On-lattice aggregation proxy signature method and system

Abstract

The invention provides an on-lattice aggregation proxy signature method and system. The method comprises the following steps: S1, generating a key pair of an original signer and a proxy signer through a key generation algorithm; s2, the original signature side uses the key pair of the original signer to generate a proxy key pair for the proxy signer; s3, the proxy signature side uses the public key of the original signer to verify the validity of the proxy key pair; s4, the proxy signature side uses the key pair of the proxy signer and the proxy key pair to generate a proxy signature; s5, the verification side uses the public key of the proxy signer and the proxy public key to verify the validity of the proxy signature; s6, performing aggregation processing on effective proxy signatures generated by all proxy signers of the same original signer; and S7, the verification side uses the public key of the proxy signer and the proxy public key to verify the validity of the aggregation signature.

Description

Technical Field

[0001] The present invention relates to the technical field of proxy signatures, and in particular to a grid-based aggregate proxy signature method and system. Background Art

[0002] Proxy signature allows the original signer to authorize his or her signature authority to the proxy signer. In the proxy signature scheme, the proxy signer can generate a valid proxy signature on behalf of the original signer. After receiving the proxy signature, the verifier can not only verify the validity of the proxy signature, but also verify the authorization of the original signer.

[0003] With the rapid development of quantum computer technology, the emergence and practical application of quantum computers are becoming increasingly possible, which seriously threatens the security of traditional cryptographic schemes based on the discrete logarithm difficulty assumption. Specifically, running Shor's algorithm on a quantum computer can efficiently solve discrete logarithm problems in polynomial time, thereby cracking these schemes. In order to meet this challenge, post-quantum cryptographic algorithms have emerged. Among them, lattice cryptography based on difficult problems on lattices (such as learning with errors (LWE) type problems, etc.) has occupied a dominant position in the post-quantum cryptographic algorithm system due to its excellent computational efficiency, provable anti-quantum security and other advantages.

[0004] Aggregate signature is an important cryptographic tool proposed by Boneh et al. It allows n different signatures on n different messages to be efficiently aggregated into a single signature. This feature not only significantly improves the verification speed, but also significantly reduces the consumption of storage space and bandwidth. Summary of the invention

[0005] In view of the defects in the prior art, the object of the present invention is to provide a grid aggregation proxy signature method and system.

[0006] A grid aggregation proxy signature method provided by the present invention includes: Step S1: Generate a key pair of the original signer and the proxy signer through a key generation algorithm; Step S2: The original signing side uses the key pair of the original signer to generate a proxy key pair for the proxy signer; Step S3: The proxy signing side verifies the validity of the proxy key pair using the public key of the original signer; Step S4: The proxy signature side generates a proxy signature using the proxy signer's key pair and the proxy key; Step S5: The verification side verifies the validity of the proxy signature using the proxy signer's public key and the proxy public key; Step S6: Aggregate the valid proxy signatures generated by all proxy signers of the same original signer; Step S7: The verification side uses the public key of the proxy signer and the proxy public key to verify the validity of the aggregate signature.

[0007] Preferably, the step S1 comprises: Step S1.1: Randomly select three matrices , and ; Wherein, Z represents an integer set; q represents a prime number; n represents a positive integer, m represents a positive integer, k represents a positive integer, and d represents a positive integer; Step S1.2: Calculation , , Step S1.3: Output the original signer's key pair and the proxy signer's key pair .

[0008] Preferably, step S2 comprises: Step S2.1: Calculation ;in, represents a hash function, ; ; Step S2.2: Calculation , ; Step S2.3: Output the proxy key pair of the proxy signer .

[0009] Preferably, step S3 comprises: Step S3.1: Calculation ;in, represents a hash function, ; ; Step S3.2: Verify the equation , if the equality holds, the verification is valid; otherwise, it is invalid.

[0010] Preferably, the step S4 comprises: Step S4.1: Select two vectors ,in, The parameter is The discrete normal distribution of Step S4.2: Calculation , ; Step S4.3: Calculation ;in, is a hash function, ; Message space ; Step S4.4: Calculation ;in, is a hash function, ; Step S4.5: Calculation , ; Step S4.6: The probability output ,by( The probability output ,in, ,in is the cardinality of natural logarithms; Step S4.7: Output signature .

[0011] Preferably, the step S5 comprises: Step S5.1: Calculation ;in, is a hash function, ; Message space ; Step S5.2: Calculation ;in, is a hash function, ; Step S5.3: Verify the equation , , and Is it true? Where s represents a real number. If it is true, the verification is valid; otherwise, it is invalid.

[0012] Preferably, step S6 comprises: Step S6.1: Calculation , ; Step S6.2: Calculation , ; Step S6.3: Output aggregate signature .

[0013] Preferably, step S7 comprises: Step S7.1: Calculation ,in, is a hash function, ; Message space ; Step S7.2: Calculation ,in, is a hash function, ; Step S7.3: Calculation , ; Step S7.4: Verify the equation , , and Is it true? If true, the verification is valid; otherwise, it is invalid.

[0014] A grid aggregation proxy signature system provided by the present invention includes: Module M1: Generates the key pair of the original signer and the proxy signer through the key generation algorithm; Module M2: The original signing side uses the original signer's key pair to generate a proxy key pair for the proxy signer; Module M3: The proxy signature side verifies the validity of the proxy key pair using the original signer’s public key; Module M4: The proxy signature side generates a proxy signature using the proxy signer's key pair and the proxy key; Module M5: The verification side verifies the validity of the proxy signature using the proxy signer's public key and the proxy public key; Module M6: Aggregate the valid proxy signatures generated by all proxy signers of the same original signer; Module M7: The verification side uses the public key of the proxy signer and the proxy public key to verify the validity of the aggregate signature.

[0015] Preferably, the module M1 comprises: Module M1.1: Randomly select three matrices , and ; Wherein, Z represents an integer set; q represents a prime number; n represents a positive integer, m represents a positive integer, k represents a positive integer, and d represents a positive integer; Module M1.2: Computation , , Module M1.3: Output the original signer's key pair and the proxy signer's key pair ; The module M2 comprises: Module M2.1: Computation ;in, represents a hash function, ; ; Module M2.2: Computing , ; Module M2.3: Output the proxy key pair of the proxy signer ; The module M3 comprises: Module M3.1: Computing ;in, represents a hash function, ; ; Module M3.2: Verifying Equations , if the equality holds, the verification is valid; otherwise, it is invalid; The module M4 comprises: Module M4.1: Selecting two vectors ,in, The parameter is The discrete normal distribution of Module M4.2: Computing , ; Module M4.3: Computing ;in, is a hash function, ; Message space ; Module M4.4: Computing ;in, is a hash function, ; Module M4.5: Computing , ; Module M4.6: ( The probability output ,by( The probability output ,in, ,in is the cardinality of natural logarithms; Module M4.7: Output Signature ; The module M5 comprises: Module M5.1: Computation ;in, is a hash function, ; Message space ; Module M5.2: Computing ;in, is a hash function, ; Module M5.3: Verifying Equations , , and Is it true? Where s represents a real number. If true, the verification is valid. Otherwise, it is invalid. The module M6 comprises: Module M6.1: Computing , ; Module M6.2: Computing , ; Module M6.3: Output aggregate signature ; The module M7 comprises: Module M7.1: Calculation ,in, is a hash function, ; Message space ; Module M7.2: Computing ,in, is a hash function, ; Module M7.3: Computing , ; Module M7.4: Verifying Equations , , and Is it true? If true, the verification is valid; otherwise, it is invalid.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention uses a trap-free technology on a lattice to construct a proxy signature method. Compared with the proxy signature scheme constructed based on the bonsai tree principle and the fixed-dimensional lattice-based delegation technology, it significantly reduces the size of the proxy private key and the proxy signature, and provides potential post-quantum security features for the proxy signature; 2. The present invention adds a signature aggregation function to the proxy signature, aggregating n different proxy signatures generated by all proxy signers of the same original signer into one signature; compared with n independent proxy signatures, the signature length is effectively reduced and the speed of signature verification is improved; during transmission and storage, only the message and the corresponding aggregate signature need to be transmitted and stored, which effectively reduces the storage space and communication overhead of the signature.

[0017] 3. The present invention realizes the proxy of signature authority and the aggregation of proxy signatures based on the trapdoor-free technology and aggregate signature technology on the lattice. Firstly, the trapdoor-free technology on the lattice provides potential post-quantum security for the proxy signature. Secondly, combined with the aggregate signature technology, it not only improves the speed of signature verification, but also reduces the storage space and communication overhead of the signature. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings: Figure 1 This is a flow chart of the aggregation proxy signature method on the grid. DETAILED DESCRIPTION

[0019] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0020] Example 1 According to a lattice-based aggregated proxy signature method and system provided by the present invention, a trapdoor-free technology based on a lattice is adopted. The trapdoor-free technology on the lattice outputs candidate signatures with a certain probability, and makes the distribution of the output signature independent of the signature private key of the signer, effectively reducing the size of the proxy private key and the proxy signature, while providing potential post-quantum security; the aggregated signature technology is adopted to aggregate n different proxy signatures generated by all proxy signers of the same original signer. Specifically, for the proxy signatures of n different messages generated by all proxy signers of the same original signer, anyone can aggregate these individual proxy signatures into a single signature. When transmitting and storing, only the message and the corresponding aggregated signature need to be transmitted and stored, which effectively reduces the storage space and communication overhead of the signature. In the verification stage, the verifier only needs to verify the aggregated proxy signature, thereby improving the speed of signature verification.

[0021] like Figure 1 As shown, the grid aggregation proxy signature method includes: Step 1: Initialize the algorithm : Generate the parameters of the grid aggregation proxy signature system. The algorithm steps are as follows: Select a security parameter .make , prime numbers, is a positive integer, ,parameter , ,in is the cardinality of natural logarithms.

[0022] Choose three hash functions: , , , where the message space .

[0023] Output system parameters .

[0024] Step 2: Key generation algorithm : Run the key generation algorithm Generate the key pair of the original signer and the proxy signer. The algorithm steps are as follows: Step 2.1: Randomly select three matrices , and ; Step 2.2: Calculation , ; Step 2.3: Output the original signer's key pair and the proxy signer's key pair .

[0025] Step 3: Proxy key generation algorithm : The original signer uses the proxy signer's And your own key pair Generate a proxy key pair for the proxy signer. The algorithm steps are as follows: Step 3.1: Calculation , Step 3.2: Calculation , , Step 3.3: Output the proxy signer's proxy key pair .

[0026] Step 4: Proxy key verification algorithm : The proxy signer uses the original signer's public key Authentication Agent Key Pair Is it valid? If it is valid, it means that the proxy signer accepts the proxy key pair, otherwise it is rejected. The algorithm steps are as follows: Step 4.1: Calculation , Step 4.2: Verify the equation , Step 4.3: If the equation holds, The algorithm outputs 1 if yes, otherwise it outputs 0.

[0027] Step 5: Proxy signature algorithm : Given a message , the proxy signer uses the proxy signer's key pair and the proxy key Generate a proxy signature. The algorithm steps are as follows: Step 5.1: Select two vectors ,in The parameter is The discrete normal distribution of Step 5.2: Calculation , ; Step 5.3: Calculation ; Step 5.4: Calculation ; Step 5.5: Calculation , ; Step 5.6: The probability output ,by( The probability output ; Step 5.7: Output signature .

[0028] Step 6: Proxy signature verification algorithm : Given a message ,sign , the public key of the proxy signer and the proxy public key Verify the validity of the proxy signature. The algorithm steps are as follows: Step 6.1: Calculation , Step 6.2: Calculation , Step 6.3: Verify the Equation , , and Is it true? If true, the Verify algorithm outputs 1; otherwise, it outputs 0.

[0029] Step 7: Aggregation Algorithm : Multiple (message, signature, (proxy signer's public key, proxy signer's proxy public key)) tuples generated by the proxy signer given the same original signer The algorithm steps are as follows: Step 7.1: Calculation , , Step 7.2: Calculation , , Step 7.3: Output aggregate signature .

[0030] Step 8: Aggregation Verification Algorithm : Given multiple (message, (proxy signer's public key, proxy signer's proxy public key)) tuples , an aggregate signature The algorithm steps are as follows: Step 8.1: Calculation , Step 8.2: Calculation , Step 8.3: Calculation , , Step 8.4: Verify the Equation , , and Is it true? If true, The algorithm outputs 1; otherwise, it outputs 0.

[0031] The present invention also provides a grid-based aggregate proxy signature system, which can be implemented by executing the process steps of the grid-based aggregate proxy signature method, that is, those skilled in the art can understand the grid-based aggregate proxy signature method as a preferred implementation of the grid-based aggregate proxy signature system.

[0032] Those skilled in the art know that, in addition to implementing the system, device and its various modules provided by the present invention in a purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers and embedded microcontrollers by logically programming the method steps. Therefore, the system, device and its various modules provided by the present invention can be considered as a hardware component, and the modules included therein for implementing various programs can also be considered as structures within the hardware component; the modules for implementing various functions can also be considered as both software programs for implementing the method and structures within the hardware component.

[0033] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A grid aggregation proxy signature method, characterized in that: include: Step S1: Generate a key pair of the original signer and the proxy signer through a key generation algorithm; Step S2: The original signing side uses the key pair of the original signer to generate a proxy key pair for the proxy signer; Step S3: The proxy signing side verifies the validity of the proxy key pair using the public key of the original signer; Step S4: The proxy signature side generates a proxy signature using the proxy signer's key pair and the proxy key; Step S5: The verification side verifies the validity of the proxy signature using the proxy signer's public key and the proxy public key; Step S6: Aggregate the valid proxy signatures generated by all proxy signers of the same original signer; Step S7: The verification side uses the public key of the proxy signer and the proxy public key to verify the validity of the aggregate signature.

2. The grid aggregation proxy signature method according to claim 1 is characterized in that: The step S1 comprises: Step S1.1: Randomly select three matrices , and ; Wherein, Z represents an integer set; q represents a prime number; n represents a positive integer, m represents a positive integer, k represents a positive integer, and d represents a positive integer; Step S1.2: Calculation , , Step S1.3: Output the original signer's key pair and the proxy signer's key pair .

3. The grid aggregation proxy signature method according to claim 2 is characterized in that: The step S2 comprises: Step S2.1: Calculation ;in, represents a hash function, ; ; Step S2.2: Calculation , ; Step S2.3: Output the proxy key pair of the proxy signer .

4. The grid aggregation proxy signature method according to claim 2 is characterized in that: The step S3 comprises: Step S3.1: Calculation ;in, represents a hash function, ; ; Step S3.2: Verify the equation , if the equality holds, the verification is valid; otherwise, it is invalid.

5. The grid aggregation proxy signature method according to claim 2 is characterized in that: The step S4 comprises: Step S4.1: Select two vectors ,in, The parameter is The discrete normal distribution of Step S4.2: Calculation , ; Step S4.3: Calculation ;in, is a hash function, ; Message space ; Step S4.4: Calculation ;in, is a hash function, ; Step S4.5: Calculation , ; Step S4.6: The probability output ,by( The probability output ,in, ,in is the cardinality of natural logarithms; Step S4.7: Output signature .

6. The grid aggregation proxy signature method according to claim 2 is characterized in that: The step S5 comprises: Step S5.1: Calculation ;in, is a hash function, ; Message space ; Step S5.2: Calculation ;in, is a hash function, ; Step S5.3: Verify the equation , , and Is it true? Where s represents a real number. If it is true, the verification is valid; otherwise, it is invalid.

7. The grid aggregation proxy signature method according to claim 5 is characterized in that: The step S6 comprises: Step S6.1: Calculation , ; Step S6.2: Calculation , ; Step S6.3: Output aggregate signature .

8. The grid aggregation proxy signature method according to claim 1 is characterized in that: The step S7 comprises: Step S7.1: Calculation ,in, is a hash function, ; Message space ; Step S7.2: Calculation ,in, is a hash function, ; Step S7.3: Calculation , ; Step S7.4: Verify the equation , , and Is it true? If true, the verification is valid; otherwise, it is invalid.

9. A grid-based aggregate proxy signature system, characterized in that: include: Module M1: Generates the key pair of the original signer and the proxy signer through the key generation algorithm; Module M2: The original signing side uses the original signer's key pair to generate a proxy key pair for the proxy signer; Module M3: The proxy signature side verifies the validity of the proxy key pair using the original signer’s public key; Module M4: The proxy signature side generates a proxy signature using the proxy signer's key pair and the proxy key; Module M5: The verification side verifies the validity of the proxy signature using the proxy signer's public key and the proxy public key; Module M6: Aggregate the valid proxy signatures generated by all proxy signers of the same original signer; Module M7: The verification side uses the public key of the proxy signer and the proxy public key to verify the validity of the aggregate signature.

10. The grid aggregation proxy signature system according to claim 9 is characterized in that: The module M1 comprises: Module M1.1: Randomly select three matrices , and ; Wherein, Z represents an integer set; q represents a prime number; n represents a positive integer, m represents a positive integer, k represents a positive integer, and d represents a positive integer; Module M1.2: Computation , , Module M1.3: Output the original signer's key pair and the proxy signer's key pair ; The module M2 comprises: Module M2.1: Computation ;in, represents a hash function, ; ; Module M2.2: Computing , ; Module M2.3: Output the proxy key pair of the proxy signer ; The module M3 comprises: Module M3.1: Computing ;in, represents a hash function, ; ; Module M3.2: Verifying Equations , if the equality holds, the verification is valid; otherwise, it is invalid; The module M4 comprises: Module M4.1: Selecting two vectors ,in, The parameter is The discrete normal distribution of Module M4.2: Computing , ; Module M4.3: Computing ;in, is a hash function, ; Message space ; Module M4.4: Computing ;in, is a hash function, ; Module M4.5: Computing , ; Module M4.6: ( The probability output ,by( The probability output ,in, ,in is the cardinality of natural logarithms; Module M4.7: Output Signature ; The module M5 comprises: Module M5.1: Computation ;in, is a hash function, ; Message space ; Module M5.2: Computing ;in, is a hash function, ; Module M5.3: Verifying Equations , , and Is it true? Where s represents a real number. If true, the verification is valid. Otherwise, it is invalid. The module M6 comprises: Module M6.1: Computing , ; Module M6.2: Computing , ; Module M6.3: Output aggregate signature ; The module M7 comprises: Module M7.1: Calculation ,in, is a hash function, ; Message space ; Module M7.2: Computing ,in, is a hash function, ; Module M7.3: Computing , ; Module M7.4: Verifying Equations , , and Is it true? If true, the verification is valid; otherwise, it is invalid.

Images