CN113810416A - Public key searchable encryption method based on SM2 public key encryption algorithm - Google Patents

Public key searchable encryption method based on SM2 public key encryption algorithm Download PDF

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CN113810416A
CN113810416A CN202111094000.9A CN202111094000A CN113810416A CN 113810416 A CN113810416 A CN 113810416A CN 202111094000 A CN202111094000 A CN 202111094000A CN 113810416 A CN113810416 A CN 113810416A
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public key
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CN113810416B (en
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林超
蒲浪
伍玮
何德彪
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Fujian Normal University
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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
    • H04L63/0442—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 wherein the sending and receiving network entities apply asymmetric encryption, i.e. different keys for encryption and decryption
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/90—Details of database functions independent of the retrieved data types
    • G06F16/903—Querying
    • G06F16/90335—Query processing
    • 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
    • H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/50—Reducing energy consumption in communication networks in wire-line communication networks, e.g. low power modes or reduced link rate

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Abstract

The invention relates to a public key searchable encryption method based on SM2 public key encryption algorithm, and provides an encryption system comprising a system administrator, a sender, a receiver and a cloud end, four entities; a system administrator calls an initialization Setup algorithm to determine system parameters and shares the system parameters to other entities; and the sender and the receiver respectively call S-KGen and R-KGen to produce public and private keys. And then, the sender calls the PEKS to generate a cipher text of the keyword, and the keyword cipher text and the corresponding data cipher text are uploaded to the cloud. Then, the receiver can call the TraDo to generate a keyword trapdoor and initiate a data retrieval request to the cloud. And finally, the cloud calls Test to search a keyword ciphertext matched with the keyword trapdoor in the database, and then returns the corresponding data ciphertext to the receiver. The invention adopts SM2 public key encryption algorithm, has the characteristics of safety, advancement and autonomous control, and the generation process of the keyword trapdoor does not need to involve bilinear pairwise operation.

Description

Public key searchable encryption method based on SM2 public key encryption algorithm
Technical Field
The invention relates to the field, in particular to a public key searchable encryption method based on an SM2 public key encryption algorithm.
Background
With the rapid development of cloud computing, a large number of users store personal data in a cloud server, so that the local storage pressure is effectively relieved, complicated data management is avoided, and convenience is provided for using data. However, the external cloud server has a Honest and Curious (curous-But-host) feature, which can correctly store the user data, But also attempt to view the data content, and seriously threatens the personal data privacy of the user. The traditional symmetric/public key encryption is a common data privacy protection method, and a user encrypts data first when uploading the data, so that the confidentiality of the data can be effectively guaranteed, and a cloud server is prevented from maliciously acquiring data contents. When the user searches data, the method downloads all the data uploaded to the server to the local, executes decryption operation and then searches. Downloading all data to local occupies a large amount of bandwidth resources, which is easy to cause server congestion; meanwhile, the decrypted and downloaded ciphertext data occupy a large amount of local computing resources and affect the service quality of data retrieval. Searchable Encryption (SE) is a special public key Encryption technology, can fully utilize huge computing power/storage resources of a cloud server, provides convenient data retrieval service on the premise of ensuring data security, and saves a large amount of local computing overhead, storage space and network communication cost for users. Although a large number of searchable encryption schemes are proposed at present, the searchable encryption schemes based on domestic commercial cryptographic algorithms are not published, and the development requirements of autonomous and controllable cryptographic core technologies in China are not met.
Disclosure of Invention
In view of this, the present invention aims to provide a public key searchable encryption method based on the SM2 public key encryption algorithm, so as to implement an encryption scheme with high security, low computation overhead, and low communication cost.
In order to achieve the purpose, the invention adopts the following technical scheme:
a public key searchable encryption method based on SM2 public key encryption algorithm provides an encryption system comprising a system administrator, a sender, a receiver and a cloud end, and comprises the following steps;
a system administrator calls an initialization Setup algorithm to determine a system parameter pp and shares the system parameter pp to other entities;
the sender and the receiver respectively call S-KGen and R-KGen to produce public and private keys;
sender calls PEKS to generate keyword ciphertext ctwThe keyword ciphertext ctwUploading the corresponding data ciphertext Edata to a cloud;
trando can be called by a receiver to generate keyword trapdoor twSending a data retrieval request to the cloud end, calling Test by the cloud end to search in the database and find the keyword trapdoor twMatched keyword ciphertext ctwAnd then returning the corresponding data cipher text Edata to the receiving party.
Further, the initializing Setup algorithm specifically includes:
inputting a safety parameter lambda, randomly selecting a large prime number q, and determining a nonsingular elliptic curve E: y2＝x3+ ax + b (mod q), wherein,
Figure BDA0003268617370000021
selecting prime n-order cyclic group from all points E and infinity points
Figure BDA0003268617370000022
And a generator
Figure BDA0003268617370000023
Random selection
Figure BDA0003268617370000024
And calculate G1＝αG；
Selecting secure hash functions
Figure BDA0003268617370000025
And a key derivation function KDF;
outputting system parameters
Figure BDA0003268617370000031
Further, the S-KGen algorithm specifically includes: inputting system parameter pp, and randomly selecting
Figure BDA0003268617370000032
Calculating Ps＝dsG,P′s＝dsG1Outputting the private key sk of the senders＝dsPublic key pks＝Ps。
Further, the R-KGen algorithm specifically includes: inputting system parameter pp, randomly selecting k-order polynomial
Figure BDA0003268617370000033
And
Figure BDA0003268617370000034
Figure BDA0003268617370000035
wherein
Figure BDA0003268617370000036
Algorithm output receiver private key skr＝(p1(x),p2(x) Public key pk)r＝(D0,…,Dk) Wherein D ist＝ctG+c′tG1(t＝0,…,k)。
Further, the PEKS algorithm specifically includes: inputting system parameter pp and sender private key sks＝dsReceiver public key pkr＝(D0,…,Dk) And a keyword w; random selection
Figure BDA0003268617370000037
Figure BDA0003268617370000038
Calculating C1＝rG、C′1＝rG1、
Figure BDA0003268617370000039
Bw＝e(Qw,G+G1)、αw＝KDF(Bw,plen)、
Figure BDA00032686173700000310
And
Figure BDA00032686173700000311
wherein plen is the bit length of the random plaintext pt; ciphertext ct of output keyword ww＝(C1,C′1,C2,C3)。
Further, the TraDo algorithm specifically includes: inputting system parameter pp and receiving party private key skr＝(p1(x),p2(x) Public key pk of sender), the public key pk of senders＝(Ps,P′s) And a keyword w; calculating p1,w＝p1(w),p2,w＝p2(w) and tw＝p1,wPs+p2, wP′s. Algorithm output keyword trapdoor tw。
Further, the Test algorithm specifically includes: inputting system parameter pp, keyword trapdoor t of receiverwAnd keyword ciphertext ctwCalculating B'w＝e(tw,C1+C′1),α′w＝KDF(B′w,plen),
Figure BDA00032686173700000312
Figure BDA00032686173700000313
If C3＝C′3And if so, outputting 1 by the algorithm to indicate that the keyword ciphertext and the trapdoor are successfully matched, and otherwise, outputting 0.
Compared with the prior art, the invention has the following beneficial effects:
the method adopts an SM2 public key encryption algorithm, has the characteristics of safety, advancement and autonomous control, and ensures that the scheme of the invention has the characteristics of high safety, low calculation overhead, low communication cost and the like because bilinear pairing operation is not required in the generation process of the keyword trapdoor.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Referring to fig. 1, the present invention provides a public key searchable encryption method based on SM2 public key encryption algorithm, and provides an encryption system including a system administrator, a sender, a receiver and a cloud, and includes the following steps;
a system administrator calls an initialization Setup algorithm to determine a system parameter pp and shares the system parameter pp to other entities;
the sender and the receiver respectively call S-KGen and R-KGen to produce public and private keys;
sender calls PEKS to generate keyword ciphertext ctwThe keyword ciphertext ctwUploading the corresponding data ciphertext Edata to a cloud;
trando can be called by a receiver to generate keyword trapdoor twSending a data retrieval request to the cloud end, calling Test by the cloud end to search in the database and find the keyword trapdoor twMatched keyword ciphertext ctwAnd then returning the corresponding data cipher text Edata to the receiving party.
In this embodiment, the adopted symbols and definitions are as follows:
q: large prime number.
k: the order of the polynomial.
Fq: a finite field containing q elements.
a,b：FqThe elements in (1), which define FqAn elliptic curve E above.
E(Fq)：FqThe set of all rational points of the upper elliptic curve E, including the point of infinity O.
#E(Fq)：E(Fq) The number of points, called elliptic curve E (F)q) The order of (a).
O: a particular point on the elliptic curve is called the infinity point or the null point.
Figure BDA0003268617370000051
A cyclic group containing all points of the elliptic curve E and points at infinity.
G: group of
Figure BDA0003268617370000052
The generator of (1).
n: order of generator G (n is # E (F)q) Prime factor of).
Figure BDA0003268617370000053
A secure cryptographic hash function.
KDF: a key derivation function.
Figure BDA0003268617370000054
A set of elements of the set {1, 2., n } that are co-prime with the element n.
p1(x),p2(x) The method comprises the following steps A polynomial of order k as the private key of the receiving party.
Dt: the public key of the receiver, where t is 0, …, k.
ds: the sender's private key.
Ps: the sender's public key.
In the embodiment, the adopted algorithm comprises six parts of system establishment (Setup), sender key generation (S-KGen), receiver key generation (S-KGen), keyword ciphertext generation (PEKS), keyword trapdoor generation (Trando) and Test (Test). The method comprises the following specific steps:
algorithm 1. initialization (Setup): inputting a safety parameter lambda by an algorithm, randomly selecting a large prime number q, and determining a nonsingular elliptic curve E: y2＝x3+ ax + b (mod q) (where,
Figure BDA0003268617370000055
) Selecting prime n-order cycles from all points E and infinity pointsRing group
Figure BDA0003268617370000056
And a generator
Figure BDA0003268617370000057
Random selection
Figure BDA0003268617370000059
And calculate G1α G. Selecting secure hash functions
Figure BDA0003268617370000058
And a key derivation function KDF. Algorithm output system parameters
Figure BDA0003268617370000061
Figure BDA0003268617370000062
The invention is designed based on the SM2 public key encryption algorithm, so the same system parameters are used as in SM2, and the specific parameter notation definition is referred to in the detailed description (1. notation and definition).
Algorithm 2. Key Generation (S-KGen): inputting system parameter pp by algorithm, and randomly selecting
Figure BDA0003268617370000063
Calculating Ps＝dsG,P′s＝dsG1The algorithm outputs the private key sk of the senders＝dsPublic key pks＝Ps。
Algorithm 3. Key Generation (R-KGen): inputting system parameter pp by algorithm, and randomly selecting polynomial of k order
Figure BDA0003268617370000064
And
Figure BDA0003268617370000065
wherein
Figure BDA0003268617370000066
Algorithm output receiver private key skr＝(p1(x),p2(x) Public key pk)r＝(D0,…,Dk) Wherein D ist＝ctG+c′tG1(t＝0,…,k)。
Algorithm 4. keyword ciphertext generation (PEKS): inputting system parameter pp and sender private key sk by algorithms＝dsReceiver public key pkr＝(D0,…,Dk) And a keyword w. Random selection
Figure BDA0003268617370000067
Calculating C1＝rG、C′1＝rG1、
Figure BDA0003268617370000068
Bw＝e(Qw,G+G1)、αw＝KDF(Bw,plen)、
Figure BDA0003268617370000069
And
Figure BDA00032686173700000610
where plen is the bit length of the random plaintext pt. Ciphertext ct of algorithm output keyword ww＝(C1,C′1,C2,C3)。
Algorithm 5. keyword trapdoor generation (Trando): inputting system parameter pp and receiving party private key sk by algorithmr＝(p1(x),p2(x) Public key pk of sender), the public key pk of senders＝(Ps,P′s) And a keyword w. Calculating p1,w＝p1(w),p2,w＝p2(w) and tw＝p1,wPs+p2, wP′s. Algorithm output keyword trapdoor tw。
Algorithm 6. Test: inputting system parameter pp and key word trapdoor t of receiver by algorithmwAnd keyword ciphertext ctwCalculating B'w＝e(tw,C1+C′1),α′w＝KDF(B′w,plen),
Figure BDA0003268617370000071
If C3＝C′3And if so, outputting 1 by the algorithm to indicate that the keyword ciphertext and the trapdoor are successfully matched, and otherwise, outputting 0.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.

Claims (7)

1. A public key searchable encryption method based on SM2 public key encryption algorithm is characterized in that an encryption system is provided and comprises a system administrator, a sender, a receiver and a cloud end, and the method specifically comprises the following steps;
a system administrator calls an initialization Setup algorithm to determine a system parameter pp and shares the system parameter pp to other entities;
the sender and the receiver respectively call S-KGen and R-KGen to produce public and private keys;
sender calls PEKS to generate keyword ciphertext ctwThe keyword ciphertext ctwUploading the corresponding data ciphertext Edata to a cloud;
trando can be called by a receiver to generate keyword trapdoor twSending a data retrieval request to the cloud end, calling Test by the cloud end to search in the database and find the keyword trapdoor twMatched keyword ciphertext ctwAnd then returning the corresponding data cipher text Edata to the receiving party.
2. The public key searchable encryption method based on the SM2 public key encryption algorithm according to claim 1, wherein the initialization Setup algorithm is specifically:
a safety parameter lambda is input and,randomly selecting a large prime number q, and determining a nonsingular elliptic curve E: y is2＝x3+ ax + b (mod q), wherein,
Figure FDA0003268617360000011
selecting prime n-order cyclic group from all points E and infinity points
Figure FDA0003268617360000012
And a generator
Figure FDA0003268617360000013
Random selection
Figure FDA0003268617360000014
And calculate G1＝αG；
Selecting secure hash functions
Figure FDA0003268617360000015
And a key derivation function KDF;
outputting system parameters
Figure FDA0003268617360000016
3. The public key searchable encryption method based on the SM2 public key encryption algorithm according to claim 1, wherein the S-KGen algorithm is specifically: inputting system parameter pp, and randomly selecting
Figure FDA0003268617360000021
Calculating Ps＝dsG，P′s＝dsG1Outputting the private key sk of the senders＝dsPublic key pks＝Ps。
4. The public key searchable encryption method based on the SM2 public key encryption algorithm according to claim 1, wherein the R-KGen algorithm is specifically: input deviceSystem parameter pp, randomly selecting k-order polynomial
Figure FDA0003268617360000022
And
Figure FDA0003268617360000023
Figure FDA0003268617360000024
wherein
Figure FDA0003268617360000025
Algorithm output receiver private key skr＝(p1(x)，p2(x) Public key pk)r＝(D0，...，Dk) Where Dt ═ ctG+c′tG1(t＝0，...，k)。
5. The public key searchable encryption method based on the SM2 public key encryption algorithm according to claim 1, wherein the PEKS algorithm is specifically: inputting system parameter pp and sender private key sks＝dsReceiver public key pkr＝(D0，...，Dk) And a keyword w; random selection
Figure FDA0003268617360000026
Computing
Figure FDA0003268617360000027
Bw＝e(Qw，G+G1)、αw＝KDF(Bw，plen)、
Figure FDA0003268617360000028
And
Figure FDA0003268617360000029
wherein plen is the bit length of the random plaintext pt; ciphertext ct of output keyword ww＝(C1，C′1，C2，C3)。
6. The public key searchable encryption method based on the SM2 public key encryption algorithm according to claim 1, wherein the TraDo algorithm is specifically: inputting system parameter pp and receiving party private key skr＝(p1(x)，p2(x) P), sender public key β ks＝(Ps，P′s) And a keyword w; calculating p1，w＝p1(w)，p2，w＝p2(w) and tw＝p1，wPs+p2，wP′s. Algorithm output keyword trapdoor tw。
7. The public key searchable encryption method based on the SM2 public key encryption algorithm according to claim 1, wherein the Test algorithm is specifically: inputting system parameter pp, keyword trapdoor t of receiverwAnd keyword ciphertext ctwCalculating B'w＝e(tw，C1+C′1)，α′w＝KDF(B′w，plen)，
Figure FDA0003268617360000031
If C3＝C′3And if so, outputting 1 by the algorithm to indicate that the keyword ciphertext and the trapdoor are successfully matched, and otherwise, outputting 0.
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