CN109889320B - BGV type multi-key fully homomorphic encryption method - Google Patents

BGV type multi-key fully homomorphic encryption method Download PDF

Info

Publication number
CN109889320B
CN109889320B CN201910065976.XA CN201910065976A CN109889320B CN 109889320 B CN109889320 B CN 109889320B CN 201910065976 A CN201910065976 A CN 201910065976A CN 109889320 B CN109889320 B CN 109889320B
Authority
CN
China
Prior art keywords
ciphertext
key
homomorphic
bgv
user
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910065976.XA
Other languages
Chinese (zh)
Other versions
CN109889320A (en
Inventor
李宁波
周潭平
杨晓元
魏立线
韩益亮
刘龙飞
吴立强
刘文超
涂广升
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Engineering University of Chinese Peoples Armed Police Force
Original Assignee
Engineering University of Chinese Peoples Armed Police Force
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Engineering University of Chinese Peoples Armed Police Force filed Critical Engineering University of Chinese Peoples Armed Police Force
Priority to CN201910065976.XA priority Critical patent/CN109889320B/en
Publication of CN109889320A publication Critical patent/CN109889320A/en
Application granted granted Critical
Publication of CN109889320B publication Critical patent/CN109889320B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Landscapes

  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention particularly relates to a high-efficiency BGV type multi-key fully homomorphic encryption method, which comprises the following steps: carrying out BGV homomorphic encryption on a plaintext of a user participating in operation to obtain a ciphertext corresponding to the user; expanding the ciphertext of the user participating in the operation to obtain an expanded ciphertext corresponding to the user set; performing homomorphic operation on the expanded ciphertext of the user set participating in the operation to obtain a high-dimensional BGV ciphertext, performing BGV homomorphic encryption and GSW homomorphic encryption on the key of the user participating in the calculation respectively, performing ciphertext expansion and mixed homomorphic multiplication on the encrypted result to obtain a calculation key, and performing dimensionality reduction on the high-dimensional BGV ciphertext through the calculation key; and (4) running a mode changing function on the ciphertext subjected to dimension reduction, reducing the noise in the ciphertext, and finally outputting a final ciphertext result of homomorphic operation. The BGV type multi-key fully homomorphic encryption method can allow homomorphic operation to be carried out between ciphertexts of users with different keys, thereby realizing a safe multi-party computing function.

Description

BGV type multi-key fully homomorphic encryption method
Technical Field
The invention belongs to the field of information security and privacy protection, and particularly relates to a high-efficiency BGV (band gap virtual) type multi-key fully homomorphic encryption method.
Background
The Full Homomorphic Encryption (FHE) can randomly calculate a ciphertext under the condition that a secret key is unknown, has the property of exchangeable encryption and operation, has high theoretical and application values in the current cloud computing environment, and can be widely applied to ciphertext retrieval, safe multi-party computation, cloud data analysis and the like. Since 2009 Gentry proposed the first lattice-based all-homomorphic encryption scheme Gen09, more and more all-homomorphic encryption schemes (DGHV10, BV11a, BV11b, BGV12, GSW13, AP14, etc.) were proposed based on the blueprints that Gentry depicts for all-homomorphic encryption.
Multi-key fully homomorphic encryption (mkhe) allows computation of ciphertexts of different private keys, an extension of fully homomorphic encryption in secure multiparty computing. LATV12 first proposes the concept of mkhe and proposes a multi-key fully homomorphic encryption scheme based on NTRU public key cryptosystem, but the security of the encryption scheme based on NTRU is based on the non-standard assumption on the polynomial ring, and the difficult problem of strict reduction to the lattice can not be solved, so the security needs to be further examined.
Clear and McGoldrick use GSW type FHE to provide a first GSW type MKFHE scheme CM15 based on error learning problem (LWE), because LWE problem can be quantum-reduced to the difficulty problem of the worst case on an ideal lattice, the safety of the scheme is guaranteed, and the number of the participator keys in the scheme has no upper limit. The CM15 is improved by Mukherjee and Wichs, and an LWE-based MKFHE scheme MW16 is provided, which can be used for realizing one-round threshold decryption protocol and realizing a two-round secure multi-party computing (MPC) protocol on the basis of the one-round threshold decryption protocol.
The CM15 and MW16 schemes need to set the number of users participating in homomorphic computation in advance, and cannot realize the addition of new users in the computation process, and this type of mkhe is called single-hop (single-hop) type mkhe in PS 16. Meanwhile, the PS16 proposes the concept of multi-hop (multi-hop) mkhe: the cryptograph of the original participant after homomorphic operation can be operated again with the cryptograph of the newly added participant, namely, any participant can be dynamically added into the cryptograph operation process in real time. BP16 proposes the concept of a fully dynamic mkhe, i.e. the number of participants does not need to be set in advance.
On TCC2017, chenlong et al propose a BGV type multi-hop mkhe based on RLWE. The scheme supports the cipher text packing technology based on the Chinese remainder theorem, simplifies the cipher text extension process in the MKFHE, and can be used for constructing two rounds of MPC protocols and threshold decryption protocols.
Currently, the BGV type MKFHE scheme supporting Batched Multi-hop is represented by CZW 17. The BGV type MKFHE scheme has the defects of ciphertext quantity, relatively large public parameter and large calculation quantity in the key generation and calculation process.
Disclosure of Invention
In order to solve the defects of relatively large cipher text amount and public parameters and large operation amount in the process of generating and calculating the key in the prior art, the invention provides a high-efficiency BGV type multi-key fully homomorphic encryption method, which can allow homomorphic operation to be carried out between cipher texts of users with different keys, thereby realizing a safe multi-party calculation function. In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an efficient BGV-type multi-key fully homomorphic encryption method comprises the following steps:
the method comprises the following steps: carrying out BGV homomorphic encryption on a plaintext of a user participating in operation to obtain a ciphertext corresponding to the user;
step two: expanding the ciphertext of the user participating in the operation to obtain an expanded ciphertext corresponding to the user set;
step three: performing homomorphic operation on the expanded ciphertext of the user set participating in the operation to obtain a high-dimensional BGV ciphertext, performing BGV homomorphic encryption and GSW homomorphic encryption on the key of the user participating in the calculation respectively, performing ciphertext expansion and mixed homomorphic multiplication on the encrypted result to obtain a calculation key, and performing dimensionality reduction on the high-dimensional BGV ciphertext through the calculation key;
step four: and (4) running a mode changing function on the ciphertext subjected to dimension reduction, reducing the noise in the ciphertext, and finally outputting a final ciphertext result of homomorphic operation.
Further, the specific operation of the step one is as follows: the safety parameter l, the integer m, the modulus q ═ ploy (n), the polynomial ring R ═ Z [ X ] are given]/ΦmAnd the ring B-bounded discrete c (B < q), the integer N ═ O (nlogq),
Figure BDA0001955653480000031
polynomial ring RqR/qR; the circuit depth is L, and the modulus q of each layer of circuitL＞＞qL-1＞＞＞＞q0A small integer p and coprime to all moduli,
Figure BDA0001955653480000032
RqR/qR; selecting L +1 random common vectors
Figure BDA0001955653480000033
L ═ 0., L; defining S as an ordered set, wherein the ordered set comprises ordered tags of all participants related to the ciphertext and no repeated elements; defining a ciphertext tuple ct ═ { c, { S }, l }, which includes ciphertext c of user set S, user set S
(1) And (3) key generation: generating the required key for the jth participant:
selection of zl,jEither ae in e, e
Figure RE-GDA0002050220520000035
Then the private key of the party is skj＝{sl,j}， l∈{L,...,0}；
Random selection
Figure RE-GDA0002050220520000036
Defining:
Figure RE-GDA0002050220520000037
l is belonged to { L.,. 0}, and a public key pk is generatedl,j＝{pl,j}，l∈{L,...,0}；
A generation unit for calculating a calculation key required for the homomorphic calculation of the ciphertext,
Figure RE-GDA0002050220520000038
(a) for m e {0l-1, j ∈ { 1., k }, ζ ∈ { 0., k }, calculating
Figure RE-GDA0002050220520000039
Figure RE-GDA00020502205200000310
(b) For j ∈ { 1.,. k }, ζ ∈ { 0.,. k }, a calculation is performed
Figure RE-GDA0002050220520000041
Figure RE-GDA0002050220520000042
Figure RE-GDA0002050220520000043
(2) And (3) encryption process: inputting plaintext mu e R to be encryptedpAnd the public key pkl,jRandomly selecting R ∈ R2And the error matrix E ═ E (E)1,e2)←χ2Generating a plaintext mujLayer i ciphertext:
Figure RE-GDA0002050220520000044
and outputting the ciphertext tuple ct ═ { c, { j }, l }.
Further, the specific operation of the second step is as follows:
BGV.CTExt(cls'): cipher text tuple
Figure RE-GDA0002050220520000045
Is extended to
Figure RE-GDA0002050220520000046
Wherein S is the same as S',
(1) decompose ciphertext c into k +1 equal parts:
Figure RE-GDA0002050220520000047
corresponding private key
Figure RE-GDA0002050220520000048
And user set S ═ i1,...,ik}；
(2) And (3) generating an extended ciphertext:
Figure RE-GDA0002050220520000049
wherein
Figure RE-GDA00020502205200000410
Corresponding extended key
Figure RE-GDA00020502205200000411
Easy to verify
Figure RE-GDA00020502205200000412
Further, the specific operation of the third step is as follows: inputting t ciphertext groups (ct) after ciphertext expansion1,…ctt) And assuming that it is in the same circuit layer, an
Figure RE-GDA00020502205200000413
j belongs to { 1.,. t }, and a public user set is generated
Figure RE-GDA00020502205200000414
(1) By calling basic homomorphic arithmetic units in the scheme
Figure RE-GDA00020502205200000415
And
Figure RE-GDA00020502205200000416
homomorphic operation circuit for t ciphertexts
Figure RE-GDA00020502205200000417
The result after the operation is
Figure RE-GDA00020502205200000418
(2) Generating a calculation key evk required in a ciphertext operationS＝MKFHE.EvkGen(emS)；
(3) For ciphertext
Figure RE-GDA0002050220520000051
And (3) performing dimensionality reduction:
Figure RE-GDA0002050220520000052
further, the specific operation of the step four is as follows: inputting a ciphertext of the layer I after homomorphic operation
Figure RE-GDA0002050220520000053
Computing
Figure RE-GDA0002050220520000054
Compared with the prior art, the invention has the beneficial effects that:
1. the invention converts the BGV ciphertext and the GSW ciphertext from a single user to multiple users, thereby reducing the size of the expanded ciphertext;
2. the invention improves the generation process of the conversion key required in the key conversion technology, replaces the original RGSW ciphertext multiplication by the mixed homomorphic multiplication of the RBGV and the RGSW ciphertext, and reduces the size of public parameters and calculation keys;
3. the value range of the private key coefficient of the user is set to be { -1,0,1}, so that the size and the number of ciphertexts in the key generation process are reduced;
4. the invention reduces the data volume in the homomorphic calculation process, and the reduction of the data volume can further reduce the calculation complexity of homomorphic calculation.
Drawings
FIG. 1 is a schematic flow diagram of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
The embodiment provides an efficient BGV-type multi-key fully homomorphic encryption method, which is characterized in that a single-user ciphertext is converted into a multi-user ciphertext by using a ciphertext expansion technology, so that a multi-key fully homomorphic encryption scheme is converted into a single-key fully homomorphic encryption scheme, the ciphertext is processed by using a key conversion technology and a mode conversion technology, and the dimensionality and the noise of the ciphertext are reduced. The BGV type multi-key fully homomorphic encryption method can be effectively applied to safe multi-party computing among multiple users in a cloud computing environment, and has the excellent characteristics of confidentiality, ciphertext availability, collusion attack resistance, quantum attack resistance and the like. Compared with the BGV type multi-key fully homomorphic encryption scheme [ CZW17],
referring to fig. 1, the BGV-type multi-key fully homomorphic encryption method includes the following steps:
the method comprises the following steps: carrying out BGV homomorphic encryption on a plaintext of a user participating in operation to obtain a ciphertext corresponding to the user;
step two: expanding the ciphertext of the user participating in the operation to obtain an expanded ciphertext corresponding to the user set;
step three: performing homomorphic operation on the expanded ciphertext of the user set participating in the operation to obtain a high-dimensional BGV ciphertext, performing BGV homomorphic encryption and GSW homomorphic encryption on the key of the user participating in the calculation respectively, performing ciphertext expansion and mixed homomorphic multiplication on the encrypted result to obtain a calculation key, and performing dimensionality reduction on the high-dimensional BGV ciphertext through the calculation key;
step four: and (4) running a mode changing function on the ciphertext subjected to dimension reduction, reducing the noise in the ciphertext, and finally outputting a final ciphertext result of homomorphic operation.
Initialization: the safety parameter l, the integer m, the modulus q ═ ploy (n), the polynomial ring R ═ Z [ X ] are given]/ΦmAnd the ring B-bounded discrete c (B < q), the integer N ═ O (nlogq),
Figure BDA0001955653480000071
polynomial ring RqR/qR; the circuit depth is L, and the modulus q of each layer of circuitL＞＞qL-1＞＞…＞＞q0A small integer p and coprime to all moduli,
Figure BDA0001955653480000072
RqR/qR; selecting L +1 random common vectors
Figure BDA0001955653480000073
L is 0, …, L; defining S as an ordered set, wherein the ordered set comprises ordered tags of all participants related to the ciphertext and no repeated elements; defining a cipher text tuple ct ═ { c, { S }, l }, wherein the cipher text c of the user set S, the user set S and the corresponding circuit are contained
And (3) key generation: generating the required key for the jth participant:
selection of zl,jEither ae in e, e
Figure RE-GDA0002050220520000065
Then the private key of the party is skj＝{sl,j}， l∈{L,...,0}；
Random selection
Figure RE-GDA0002050220520000071
Defining:
Figure RE-GDA0002050220520000072
l is belonged to { L.,. 0}, and a public key pk is generatedl,j＝{pl,j}，l∈{L,...,0}；
A generation unit for calculating a calculation key required for the homomorphic calculation of the ciphertext,
Figure RE-GDA0002050220520000073
(a) for m e {0l-1, j ∈ { 1., k }, ζ ∈ { 0., k }, calculating
Figure RE-GDA0002050220520000074
Figure RE-GDA0002050220520000075
(b) For j ∈ { 1.,. k }, ζ ∈ { 0.,. k }, a calculation is performed
Figure RE-GDA0002050220520000076
Figure RE-GDA0002050220520000077
Figure RE-GDA0002050220520000078
And (3) encryption process: inputting plaintext mu e R to be encryptedpAnd the public key pkl,jRandomly selecting R ∈ R2And the error matrix E ═ E (E)1,e2)←χ2Generating a plaintext mujLayer i ciphertext:
Figure RE-GDA0002050220520000079
and outputting the ciphertext tuple ct ═ { c, { j }, l }.
And (3) decryption process: input device
Figure RE-GDA00020502205200000710
And corresponding private key, outputting the plaintext
Figure RE-GDA00020502205200000711
Outputting the plaintext
Figure RE-GDA00020502205200000712
BGV ciphertext expansion process:
BGV.CTExt(cls'): cipher text tuple
Figure RE-GDA00020502205200000713
Is extended to
Figure RE-GDA00020502205200000714
Wherein S is the same as S',
(1) decompose ciphertext c into k +1 equal parts:
Figure RE-GDA0002050220520000081
corresponding private key
Figure RE-GDA0002050220520000082
And user set S ═ i1,...,ik}；
(2) And (3) generating an extended ciphertext:
Figure RE-GDA0002050220520000083
wherein
Figure RE-GDA0002050220520000084
Corresponding extended key
Figure RE-GDA0002050220520000085
Easy to verify
Figure RE-GDA0002050220520000086
The homomorphic operation process of the multi-user ciphertext: inputting t ciphertext groups (ct) after ciphertext expansion1,…,ctt) And assuming that it is in the same circuit layer, an
Figure RE-GDA0002050220520000087
j belongs to {1, …, t }, and a public user set is generated
Figure RE-GDA0002050220520000088
(1) By calling basic homomorphic arithmetic units in the scheme
Figure RE-GDA0002050220520000089
And
Figure RE-GDA00020502205200000810
homomorphic operation circuit for t ciphertexts
Figure RE-GDA00020502205200000811
The result after the operation is
Figure RE-GDA00020502205200000812
(2) Generating a calculation key evk required in a ciphertext operationS＝MKFHE.EvkGen(emS)；
(3) For ciphertext
Figure RE-GDA00020502205200000813
And (3) performing dimensionality reduction:
Figure RE-GDA00020502205200000814
and (3) die changing process: inputting a ciphertext of the layer I after homomorphic operation
Figure RE-GDA00020502205200000815
Computing
Figure RE-GDA00020502205200000816
And (3) safety analysis: in terms of basic scheme, the invention and CZW17 use the same BGV encryption scheme and GSW encryption scheme. The main differences between the present invention and CZW17 are two points: on one hand, a mixed homomorphic multiplication function among a BGV ciphertext nested expansion function, a GSW type ciphertext split expansion function and an RBGV ciphertext and an RGSW ciphertext is provided, the input and the output of the three functions are ciphertexts, and the calculation process is on the ciphertexts, so the safety of the scheme cannot be reduced; on the other hand, the coefficient value of the private key of the BGV ciphertext is limited to {0,1} from c, so the dimensionality N of the polynomial needs to be increased to a certain extent to ensure the safety of the scheme.
The invention is compared with the storage overhead of CZW 17:
Figure BDA0001955653480000103
the foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (1)

1. A BGV-type multi-key fully homomorphic encryption method is characterized by comprising the following steps:
the method comprises the following steps: the method comprises the steps of conducting BGV type homomorphic encryption on a plaintext of a user participating in operation to obtain a ciphertext corresponding to the user, specifically, giving a security parameter l, an integer m, a modulus q ═ ploy (n), a polynomial ring R ═ Z [ X ], (n)]/ΦmAnd a ring B-bounded discrete component c, B < q, the integer N ═ O (nlogq),
Figure FDA0003333605160000011
polynomial ring RqR/qR; the circuit depth is L, and the modulus q of each layer of circuitL＞＞qL-1＞＞…＞＞q0A small integer p and coprime to all moduli,
Figure FDA0003333605160000012
RqR/qR; selecting L +1 random common vectors
Figure FDA0003333605160000013
L ═ 0., L; definition S is an ordered set, whichThe method comprises the steps of including the tags with sequences of all the participants involved in the ciphertext, wherein the tags have no repeated elements; defining a ciphertext tuple ct ═ { c, { S }, l }, wherein the ciphertext c of the user set S, the user set S and corresponding circuit level l are included;
(1) and (3) key generation: generating the required key for the jth participant:
selection of zl,jEither ae in e, e
Figure FDA0003333605160000014
Then the private key of the party is skj＝{sl,j}，l∈{L,...,0}；
Random selection
Figure FDA0003333605160000015
Defining:
Figure FDA0003333605160000016
l is belonged to { L.,. 0}, and a public key pk is generatedl,j＝{pl,j}，l∈{L,...,0}；
A generation unit for calculating a calculation key required for the homomorphic calculation of the ciphertext,
Figure FDA0003333605160000017
(a) for m e {0l-1, j ∈ { 1., k }, ζ ∈ { 0., k }, calculating
Figure FDA0003333605160000018
(b) For j ∈ { 1.,. k }, ζ ∈ { 0.,. k }, a calculation is performed
Figure FDA0003333605160000019
Figure FDA0003333605160000021
Figure FDA0003333605160000022
(2) And (3) encryption process: inputting plaintext mu e R to be encryptedpAnd the public key pkl,jRandomly selecting R ∈ R2And the error matrix E ═ E (E)1,e2)←χ2Generating a plaintext mujLayer i ciphertext:
Figure FDA0003333605160000023
outputting a ciphertext tuple ct ═ { c, { j }, l };
step two: expanding the ciphertext of the user participating in the operation to obtain an expanded ciphertext corresponding to the user set, wherein the BGV ciphertext expansion process comprises the following steps: CTExt (c)lS'): cipher text tuple
Figure FDA0003333605160000024
Is extended to
Figure FDA0003333605160000025
Wherein S belongs to S', (1) decomposing the ciphertext c into k +1 equal parts:
Figure FDA0003333605160000026
corresponding private key
Figure FDA0003333605160000027
And user set S ═ i1,...,ik}; (2) and (3) generating an extended ciphertext:
Figure FDA0003333605160000028
wherein
Figure FDA0003333605160000029
Corresponding extended key
Figure FDA00033336051600000210
Easy to verify
Figure FDA00033336051600000211
Step three: performing homomorphic operation on the expanded ciphertext of the user set participating in the operation to obtain a high-dimensional BGV ciphertext, performing BGV homomorphic encryption and GSW homomorphic encryption on the key of the user participating in the calculation respectively, performing ciphertext expansion and mixed homomorphic multiplication on the encrypted result to obtain a calculation key, performing dimensionality reduction on the high-dimensional BGV ciphertext through the calculation key, and performing a multi-user ciphertext homomorphic operation process: inputting t ciphertext groups (ct) after ciphertext expansion1,...ctt) And assuming that it is in the same circuit layer, an
Figure FDA00033336051600000212
j belongs to { 1.,. t }, and a public user set is generated
Figure FDA00033336051600000213
(1) By calling basic homomorphic arithmetic units in the scheme
Figure FDA00033336051600000214
And
Figure FDA00033336051600000215
for t ciphertext homomorphic operation circuits C, the result after operation is
Figure FDA00033336051600000216
(2) Generating a calculation key evk required in a ciphertext operationS＝MKFHE.EvkGen(emS) (ii) a (3) For ciphertext
Figure FDA00033336051600000217
To carry outAnd (3) reducing the dimensionality:
Figure FDA00033336051600000218
step four: and (3) operating a mode changing function on the ciphertext subjected to dimension reduction, reducing noise in the ciphertext, and finally outputting a final ciphertext result of homomorphic operation, wherein the mode changing function is as follows: inputting a ciphertext of the layer I after homomorphic operation
Figure FDA0003333605160000031
Computing
Figure FDA0003333605160000032
CN201910065976.XA 2019-01-24 2019-01-24 BGV type multi-key fully homomorphic encryption method Active CN109889320B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910065976.XA CN109889320B (en) 2019-01-24 2019-01-24 BGV type multi-key fully homomorphic encryption method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910065976.XA CN109889320B (en) 2019-01-24 2019-01-24 BGV type multi-key fully homomorphic encryption method

Publications (2)

Publication Number Publication Date
CN109889320A CN109889320A (en) 2019-06-14
CN109889320B true CN109889320B (en) 2022-04-15

Family

ID=66926677

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910065976.XA Active CN109889320B (en) 2019-01-24 2019-01-24 BGV type multi-key fully homomorphic encryption method

Country Status (1)

Country Link
CN (1) CN109889320B (en)

Families Citing this family (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110266721B (en) * 2019-07-05 2020-04-28 西南交通大学 Homomorphic-based cloud-assisted dynamic universal secure multi-party computing method
CN110855421B (en) * 2019-10-25 2023-11-07 高秀芬 Improved isomorphic encryption method
CN110889139B (en) * 2019-11-26 2021-03-23 支付宝(杭州)信息技术有限公司 Method and device for multi-party combined dimensionality reduction processing aiming at user privacy data
CN111342950A (en) * 2019-12-16 2020-06-26 中国人民武装警察部队工程大学 BGV type multi-key fully homomorphic encryption method with directional decryption function
CN112152777B (en) * 2020-08-18 2022-04-22 西安交通大学 Homomorphic cryptographic operation-oriented key conversion method, system, equipment and readable storage medium

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103475472A (en) * 2013-07-22 2013-12-25 浙江万里学院 Method for NTRU-type fully-homomorphic encryption on LWE circle
CN107359979A (en) * 2017-07-25 2017-11-17 西安电子科技大学 Symmetrical full homomorphic cryptography method based on Representation theorem

Family Cites Families (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9281941B2 (en) * 2012-02-17 2016-03-08 International Business Machines Corporation Homomorphic evaluation including key switching, modulus switching, and dynamic noise management
US9749128B2 (en) * 2014-05-15 2017-08-29 Xerox Corporation Compact fuzzy private matching using a fully-homomorphic encryption scheme
US9846785B2 (en) * 2015-11-25 2017-12-19 International Business Machines Corporation Efficient two party oblivious transfer using a leveled fully homomorphic encryption
FR3057090B1 (en) * 2016-09-30 2018-10-19 Safran Identity & Security METHODS FOR SECURELY LEARNING PARAMETERS FROM A CONVOLVED NEURON NETWORK AND SECURED CLASSIFICATION OF INPUT DATA
CN106534313B (en) * 2016-11-17 2019-09-13 浙江工商大学 The frequency measuring method and system of facing cloud end data publication protection safety and privacy
US10439799B2 (en) * 2017-02-27 2019-10-08 United States Of America As Represented By Secretary Of The Navy System and method for automating indirect fire protocol using fully homomorphic encryption
CN107147484B (en) * 2017-05-12 2020-03-31 南京邮电大学 Floating point number fully homomorphic encryption method facing privacy protection
CN107864033B (en) * 2017-05-16 2020-04-24 中国人民武装警察部队工程大学 Bootstrap type symmetrical fully homomorphic encryption method
CN107294698B (en) * 2017-07-25 2019-11-26 西安电子科技大学 The full homomorphic cryptography method that single ciphertext homomorphism calculates
CN107592195A (en) * 2017-09-12 2018-01-16 北京电子科技学院 A kind of accurate full homomorphism ciphertext data manipulation method and system
CN108718231B (en) * 2018-07-04 2023-05-23 深圳大学 Fully homomorphic encryption method, fully homomorphic encryption device and computer readable storage medium

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103475472A (en) * 2013-07-22 2013-12-25 浙江万里学院 Method for NTRU-type fully-homomorphic encryption on LWE circle
CN107359979A (en) * 2017-07-25 2017-11-17 西安电子科技大学 Symmetrical full homomorphic cryptography method based on Representation theorem

Also Published As

Publication number Publication date
CN109889320A (en) 2019-06-14

Similar Documents

Publication Publication Date Title
CN109889320B (en) BGV type multi-key fully homomorphic encryption method
CN109936435B (en) NTRU type multi-key fully homomorphic encryption method with fast homomorphic operation process
Almaiah et al. A new hybrid text encryption approach over mobile ad hoc network
Wang et al. Cryptanalysis of a symmetric fully homomorphic encryption scheme
CN111510281B (en) Homomorphic encryption method and device
CN109831297A (en) A kind of full homomorphic cryptography method of more identity for supporting thresholding to decrypt
CN107864033B (en) Bootstrap type symmetrical fully homomorphic encryption method
CN111342950A (en) BGV type multi-key fully homomorphic encryption method with directional decryption function
Chotard et al. Multi-client functional encryption with repetition for inner product
Al-Arjan et al. Intelligent security in the era of AI: The key vulnerability of RC4 algorithm
Phuong et al. Efficient hidden vector encryption with constant-size ciphertext
Han et al. Attribute-based signcryption scheme with non-monotonic access structure
Wu et al. New identity based proxy re-encryption scheme from lattices
Ahila et al. State of art in homomorphic encryption schemes
JP2000047581A (en) Ciphering method, ciphering and deciphering device, and cipher communication system
Zhao et al. Improved linear cryptanalysis of CAST-256
Nalwaya et al. A cryptographic approach based on integrating running key in feedback mode of elgamal system
Parenreng et al. The E-mail security system using El-Gamal hybrid algorithm and AES (advanced encryption standard) algorithm
CN115001651A (en) Multi-party computing method based on fully homomorphic encryption and suitable for semi-honest model
Nuida et al. On the security of pseudorandomized information-theoretically secure schemes
Ali Randomly encryption using genetic algorithm
Apon et al. Bi-deniable inner product encryption from LWE
Wang et al. A fully secure unidirectional and multi-use proxy re-encryption scheme
CN111130786A (en) Multi-party cooperative SM2 key generation and ciphertext decryption method and medium
Tiplea A brief introduction to quadratic residuosity based cryptography

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant