ciphertext of j, p indicate the private key of decryption side.
Further, the Encryption Model that the full homomorphism operation is related to are as follows:
Wherein, plaintext space M, decryption side a P, multiple encryption side Pi, i is some encryption side, mi∈ M's, P is public and private
Key is to (pk, sk), PiPublic private key pair (pki,ski), Encryption Algorithm Encrypt (pk, m), decipherment algorithm Decrypt (sk, c),Indicate certain full homomorphism operation, i ≠ j.
The present invention has the following advantages and effects with respect to the prior art:
1) the full homomorphic encryption algorithm of many-one of the invention, encryption side is expanded to multiple, and multiple encryption sides are permissible
Operation efficiency is improved to Cloud Server transmission message to increase volume of transmitted data simultaneously.
2) present invention, which suggests plans, to carry out full homomorphic cryptography and decryption to multiple and different message, therefore improves meter
Calculate efficiency.
3) present invention, which suggests plans, has been experimentally confirmed, and has feasibility in integer range, can satisfy user's
System response.
Detailed description of the invention
Fig. 1 is technical solution of the present invention schematic diagram.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.
Embodiment
1 pair of technical solutions according to the invention is described in detail with reference to the accompanying drawing.
Inventing the technical solution mainly includes；Two kinds of elements, i.e. Cloud Server and user, the communication between them are
Using wireless communication or wire communication can be used.
The ciphertext that Cloud Server is mainly responsible for storage and each user of homomorphic decryption uploads, while generating the public affairs of decryption side
Private key.
User, which is mainly responsible for, is uploaded to Cloud Server for the encryption of oneself information, while can verify on Cloud Server oneself
Store the correctness of information.
Assuming that Cloud Server is (pk, sk) as the public and private key of decryption side by taking S user and j-th user as an example, use
The public and private key of family S is (pks,sks), the public and private key of user J is (pkj,skj)。
Step S1, system initialization step, the step generate cloud service by approximate greatest common factor (G.C.F.) difficult problem first
Then the public private key pair (pk, sk) of device converts to obtain multiple user P by public keyiPublic private key pair (ski,pki)；
It is realized especially by following steps:
Step S11, one η odd-integral numbers are chosenAs private key sk, i.e. sk=p,
Wherein $ expression randomly selects, and η indicates the length of odd-integral number p,Indicate integer；
Step S12, it selectsWherein q0It is maximum and be odd number, it enables
x0=pq0+r0,0≤i≤τ.Public key pk=< x0,x1,…,xτ>, wherein q0,r0It is the q randomly selectedi,
riIn maximum value, τ indicate public key in element number.
Step S13, encryption side, i.e. user S randomly choose an integerAs certainly
Oneself private key, i.e. sks=ps。
Step S14, user S carries out vector transformation to the public key pk of Cloud Server, randomly selects vectorAnd vectorSo that
xs,0←x0ks,0+2ls,0, xs,j←xsks,j+2ls,j, j ∈ { 0,1,2 ..., τi}.Assuming that xs,0Maximum then takesGenerate the public and private key (pk of user Ss,sks), the public key pk of user Ss=< xs,0,xs,1,…,xs,τ>,
Wherein vector K, L indicate that two vectors of user S stochastic transformation, s indicate that the public key element of user S, j indicate in the public key of S
J-th of element.
Step S2, ciphertext generation step, user choose the clear-text message to be encrypted, and encryption obtains ciphertext.Specifically, encryption
Just choose the message m to be encryptedi, utilize the private key sk of oneselfiMessage encryption is obtained into ciphertext ci, i i-th of user of expression.
Wherein, the formula that ciphertext is obtained in step S2 is as follows:
Wherein, s indicates s-th of user, and ms is the plaintext to be encrypted,For the set of integers randomly selected
It closes,For the integer randomly selected.
Step S3, decryption step is decrypted using private key, obtains clear-text message.
It is as follows respectively there are two ways to being decrypted using private key in the step:
Oneself private key sk of S31, user Ss=psCiphertext is decrypted, the formula being related to is as follows:
Wherein, csIt indicates the ciphertext that user S needs to decrypt, plaintext m is obtained by modular arithmetics。
S32, Cloud Server decrypt ciphertext with the private key sk=p of oneself, and the formula being related to is as follows:
Wherein, csIt indicates the ciphertext that Cloud Server needs to decrypt, plaintext m is obtained by modular arithmetics。
The correctness that the correctness of verifying user S decryption below, i.e. verifying user S are decrypted in step S31:
Show x in step S14s,0It is maximized, takes | xs,0| > | xs,j|, j ∈ { 0,1 ..., τi, so there are asSo that
(1) formula can abbreviation are as follows:
cs=ms+2ts+∑j∈Sxs,j-asxs,0, | as|≤τs(4),
Arbitrarily selection j ∈ 0,1 ..., τi, all there is ks,jAnd ls,jSo that following two equation is set up:
xs,j←psks,j+2ls,j(5),
xs,0←psks,0+2ls,0(6),
(5) and (6) formula are substituted into (4) Shi Ke get:
cs=ms+ps(∑j∈Sks,j-asks,0)+2(ts+∑j∈Sls,j-asls,0) (7),
From the concept of full homomorphic cryptography: | ms+2(ts+∑j∈Sls,j-asls,0) | < ps, so enable equation at
It is vertical:
bs=∑j∈Sks,j-asks,0, ds=ts+∑j∈Sls,j-asls,0(8),
(8) formula is substituted into (7) Shi Ke get:
cs=ms+bsps+2ds(9),
Wherein s is the expression of user S.Therefore it can obtainUser S can decrypt to obtain just in step S31
True plaintext.
Then the correctness that the correctness of verifying Cloud Server decryption, i.e. verifying Cloud Server are decrypted in step S32:
On the basis of (4) formula, the formula obtained by step S14 is as follows:
xs,0←x0ks,0+2ls,0, xs,j←xsks,j+2ls,j(10),
It is as follows that (10) formula is substituted into formula obtained by (4) formula:
cs=ms+2ts+∑j∈S(xsks,j+2ls,j)-as(x0ks,0+2ls,0) (11),
Formula can be obtained by step S12: xs=pqs+2rs, substituted into (11) Shi Ke get:
cs=ms+p(∑j∈Sqsks,j-asq0ks,0)+2(ts+∑j∈Srsks,jls,j-asr0ks,0-asls,0) (12),
From the concept of full homomorphic cryptography: | ms+2(ts+∑j∈Srsks,jls,j-asr0ks,0-asks,0) | < p, so enabling
Following equation is set up:
bs=(∑j∈Sqsks,j-asq0ks,0) (13),
ds=(ts+∑j∈Srsks,jls,j-asr0ks,0-asls,0) (14),
(13) and (14) formula are substituted into (12) Shi Ke get:
cs=ms+bsp+2ds(15),
Therefore it can obtainCloud Server can be decrypted to obtain correct plaintext in step S32.
Step S4, full homomorphism appraisal procedure, inputs multiple ciphertexts of the same user or different user, carries out full homomorphism fortune
It is decrypted after calculation.
Specifically, the ciphertext number of the ciphertext or user S and user J of t user S of input and be t, t satisfactionHomomorphism circuit C is inputted simultaneously, then carries out full homomorphism operation, the ciphertext after operation recycles cloud clothes
Business device is decrypted, and obtains correct plaintext.
Encryption side of the invention encrypts the message for needing to upload to Cloud Server with the private key of oneself, so encryption
Side can carry out the verifying in later period to the data of encryption, and decryption side can carry out the message of all uploads after full homomorphism operation
It decrypts again, not only saved operation time in this way but also improves the efficiency of operation.
Full homomorphic cryptography includes additive homomorphism and multiplicative homomorphic, below with regard to the isomorphism of multiple users in step S4
Following derivation is made in operation:
1) key pair (pk of user Ss,sks), the key pair (pk of user Jj,skj)。
2) user chooses plaintext ms,mj∈ { 0,1 } can obtain ciphertext c by step S2s,cj, just by above-mentioned verifying decryption
Formula can be obtained in the step of true property:
cs=pbs+2ds+ms, cj=pbj+2dj+mj(16),
So additive homomorphism operation is as follows:
cs+cj=p (bs+bj)+2(ds+dj)+(ms+mj) (17),
Multiplicative homomorphic operation is as follows:
cs·cj=p (bs(pbj+2dj+mj)+bj(2ds+ms))+2(2dsdj+dsmj+msdj)+msmj(18),
Because of ms,mj∈ { 0,1 }, so ms+mj∈ { 0,1 }, ms·mj∈ { 0,1 }, i.e. following formula are set up:
|2(ds+dj)+(ms+mj) | < p, | 2 (2dsdj+dsmj+msdj)+msmj| < p (19),
The Encryption Model that full homomorphism operation is related to are as follows:
Wherein, plaintext space M, a decryption side P,；Two encryption side Ps,Pj, ms,mj∈ M, P public private key pair (pk,
Sk), PsPublic private key pair (pks,sks), Encryption Algorithm is expressed as E, and decipherment algorithm is expressed as D,Indicate certain full homomorphism fortune
It calculates, i ≠ j；(20) formula and (21) formula illustrate the property of multiple one decryption side in encryption side, i.e. decryption side P can decrypt encryption
Square PsThe information and P of encryptionsAnd PjThe ciphertext of encryption can be decrypted by P and can be with homomorphism operation.
It is as follows that formula can be obtained by the decryption of step S31:
Full homomorphism operation can correctly be carried out by step S4.
By above step, it can show that user S and user J meet full isomorphism.
In method of the invention, the number of the side of encryption is controlled in the range of capable of being decrypted correctly, and passes through experiment
It proves, the method has feasibility in integer range, meets the needs of user response.The invention proposes multipair on integer
Application method of the one full homomorphic encryption algorithm on Cloud Server, increases the transmission quantity of information, improves transmission speed, more accord with
Close the demand of existing big data society.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (9)
1. a kind of full homomorphic encryption algorithm of many-one, which comprises the steps of:
System initialization step, the step generate the public and private key of Cloud Server P by approximate greatest common factor (G.C.F.) difficult problem first
It is right, it then converts to obtain multiple user P by public keyiPublic private key pair；
Ciphertext generation step, user choose the clear-text message to be encrypted, and encryption obtains ciphertext；
Decryption step is decrypted using private key, obtains clear-text message；
Full homomorphism appraisal procedure, inputs multiple ciphertexts of the same user or different user, decrypts after carrying out full homomorphism operation.
2. the algorithm according to claim 1, which is characterized in that the Cloud Server P is decryption side, the user PiTo add
Close side.
3. algorithm according to claim 1 or 2, which is characterized in that in the system initialization step, the Cloud Server
Public and private key generate include following sub-step:
Choose one η odd-integral numbersAs private key sk, i.e. sk=p；
SelectionWherein q0It is maximum and be odd number, enable x0=pq0+r0,0≤i≤τ；Public key pk=< x0,x1,…,xτ>。
4. algorithm according to claim 1 or 2, which is characterized in that in the system initialization step, the public affairs of the user
It includes following sub-step that private key, which obtains:
User Pi(i=0,1 ..., τ) one integer of random selectionAs the private key of oneself,
That is ski=pi；
PiVector transformation is carried out to the public key pk of Cloud Server P, randomly selects vectorAnd vectorMake
Obtain xi,0←x0ki,0+2li,0, xi,j←xiki,j+2li,j, j ∈ { 0,1,2 ..., τi}；Assuming that xi,0Maximum then takesThat is PiPublic key pki=< xi,0,xi,1,…,xi,τ>。
5. algorithm according to claim 1 or 2, which is characterized in that in the ciphertext generation step, the cipher mode that is related to
Are as follows:
Wherein, miFor the plaintext to be encrypted,For the integer set randomly selected,With
The integer that machine is chosen.
6. algorithm according to claim 1 or 2, which is characterized in that in the decryption step, the manner of decryption that is related to
Are as follows:
User PiWith the private key sk of oneselfi=piDecrypt ciphertext, the formula being related to are as follows:
Cloud Server P decrypts ciphertext, the formula being related to the private key sk=p of oneself are as follows:
mi←[[ci]p]2；
Wherein, ciIt indicates the ciphertext for needing to decrypt, is obtained in plain text by modular arithmetic.
7. algorithm according to claim 1 or 2, which is characterized in that in the full homomorphism appraisal procedure, participate in full homomorphism
The number of the user of operation or the formula of ciphertext number are as follows:
Wherein, u indicates the number of user or the number of ciphertext, and η indicates private key length, and ρ ' indicates noise, and f expression passes through gate circuit
Multinomial.
8. the algorithm according to claim 7, which is characterized in that in the full homomorphism appraisal procedure, meet multiple users'
It full homomorphism operation and can be decrypted correctly, be expressed as follows:
ci+cj=p (ai+aj)+2(bi+bj)+(mi+mj)；
ci·ci=p (ai(paj+2bj+mj)+aj(2bi+mi))+2(2bibj+bimj+mibj)+mimj；
Dsk(ci+cj)=mi+mj,
Dsk(ci·ci)=mi·mj,
Wherein ci,cjIndicate user i, the ciphertext of j, mi,mjIndicate that user i, the ciphertext of j, p indicate the private key of decryption side.
9. the algorithm according to claim 1, which is characterized in that the Encryption Model that the full homomorphism operation is related to are as follows:
Wherein, plaintext space M, decryption side a P, multiple encryption side Pi, i is some encryption side, miThe public private key pair of ∈ M, P
(pk, sk), PiPublic private key pair (pki,ski), Encryption Algorithm Encrypt (pk, m), decipherment algorithm Decrypt (sk, c),Table
Show certain full homomorphism operation, i ≠ j.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110391895A (en) * | 2019-07-31 | 2019-10-29 | 阿里巴巴集团控股有限公司 | Data preprocessing method, ciphertext data capture method, device and electronic equipment |
| CN111865555A (en) * | 2020-07-09 | 2020-10-30 | 暨南大学 | Homomorphic encryption method based on k-Lin hypothesis |
| CN112214777A (en) * | 2020-10-20 | 2021-01-12 | 豪符密码检测技术(成都)有限责任公司 | Data encryption protection and use detection method supporting ciphertext data calculation |
| CN113259107A (en) * | 2021-06-22 | 2021-08-13 | 西安工程大学 | Grid-based dual-mode encryption method |
-
2019
- 2019-03-11 CN CN201910180640.8A patent/CN110011782A/en active Pending
Non-Patent Citations (1)
| Title |
|---|
| 王彩芬等: "基于整数的多对一全同态加密方案", 《电子与信息学报》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110391895A (en) * | 2019-07-31 | 2019-10-29 | 阿里巴巴集团控股有限公司 | Data preprocessing method, ciphertext data capture method, device and electronic equipment |
| CN111865555A (en) * | 2020-07-09 | 2020-10-30 | 暨南大学 | Homomorphic encryption method based on k-Lin hypothesis |
| CN111865555B (en) * | 2020-07-09 | 2023-08-22 | 暨南大学 | Homomorphic encryption method based on k-Lin hypothesis |
| CN112214777A (en) * | 2020-10-20 | 2021-01-12 | 豪符密码检测技术(成都)有限责任公司 | Data encryption protection and use detection method supporting ciphertext data calculation |
| CN113259107A (en) * | 2021-06-22 | 2021-08-13 | 西安工程大学 | Grid-based dual-mode encryption method |
| CN113259107B (en) * | 2021-06-22 | 2022-06-21 | 西安工程大学 | Grid-based dual-mode encryption method |
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Application publication date: 20190712 |