CN116074013A - Public key searchable encryption method for resisting back door attack - Google Patents
Public key searchable encryption method for resisting back door attack Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 39
- 230000002441 reversible effect Effects 0.000 claims abstract description 32
- 238000012795 verification Methods 0.000 claims description 17
- 238000012360 testing method Methods 0.000 claims description 13
- 125000004122 cyclic group Chemical group 0.000 claims description 5
- 238000004364 calculation method Methods 0.000 claims description 4
- 230000006978 adaptation Effects 0.000 description 2
- 238000013459 approach Methods 0.000 description 2
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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
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
- H04L9/3255—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using group based signatures, e.g. ring or threshold signatures
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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
- H04L63/02—Network architectures or network communication protocols for network security for separating internal from external traffic, e.g. firewalls
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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
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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
- H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters
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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
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
- H04L9/3257—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using blind signatures
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- Computer Security & Cryptography (AREA)
- Computer Networks & Wireless Communication (AREA)
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- Computing Systems (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- General Engineering & Computer Science (AREA)
- Data Exchanges In Wide-Area Networks (AREA)
Abstract
The invention provides a public key searchable encryption method for resisting back door attacks, which is used for effectively resisting the back door attacks by subverting two latent channels in the realization by introducing a public key searchable encryption method assisted by a password reverse firewall removal server. Firstly, when generating a server derived keyword, the password reverse firewall processes messages sent and received by a user computer, and confidentiality of the keyword is ensured while protocol functions and security are maintained. And secondly, the password reverse firewall and the user execute a cooperative random number generation protocol to ensure that random numbers used by the encryption algorithm follow the random number generation algorithm specification, so that a latent channel in the subversion realization of the encryption algorithm is invalid, and the plaintext information is prevented from being revealed. In addition, the invention uses a plurality of key servers to assist the user in generating the server derived keywords, and can avoid the problem of single-point failure while resisting the guessing attack of the offline keywords.
Description
Technical Field
The invention belongs to the technical field of information security, and particularly relates to a public key searchable encryption method for resisting back door attacks.
Background
The cloud storage service enables users to outsource data to a cloud server and efficiently retrieve target data using keywords. In real life, because data may be sensitive, users often need to encrypt the data before outsourcing to protect personal privacy. However, the conventional encryption method may prevent the keyword search function in the cloud storage service from operating normally. In order to ensure confidentiality of data while maintaining a keyword search function, a public key searchable encryption PEKS has been developed. In PEKS, the sender encrypts data and keywords using the public key of the receiver and outsources the ciphertext to the cloud server. To retrieve the target data, the recipient uses the private key to generate a trapdoor corresponding to the particular key, and the cloud server performs the data retrieval by testing whether the trapdoor matches the server derived key ciphertext (referred to as PEKS ciphertext). However, PEKS is vulnerable to offline keyword guessing attacks: given a trapdoor, an attacker (e.g., a malicious cloud server) may exhaust the key space, generate PEKS ciphertext using the recipient's public key, and identify ciphertext that matches the trapdoor. In this way, the adversary may reveal keywords contained in trapdoors, thereby violating user privacy.
To combat off-line keyword guess attacks, a method called Server-assisted PEKS (Server-assisted PEKS) is proposed. In this method, the key to be encrypted is derived from a key server based on the original key. To obtain such server-derived keywords without revealing any information of the original keywords, the key server and the user together perform a blind signature protocol. More specifically, the user blinds the key using a random number and sends the blinded value to a key server, which signs the blinded value. The user may blinde the signature to obtain the server derived key. Because the key Server is introduced to enable an attacker to generate the PEKS ciphertext offline, the Server-aided PEKS can effectively resist the offline keyword guessing attack. Although Server-assisted PEKS has many benefits, the security of this approach relies on the reliability of the key Server, with a single point of failure problem. Once the key server is breached by or colluded with the adversary, the method will be immediately compromised by an offline key guessing attack. To address this problem, the generation of server derived keys may be distributed to multiple key servers using a threshold blind signature protocol. In such Server-assisted PEKS, each key Server has a share of the signature private key, and less than a threshold number of key servers are breached by or colluded with adversaries without compromising the security of the method.
In order to access the secure cloud storage services provided by the Server-enabled PEKS, users need to use a software system with the method implemented correctly. However, this faces a great challenge in the real world. An adversary (e.g., a malicious manufacturer) may be privately embedded in the implementation of the back door to the method to break the security of the method. An adversary with a back door can obtain secret information from the output of such a subversion, which is imperceptible and undetectable to the user. Such back door attacks (also known as subversion attacks) are extremely destructive. As disclosed by the snooker event, the national security agency has launched the attack for many years to illegally collect a large number of confidential messages from microsoft, ***, apple, yahoo, etc. companies to monitor personal information of citizens.
Subversion attacks against randomization algorithms (such as encryption algorithms and blind signatures) have been proposed since the snoden event. The core idea of the attack is to introduce a latent channel into the subversion implementation of the randomization algorithm: the subversion implementation may carefully pick the random number to produce a biased output (e.g., PEKS ciphertext or blinded value) to implicitly reveal the secret information. Since Server-aided PEKS contains both encryption algorithms and blind signature randomization algorithms, this approach is inherently subject to this potential threat, where subversion implementations of encryption algorithms may reveal plaintext information and subversion implementations of blind signatures may reveal keyword information. In order to remove the latent channel in the randomization algorithm to resist back door attacks, the invention introduces a cryptographic reverse firewall in the Server-aided PEKS. A cryptographic reverse firewall is deployed between the user's computer and the outside world, which participates in both parts of the Server-secured PEKS to provide security protection. First, when the user and the key server execute the blind signature protocol generation server to derive the key, the cryptographic reverse firewall modifies the messages received and sent by the user computer, preventing adversaries from obtaining any key related information while preserving the protocol function and security. Second, it and the user computer provide a random number for the encryption algorithm by executing a cooperative random number generation protocol. The protocol can ensure that the password reverse firewall cannot obtain any information of the random number, and the generated random number accords with the specification of a random number generation algorithm. The integration of the collaborative random number generation protocol into the Server-proposed PEKS can effectively remove the latent channel in the subversion implementation of the encryption algorithm, and prevent the leakage of plaintext information. In addition, the invention uses a plurality of key servers to assist the user in generating the server derived keywords, and can avoid the problem of single-point failure while resisting the guessing attack of the offline keywords.
Disclosure of Invention
The problem to be solved by the invention is how to prevent adversaries, such as malicious manufacturers, from obtaining secret information from subversion implementations of server-assisted public-key searchable encryption methods.
The invention adopts a technical method for solving the problems, namely, a public key searchable encryption method for resisting back door attacks, which is characterized in that a password reverse firewall is utilized to remove a latent channel in subversion realization of the server-assisted public key searchable encryption method so as to resist back door attacks; the method specifically comprises the following steps:
initializing: initializing a system according to the security parameters, and determining common parameters of the system; the receiver generates a public-private key; a plurality of key servers collectively generating master secrets shared in a threshold manner;
generating a server derived keyword:
1) The user blindly sends the keywords to the password reverse firewall; the user is a sender or a receiver;
2) The password reverse firewall re-randomizes the blinded keywords and sends the blinded keywords to each key server;
3) The key server signs the re-randomized blind keywords by using own master secret sharing and returns the re-randomized blind keywords to the password reverse firewall;
4) The password reverse firewall processes the received signature to obtain a signature of the key server on the blinded keyword, and sends the signature to the user;
5) The user verifies the correctness of each signature, if the signatures with the number larger than the threshold value pass the verification, the signature of the key server on the key word is obtained by the calculation of the verified signatures, and the correctness of the signature is verified; if the key word is correct, calculating a server derived key word, otherwise, terminating operation;
PEKS ciphertext generation:
1) The sender and the password reverse firewall execute a cooperative random number generation protocol to generate a random number;
2) The sender obtains a PEKS ciphertext by utilizing the generated random number and a derivative keyword of a public key encryption server of the receiver, and sends the ciphertext to a password reverse firewall;
3) The password reverse firewall verifies the legitimacy of the PEKS ciphertext; if the verification is passed, forwarding the PEKS ciphertext to the cloud server, otherwise, terminating the operation;
trapdoor generation:
the receiver calculates trapdoors corresponding to the server derived keywords and sends the trapdoors to the cloud server;
the testing steps are as follows:
the cloud server verifies whether the PEKS ciphertext is matched with a given trapdoor, if so, the PEKS ciphertext passes the test, and if not, the test fails.
The invention provides a public key searchable encryption method for resisting back door attacks, which removes a server-assisted public key searchable encryption method by introducing a password reverse firewall to subvert a latent channel in realization, thereby resisting the back door attacks; when a user generates a server derived keyword, the password reverse firewall processes messages sent and received by a user computer, and ensures confidentiality of the keyword while maintaining protocol functions and safety; in addition, the password reverse firewall and the user execute a cooperative random number generation protocol to ensure that random numbers used by the encryption algorithm follow the random number generation algorithm specification, so that a latent channel in the subversion realization of the encryption algorithm is invalid, and the plaintext information is effectively prevented from being leaked; the plurality of key servers assist the user in generating server derived keywords, and can avoid single point failure problems while resisting off-line keyword guessing attacks.
The beneficial effects of the invention are as follows:
(1) The public key searchable encryption method for resisting the back door attack is provided based on the password reverse firewall, and the server-assisted public key searchable encryption method can be effectively removed to subvert the latent channel in the realization, so that the back door attack is resisted;
(2) The key servers are used for assisting the user in generating server derived keywords, and the single-point fault problem can be avoided while the offline keyword guessing attack is resisted.
Detailed Description
Initialization step (one)
Determining a set of system common parameters from security parameters
Where q is a prime number, G is an addition cyclic group of order q, P is a generator of G, G T Is a cyclic group of order q, e: G x G → G T Is a bilinear map, Z q Is an integer remainder class ring of modulo q, +.>
Multiplication cycle group of reversible integer when modulo q,>
is a secure hash function, F is a pseudo-random function, t (0<t.ltoreq.n) is a threshold in the threshold secret sharing method, n is the number of key servers;
receiver(s)
Randomly select->
As private key and calculates the corresponding public key +.>
Key server
Generating a master secret shared in a threshold manner as follows>
1) Ith key server
Random selection->
And Z q Polynomial f of degree t-1 above i (x)＝a i,0 +a i,1 x+…+a i,t-1 x t-1 ；
2)
Calculate and send a i,k P to other key servers, where k=0, …, t-1; />
Polynomial value f through secure channel i (j) Send to key server->
Where j=1, …, n, j+.i;
3)
verify equation->
If true, reject f if verification fails j (i)；
4)
Calculate master secret +.>
Is->
And master secret->
Is to share the corresponding public key Q i ＝s i P；
5)
Calculate->
Corresponding public key->
Secret storage s i Save { Q, Q 1 ,…,Q n And delete other values.
(II) Server derived keyword Generation step
1) User' s
Selecting random number +.>
Calculate the blinded value w=rh (W) of the key W and send it to the cryptographic reverse firewall +.>
2)
Selecting random number +.>
Re-randomizing the blind keyword W to obtain a re-randomized blind keyword W '=αw, and transmitting W' to the key server +.>
3)
(i=1, …, n) signing W ' to obtain the signature σ ' of the re-randomized blinded key ' i ＝s i W ', send sigma' i Give->
4)
Calculating signature sigma i ＝α -1 σ i And sends it to +.>
Wherein alpha is -1 Is alpha is +>
The inverse of (a) is used;
5)
receipt of sigma i After that, verify equation e (σ i ,P)＝e(W,Q i ) Check if it is true i Accuracy of (3); if t sigma i By verification we express it as +.>
Calculate intermediate value +.>
Signature
If sigma w Satisfy equation e (σ w P) =e (H (w), Q), then +.>
Believes sigma w Is the correct signature generated by the key server, otherwise the operation is terminated;
6)
computing server derived keywords sdk w ＝F(h(σ w ),w)。
(III) PEKS ciphertext generation step
1) Sender(s)
Firewall reverse to password->
Executing a cooperative random number generation protocol to generate a random number η:
①
select random number +.>
Calculating a pair random number a 1 Commitment c=h' (a) 1 B) and sends c to +.>
②
Select random number +.>
Calculating element d=a in G 2 P and send to->
③
Transmitting (a) 1 B) giving->
To open the commitment c and calculate the verification value v=d+a 1 P；
④
Validating equation h' (a 1 Whether b) =c is true, if so, +.>
Accept a 1 Calculate and output a random number η=a 1 +a 2 Otherwise, the verification fails to terminate the operation;
2)
calculate the intermediate value τ=e (H 1 (sdk w ),/>
And server derived keywords sdk w PEKS ciphertext c of (c) w ＝(ηP,H 2 (τ)) and then sends c w Give->
3)
Received ciphertext c w After= (a, B), checking if a is equal to V, if yes, verifying successfully and forwarding c w And giving the cloud server, otherwise, stopping running after verification failure.
(IV) trapdoor generation step
Given a server derived key sdk w′ The receiver
Calculation sdk w′ Corresponding trapdoor
And sends it to the cloud server.
(fifth) test step
Given a PEKS ciphertext c w = (a, B) and a trapdoor
Cloud server verification equation
Whether or not to establish; if the equation is satisfied, the test is passed, otherwise the test fails.
In real life, server-assisted public key searchable encryption methods are threatened by back door attacks. An attacker may surreptitiously embed a backdoor into the implementation of the method to establish a latent channel and reveal the user's secret information through the latent channel in an imperceptible manner. In order to remove the latent channel to resist the back door attack, the invention provides a public key searchable encryption method for resisting the back door attack and describes the method in detail. The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to facilitate an understanding of the method of the present invention and its core ideas. It should be noted that it will be apparent to those skilled in the art that various modifications and adaptations of the invention can be made without departing from the principles of the invention and these modifications and adaptations are intended to be within the scope of the invention as defined in the following claims.
Claims (6)
1. A public key searchable encryption method for resisting back door attack is characterized by comprising the following steps:
initializing: initializing a system according to the security parameters, and determining common parameters of the system; the receiver generates a public-private key; a plurality of key servers collectively generating master secrets shared in a threshold manner;
generating a server derived keyword:
1) The user blindly sends the keywords to the password reverse firewall; the user is a sender or a receiver;
2) The password reverse firewall re-randomizes the blinded keywords and sends the blinded keywords to each key server;
3) The key server signs the re-randomized blind keywords by using own master secret sharing and returns the re-randomized blind keywords to the password reverse firewall;
4) The password reverse firewall processes the received signature to obtain a signature of the key server on the blinded keyword, and sends the signature to the user;
5) The user verifies the correctness of each signature, if the signatures with the number larger than the threshold value pass the verification, the signature of the key server on the key words is obtained through the calculation of the signatures passing the verification, and the correctness is verified;
if the key word is correct, calculating a server derived key word, otherwise, terminating operation;
generating a server derived keyword ciphertext:
1) The sender and the password reverse firewall execute a cooperative random number generation protocol to generate a random number;
2) The sender encrypts a server derived keyword by using the generated random number and the public key of the receiver to obtain a server derived keyword ciphertext, and sends the ciphertext to the password reverse firewall;
3) The password reverse firewall verifies the legality of the keyword ciphertext derived by the server; if the verification is passed, the server derives the keyword ciphertext to the cloud server, otherwise, the operation is terminated;
trapdoor generation:
the receiver calculates trapdoors corresponding to the server derived keywords and sends the trapdoors to the cloud server;
the testing steps are as follows:
the cloud server verifies whether the derived keyword ciphertext of the server is matched with a given trapdoor, if so, the cloud server passes the test, and if not, the test fails.
2. The method of claim 1, wherein the initializing step is specifically:
determining a set of system common parameters from security parameters
Where q is a prime number, G is an addition cyclic group of order q, P is a generator of G, G T Is a cyclic group of order q, e: G x G → G T Is a bilinear map, Z q Is an integer remainder class ring of modulo q, +.>
Is a multiplication cyclic group of reversible integers when the modulus is q, and h is G-Z q ,
H,H 1 :{0,1} * →G,/>
Is a secure hash function, F is a pseudo-random function, t is a threshold in a threshold secret sharing method, n is the number of key servers, 0<t≤n；
Receiver(s)
Randomly select->
As private key and calculates the corresponding public key +.>
Key server
Generating a master secret shared in a threshold manner as follows>
1) Ith key server
Random selection->
And Z q Polynomial of degree t-1 above
f i (x)＝a i,0 +a i,1 x+…+a i,t-1 x t-1 ，i＝1,…,n；
2)
Calculate and send a i,k P to other key servers, where k=0, …, t-1; />
Polynomial value f through secure channel i (j) Send to key server->
Where j=1, …, n, j+.i; />
3)
Verify equation->
If true, reject f if verification fails j (i)；
4)
Calculate master secret +.>
Is->
And master secret->
Is to share the corresponding public key Q i ＝s i P；
5)
Calculate->
Corresponding public key->
Secret storage s i Save { Q, Q 1 ,…,Q n And delete other values.
3. The method of claim 2, wherein the server derived key generating step is specifically as follows:
1) User' s
Selecting random number +.>
Calculate the blinded value w=rh (W) of the key W and send it to the cryptographic reverse firewall +.>
2)
Selecting random number +.>
Re-randomizing blind keyword W to obtain re-followingThe motorized blind keyword W '=αw and sends W' to the key server +.>
3)
Signing the W ' to obtain signature sigma ' of the blind keyword after re-randomization ' i ＝s i W ', send sigma' i Give->
4)
Calculating signature sigma i ＝α -1 σ′ i And sends it to +.>
Wherein alpha is -1 Is alpha is +>
The inverse of (a) is used;
5)
receipt of sigma i After that, verify equation e (σ i ,P)＝e(W,Q i ) Check if it is true i Accuracy of (3);
if t sigma i By verification we represent it as
Calculate intermediate value +.>
And signature->
If sigma w Satisfy equation e (σ w P) =e (H (w), Q), then +.>
Believes sigma w Is the correct signature generated by the key server, otherwise the operation is terminated;
6)
computing server derived keywords sdk w ＝F(h(σ w ),w)。
4. The method of claim 3, wherein the server-derived keyword ciphertext generating step is specifically as follows:
1) Sender(s)
Firewall reverse to password->
Executing a cooperative random number generation protocol to generate a random number η:
①
selecting a random number a 1 ,/>
Calculating a pair random number a 1 Commitment c=h' (a) 1 B) and sends c to +.>
②
Select random number +.>
Calculating element d=a in G 2 P and send to->
③
Transmitting (a) 1 B) giving->
To open the commitment c and calculate the verification value v=d+a 1 P；
④
Validating equation h' (a 1 Whether b) =c is true, if so, +.>
Accept a 1 Calculate and output a random number η=a 1 +a 2 Otherwise, the verification fails to terminate the operation;
2)
calculate intermediate value +.>
And server derived keywords sdk w Server derived key ciphertext c w ＝(ηP,H 2 (τ)) and then sends c w Give->
3)
Received ciphertext c w After= (a, B), checking if a is equal to V, if yes, verifying successfully and forwarding c w And giving the cloud server, otherwise, stopping running after verification failure.
5. The method of claim 4, wherein the trapdoor generating step is specifically as follows:
given a server derived key sdk w′ The receiver
Calculation sdk w′ Corresponding trapdoor
And sends it to the cloud server.
6. The method of claim 5, wherein the testing step is specifically as follows:
given a server derived key ciphertext c w = (a, B) and a trapdoor
Cloud server verification equation
Whether or not to establish; if the equation is satisfied, the test is passed, otherwise the test fails. />
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