CN114844908B - Modular index outsourcing fair payment method based on block chain - Google Patents

Modular index outsourcing fair payment method based on block chain Download PDF

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CN114844908B
CN114844908B CN202210337188.3A CN202210337188A CN114844908B CN 114844908 B CN114844908 B CN 114844908B CN 202210337188 A CN202210337188 A CN 202210337188A CN 114844908 B CN114844908 B CN 114844908B
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CN114844908A (en
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任艳丽
杨丹玲
郭筝
胡艺萌
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Zhixun Password Shanghai Testing Technology Co ltd
University of Shanghai for Science and Technology
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University of Shanghai for Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00—Network arrangements or protocols for supporting network services or applications
    • H04L67/01—Protocols
    • H04L67/10—Protocols in which an application is distributed across nodes in the network
    • H04L67/1097—Protocols in which an application is distributed across nodes in the network for distributed storage of data in networks, e.g. transport arrangements for network file system [NFS], storage area networks [SAN] or network attached storage [NAS]
    • 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
    • H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
    • 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
    • H04L63/20—Network architectures or network communication protocols for network security for managing network security; network security policies in general
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
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    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • 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
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Abstract

The invention relates to a modular exponentiation fair payment method based on a blockchain, which comprises the following steps: firstly, a user invokes a subroutine to generate random data and random blinding pairs; then, the user utilizes random blinding to split the privacy data and the random data, and the data which needs to be calculated after the splitting is uploaded to the blockchain. The cloud server downloads and calculates, and submits the result to the blockchain; finally, the user downloads and verifies the result. If the result is correct, the user obtains the required outsourcing result; otherwise, the user applies for the blockchain to arbitrate so as to judge whether the server is malicious or not. If the blockchain judges that the server does have malicious behaviors, deducting deposit of the server; if the blockchain determination server calculates correctly, the protocol fails. The method can solve the problem that the local resources are limited and cannot be solved on the premise of protecting the self data privacy, and can resist the malicious behavior of the cloud server.

Description

Modular index outsourcing fair payment method based on block chain
Technical Field
The invention relates to the fields of cloud computing, privacy protection and outsourcing computing, in particular to a modular exponential outsourcing fair payment method based on a blockchain.
Background
A new calculation appears in cloud computing: and (5) outsourcing calculation. Outsourcing computing allows users with limited computing power to hand the computing to a cloud server, thereby enabling users to obtain services on demand to improve work efficiency and pay for the services used.
Cloud servers are not fully trusted, so there are many security challenges in outsourcing: it is possible for the cloud server to find some sensitive information in the user data. Thus, outsourcing computing requires ensuring the privacy of user data. In addition, cloud servers may submit erroneous results for malicious intent. Thus, outsourcing computing also ensures verifiability of the results.
In cryptographic systems, modular exponentiation is the most basic operation. For users with limited computing resources, the modular exponentiation has excessive computational complexity and excessive computational cost. Currently, the main studies for the modulo exponential outsourcing are as follows: hohenberger et al proposed a first modular exponential outsourcing scheme in 2005 that achieved a verifiable probability of 1/2. The modulo exponential outsourcing scheme proposed by Chen et al in 2012 is also based on a dual server, and the verifiable probability can reach 2/3. In 2015, ye et al improve on the basis of Chen scheme, and realize a modular exponential security outsourcing scheme with verifiable probability reaching 19/20 based on double servers. In 2017, the single server-based outsourcing scheme proposed by Ding has a verifiable probability close to 1. Under the cloud computing environment, a cloud server is not completely trusted, and collusion attack is easy to occur in a double-server system. Meanwhile, the existing modular exponentiation calculation scheme based on the single cloud server has the problems that data privacy is not achieved, the number of times of interaction between the cloud server and a user is excessive, and the probability of verification is low. Therefore, the research of the modular exponentiation scheme in the single cloud server environment is of great significance.
While outsourcing computing is becoming more popular, outsourcing unfairness occurs, preventing the development of outsourcing computing. The existing outsourcing modulus index scheme only considers whether the cloud server provides a correct outsourcing result, but does not consider the situation that whether the cloud server can obtain service fees after completing tasks in honest, and whether a user can obtain corresponding compensation under the situation that the user does not obtain a correct calculation result. Moreover, the traditional payment scheme does not realize decentralization, so that a trusted third party exists to a great extent, and the decentralization is not easy to realize in a real situation. Therefore, a payment method for achieving decentralization and ensuring fairness is necessary.
Disclosure of Invention
Aiming at the problems that user sensitive data is easy to leak, the verifiable probability is low, the payment scheme depends on a trusted third party and the like in the existing outsourcing process, the invention discloses a secure modulus outsourcing payment method under a single cloud server based on a blockchain.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a modular exponentiation payment method based on block chain, the user needs to give complex modular exponentiation calculation task to cloud server for calculation because of local resource limitation, the whole outsourcing process steps are as follows:
firstly, initializing and setting a user, namely generating random data and random blinding pairs by using a subprogram, uploading deposit and remuneration by the user, and uploading the deposit to a block chain end by a cloud server;
secondly, the user uses the first step to generate a random blinding pair to process the private data and the random data, and packages and uploads the processed data to the blockchain;
thirdly, after the cloud server downloads data from the block chain, performing modular exponentiation calculation, and uploading the result to the block chain;
step four, the user firstly verifies the result after downloading the result from the blockchain, and if the result passes the verification, a required answer is obtained; otherwise, refusing to accept the result and requiring the blockchain to carry out auxiliary verification;
and fifthly, performing auxiliary verification by using a calculation result of random data provided by a user, judging whether the cloud server is malicious or not, and punishing the malicious server.
The first step comprises two sub-steps:
1) Generating random data: user calls subprogram Rand to generate private data u a Similar random data r b ；
2) Generating a random blinding pair: first, the user invokes the subroutine RandG to generate 8 pairs of random pairs (α, g α ),(β,g β ),(ρ,g ρ ),(σ,g σ ),(γ,g γ ),(δ,g δ ),(η,g η ),(λ,g λ ) Then, define v 1 ＝g α mod p,v 2 ＝g ρ mod p,s 1 ＝g γ mod p,s 2 ＝g η mod p。
The second step is that the user locally utilizes random blinding to logically split two groups of private data and random data respectively;
for private data u a Performing a first set of logical splits: splitting for the first time: u (u) a ＝(v 1 w 1 ) a ＝g αa w 1 a Wherein w is 1 ＝u/v 1 The method comprises the steps of carrying out a first treatment on the surface of the And (3) splitting for the second time:
Figure BDA0003574810300000021
wherein c 1 ＝αa-βmod p,d 1 ＝a-k 1 l 1 mod p; then to the privacy data u a Performing a second set of logical splits: u (u) a ＝(v 2 w 2 ) a ＝g ρa w 2 a Wherein w is 2 ＝u/v 2 ；
Figure BDA0003574810300000022
Wherein c 2 ＝ρa-σmod p,d 2 ＝a-k 2 l 2 mod p；
Subsequently, for random data r b Performing a first set of logical splits, the first split r b ＝(s 1 t 1 ) b ＝g γb t 1 b Wherein t is 1 ＝r/s 1 The method comprises the steps of carrying out a first treatment on the surface of the Second time of detachment
Figure BDA0003574810300000023
Wherein e 1 ＝γb-δmod p,f 1 ＝b-m 1 n 1 mod p; and then to random data r b Performing a second set of logical splits: r is (r) b ＝(s 2 t 2 ) b ＝g ηb t 2 b Wherein t is 2 ＝r/s 2 ；
Figure BDA0003574810300000024
Wherein e 2 ＝ηb-λmod p,f 2 ＝b-m 2 n 2 mod p；
At this time, the random number pair (v 1 ,w 1 ),(v 2 ,w 2 ) Sum(s) 1 ,t 1 ),(s 2 ,t 2 ) The base number u in the private data and the base number r in the random data are subjected to blind hiding treatment respectively; random value c 1 ,d 1 ,k 1 ,l 1 ,c 2 ,d 2 ,k 2 ,l 2 And e 1 ,f 1 ,m 1 ,n 1 ,e 2 ,f 2 ,m 2 ,n 2 The indexes a and b are respectively blindly hidden; the user uploads the blinded data pair (c 1 ,g),(d 1 ,w 1 ),(k 1 ,w 1 ),(c 2 ,g),(d 2 ,w 2 ),(k 2 ,w 2 ) (e) 1 ,g),(f 1 ,t 1 ),(m 1 ,t 1 ),(e 2 ,g),(f 2 ,t 2 ),(m 2 ,t 2 ) To the blockchain.
The third step is specifically that the cloud server downloads the task and calculates the result
Figure BDA0003574810300000031
Commit to blockchain:
Figure BDA0003574810300000032
the fourth step is specifically that the user downloads the result from the blockchain and utilizes the secret value l 1 ,l 2 Judging
Figure BDA0003574810300000033
Whether or not to establish; if the equation is true, the user calculates the final answer +.>
Figure BDA0003574810300000034
Otherwise, the user judges that the cloud server is malicious and applies for the auxiliary verification of the blockchain.
The fifth step is specifically that the userUploading the result of the random data calculation to the blockchain, which uses the secret value n 1 n 2 Verification
Figure BDA0003574810300000035
Whether or not to establish; if the equation is not established, the cloud server is malicious; if the equation is true, the protocol fails; after conclusion, the blockchain forwards the deposit and the remuneration to the entitled parties to achieve fair payment.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention only relates to one cloud server, is a security model of a single server, and can effectively prevent collusion attack of a double cloud server system.
2. The invention realizes data privacy. The server can obtain the data of the user, but knows that the data can not deduce the modular exponentiation value required by the user, and the modular exponentiation base number and the exponent are blindly processed, so that the server can not obtain any privacy information in the whole outsourcing process.
3. The calculation cost of the outsourced user is far less than the cost of the user to perform the modular exponentiation calculation. The user needs to perform 4 inversions, 14+1.5lbl 1 +1.5lbl 2 The subroutine is called 9 times and the server is requested 12 times.
4. The verifiable probability is 1. The scheme realizes high verifiability of the user to the package result.
5. The modular exponentiation problem solved by the invention can be independently deployed and can be used as a solution idea of more complex problems based on the modular exponentiation problem, and a user can solve a series of problems with little calculation cost and storage space.
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Fig. 1 is a system framework of the present invention.
Detailed Description
Specific embodiments of the present invention will be further described below with reference to the accompanying drawings.
Example 1
In this embodiment, in a modular exponentiation payment method based on blockchain, a user needs to submit a complex modular exponentiation calculation task to a cloud server for calculation due to local resource limitation, and the whole outsourcing process includes the following steps:
firstly, initializing and setting a user, namely generating random data and random blinding pairs by using a subprogram, uploading deposit and remuneration by the user, and uploading the deposit to a block chain end by a cloud server;
secondly, the user uses the first step to generate a random blinding pair to process the private data and the random data, and packages and uploads the processed data to the blockchain;
thirdly, after the cloud server downloads data from the block chain, performing modular exponentiation calculation, and uploading the result to the block chain;
step four, the user firstly verifies the result after downloading the result from the blockchain, and if the result passes the verification, a required answer is obtained; otherwise, refusing to accept the result and requiring the blockchain to carry out auxiliary verification;
and fifthly, performing auxiliary verification by using a calculation result of random data provided by a user, judging whether the cloud server is malicious or not, and punishing the malicious server.
The embodiment adopts the secure mode index outsourcing payment method based on the blockchain single cloud server, so that the user sensitive data is not easy to leak, the verifiable probability is high, and the problem that the payment scheme depends on a trusted third party is solved.
Example two
In this embodiment, the participants: subroutine, user, cloud server, blockchain.
The subroutine: each call can return a form (alpha, g) α ) Is used to call RandG to improve efficiency.
The user: the computing power is weak and the computing task is heavy, thus outsourcing the computing task.
Cloud server: outsourcing calculators willing to perform tasks for users. The computing power is strong, but the computing power is not completely trusted, and the correct result of the user can be returned, and partial error result can be returned, so that malicious influence is caused to the user.
Blockchain: and a third party in the traditional scheme is replaced, and the decentralization function is realized. An auxiliary arbitration function is provided and payment is engaged.
The modular exponentiation payment scheme based on the blockchain comprises three participating members, namely a user, a cloud server and the blockchain. The complex problem cannot be solved due to insufficient computing power of users, and the modulus index calculation needs to be handed to a cloud server for solving. The cloud server has powerful computing resources, but is not completely trusted, if the user verifies that the outsourcing result finds that the result is incorrect, the computing result of the random data and the corresponding secret value thereof can be sent to the blockchain, and the blockchain performs auxiliary verification and arbitrates. The whole process comprises the following steps: firstly, initializing a user, generating required random data and blind random pairs, logically splitting private data and random data, and then sending the split private data and random data to a blockchain. The cloud server then begins computing the task downloaded from the blockchain and uploads the results to the blockchain. And finally, verifying the result by the user, and calculating the required answer.
Referring to fig. 1, a modular exponentiation payment method based on blockchain in this embodiment is specifically as follows:
the first step, the user initializes, generates random data and a plurality of blinded random pairs, so as to facilitate the subsequent use of the blinded data.
The random data is generated by the following specific steps: private data u a In which there is a large prime number p, G is a cyclic group of order p, the base u.epsilon R G, index a E R Z p . Initializing a subprogram Rand, and calling Rand to generate and secret data u by a user a Similar random data r b Wherein the base r epsilon R G, index b E R Z p 。
The generation mode of the random blinding pair is specifically as follows: the generator G of a p-order cyclic group G is used as the input of a subprogram RandG, and outputs a code (a, G) once called a ) Is used for the blind pairs of the pair,
Figure BDA0003574810300000052
the user invokes the subroutine RandG 8 times to generate a blinded random pair (α, g) α ),(β,g β ),(ρ,g ρ ),(σ,g σ ),(γ,g γ ),(δ,g δ ),(η,g η ),(λ,g λ ) And define v 1 ＝g α mod p,v 2 ＝g ρ mod p,s 1 ＝g γ mod p,s 2 ＝g η mod p。
And secondly, logically splitting all data by a user and uploading the data to the blockchain. The logic splitting is to split the original data into random pieces, so that the cloud server cannot acquire sensitive information in the calculation process. Namely, the private data and the random data are respectively split into two parts, and the data obtained after each part of split consists of two parts: a random number pair for outsourcing and a secret value for verifying the result. After the user obtains the outsourcing result, two groups of outsourcing results of private data can be verified by the secret value, and the correctness of the outsourcing results can be rapidly judged by comparing whether the two groups of values are equal. The method comprises the following specific steps: the user needs to use blind random pairs to respectively pair the private data u a And random data r b And performing two groups of logic splitting.
Wherein, for u a Is split as follows: first split into u a ＝(v 1 w 1 ) a ＝g αa w 1 a Wherein w is 1 ＝u/v 1 . Second logical split into
Figure BDA0003574810300000051
Wherein c 1 ＝αa-βmod p,d 1 ＝a-k 1 l 1 mod p. Then to u a Performing a second set of logical partitions, the first logical partition being u a ＝(v 2 w 2 ) a ＝g ρa w 2 a Wherein w is 2 ＝u/v 2 . The second logical split is +.>
Figure BDA0003574810300000061
Wherein c 2 ＝ρa-σmod p,d 2 ＝a-k 2 l 2 mod p。
Wherein, for r b Is split as follows: first logical split into r b ＝(s 1 t 1 ) b ＝g γb t 1 b Wherein t is 1 ＝r/s 1 . Second logical split into
Figure BDA0003574810300000062
Wherein e 1 ＝γb-δmod p,f 1 ＝b-m 1 n 1 mod p. And then to r b Performing a second set of logical partitions, the first logical partition being r b ＝(s 2 t 2 ) b ＝g ηb t 2 b Wherein t is 2 ＝r/s 2 . The second logical split is +.>
Figure BDA0003574810300000063
Wherein e 2 ＝ηb-λmod p,f 2 ＝b-m 2 n 2 mod p。
At this time, the random number pair (v 1 ,w 1 ),(v 2 ,w 2 ) Sum(s) 1 ,t 1 ),(s 2 ,t 2 ) And performing blind hiding treatment on the base number u in the private data and the base number r in the random data respectively. Random value c 1 ,d 1 ,k 1 ,l 1 ,c 2 ,d 2 ,k 2 ,l 2 And e 1 ,f 1 ,m 1 ,n 1 ,e 2 ,f 2 ,m 2 ,n 2 The indices a and b are blindly hidden, respectively. Finally, the user uploads the blinded random number pair (c 1 ,g),(d 1 ,w 1 ),(k 1 ,w 1 ),(c 2 ,g),(d 2 ,w 2 ),(k 2 ,w 2 ) (e) 1 ,g),(f 1 ,t 1 ),(m 1 ,t 1 ),(e 2 ,g),(f 2 ,t 2 ),(m 2 ,t 2 ) To the blockchain. To improve security, a random number l 1 ,l 2 ,n 1 ,n 2 Is at least 64b in length. Probabilities of adversaries recovering a and b by guessingAnd neglected.
Thirdly, the cloud server downloads the task and calculates the result
Figure BDA0003574810300000064
Uploading to the blockchain:
Figure BDA0003574810300000065
and step four, the user downloads and verifies the wrapping result.
The verification of the returned result is specifically as follows: using secret value l 1 ,l 2 Judging whether the following is true:
Figure BDA0003574810300000066
if the equation is satisfied, the user calculates the final answer through verification
Figure BDA0003574810300000067
Otherwise, the user judges that the cloud server is malicious and applies for the auxiliary verification of the blockchain.
Fifth step, the blockchain utilizes the secret value n 1 ,n 2 And the result of the random data calculation, i.e. using the secret value n 1 ,n 2 Verification
Figure BDA0003574810300000071
Whether or not it is. If the cloud server is not established, the cloud server is malicious, and the blockchain transfers the deposit of the cloud server to the user as compensation, and returns the deposit and the remuneration to the user, so that fairness is realized; if the equation is true, the protocol fails.
Probability of protocol failure: when the private data and the random data are wrapped for n times, if the user determines that the result is wrong, the blockchain determines that the result is correct, and the protocol fails. Probability is
Figure BDA0003574810300000072
Negligible.
Thus, the entire embodiment of the present invention is completed.
The embodiment of the invention provides a verifiable modular exponentiation outsourcing fair payment scheme based on a blockchain, and a user can outsource modular exponentiation to a cloud server and realize fair payment of the user and the server. The outsourcing process comprises the following steps: firstly, a user invokes a subroutine to generate random data and random blinding pairs; then, the user utilizes random blinding to split the privacy data and the random data, and the data to be calculated after the splitting is uploaded to the blockchain. The cloud server downloads and calculates, and submits the result to the blockchain; finally, the user downloads and verifies the result. If the result is correct, the user obtains the required outsourcing result; otherwise, the user applies for the blockchain to arbitrate so as to judge whether the server is malicious or not. If the blockchain judges that the server does have malicious behaviors, deducting deposit of the server; if the blockchain determination server calculates correctly, the protocol fails. According to the scheme provided by the invention, the user can solve the problem that the local resource is limited and can not be solved on the premise of protecting the self data privacy, and the malicious behavior of the cloud server can be resisted. The above embodiments of the present invention demonstrate the correctness and integrity thereof through specific deduction and can be fully utilized. The invention greatly saves the calculation cost of the user on the premise of protecting the privacy of the user, and can effectively verify the correctness of the returned result.

Claims (4)

1. The modular exponentiation fair payment method based on the blockchain is characterized in that a user needs to give a complex modular exponentiation calculation task to a cloud server for calculation due to limited local resources, and the whole outsourcing process comprises the following steps:
firstly, initializing and setting a user, namely generating random data and random blinding pairs by using a subprogram, uploading deposit and remuneration by the user, and uploading the deposit to a block chain end by a cloud server;
secondly, the user uses the first step to generate a random blinding pair to process the private data and the random data, and packages and uploads the processed data to the blockchain;
thirdly, after the cloud server downloads data from the block chain, performing modular exponentiation calculation, and uploading the result to the block chain;
step four, the user firstly verifies the result after downloading the result from the blockchain, and if the result passes the verification, a required answer is obtained; otherwise, refusing to accept the result and requiring the blockchain to carry out auxiliary verification;
fifthly, performing auxiliary verification by using a calculation result of random data provided by a user, judging whether the cloud server is malicious or not, and punishing the malicious server;
the first step comprises two sub-steps:
1) Generating random data: user calls subprogram Rand to generate private data u a Similar random data r b ；
2) Generating a random blinding pair: first, the user invokes the subroutine RandG to generate 8 pairs of random pairs (α, g α ),(β,g β ),(ρ,g ρ ),(σ,g σ ),(γ,g γ ),(δ,g δ ),(η,g η ),(λ,g λ ) Then, define v 1 ＝g α mod p,v 2 ＝g ρ mod p,s 1 ＝g γ mod p,s 2 ＝g η mod p；
The second step is that the user locally utilizes random blinding to logically split two groups of private data and random data respectively;
for private data u a Performing a first set of logical splits: splitting for the first time: u (u) a ＝(v 1 w 1 ) a ＝g αa w 1 a Wherein w is 1 ＝u/v 1 The method comprises the steps of carrying out a first treatment on the surface of the And (3) splitting for the second time:
Figure FDA0004155941780000011
wherein the method comprises the steps of
c 1 ＝αa-βmod p,d 1 ＝a-k 1 l 1 mod p; then to the privacy data u a Performing a second set of logical splits:
u a ＝(v 2 w 2 ) a ＝g ρa w 2 a wherein w is 2 ＝u/v 2 ；
Figure FDA0004155941780000012
Wherein,,
c 2 ＝ρa-σmod p,d 2 ＝a-k 2 l 2 mod p；
subsequently, for random data r b Performing a first set of logical splits, the first split r b ＝(s 1 t 1 ) b ＝g γb t 1 b Wherein t is 1 ＝r/s 1 The method comprises the steps of carrying out a first treatment on the surface of the Second time of detachment
Figure FDA0004155941780000013
Wherein e 1 ＝γb-δmod p,f 1 ＝b-m 1 n 1 mod p; and then to random data r b Performing a second set of logical splits: r is (r) b ＝(s 2 t 2 ) b ＝g ηb t 2 b Wherein t is 2 ＝r/s 2 ；
Figure FDA0004155941780000014
Wherein e 2 ＝ηb-λmod p,f 2 ＝b-m 2 n 2 mod p；
At this time, the random number pair (v 1 ,w 1 ),(v 2 ,w 2 ) Sum(s) 1 ,t 1 ),(s 2 ,t 2 ) The base number u in the private data and the base number r in the random data are subjected to blind hiding treatment respectively; random value c 1 ,d 1 ,k 1 ,l 1 ,c 2 ,d 2 ,k 2 ,l 2 And e 1 ,f 1 ,m 1 ,n 1 ,e 2 ,f 2 ,m 2 ,n 2 The indexes a and b are respectively blindly hidden; the user uploads the blinded data pair (c 1 ,g),(d 1 ,w 1 ),(k 1 ,w 1 ),(c 2 ,g),(d 2 ,w 2 ),(k 2 ,w 2 ) (e) 1 ,g),(f 1 ,t 1 ),(m 1 ,t 1 ),(e 2 ,g),(f 2 ,t 2 ),(m 2 ,t 2 ) To the blockchain.
2. The modular exponentiation payment method based on blockchain as in claim 1, wherein the third step is specifically that a cloud server downloads a task and calculates the result
Figure FDA0004155941780000021
Commit to blockchain: />
Figure FDA0004155941780000023
Figure FDA0004155941780000024
Figure FDA0004155941780000025
Figure FDA0004155941780000026
3. The modular exponentiation payment method based on blockchain of claim 1, wherein the fourth step is to download the result from the blockchain by the user using the secret value l 1 ,l 2 Judging
Figure FDA0004155941780000027
Whether or not to establish; if the equation is true, the user calculates the final answer +.>
Figure FDA0004155941780000028
Otherwise, the user judges that the cloud server is malicious and applies for the auxiliary verification of the blockchain.
4. The modular exponentiation payment method based on blockchain of claim 1, wherein the fifth step is specifically that the user uploads the result of the calculation of the random data to the blockchain, and the blockchain uses the secret value n 1 n 2 Verification
Figure FDA0004155941780000029
Whether or not to establish; if the equation is not established, the cloud server is malicious; if the equation is true, the protocol fails; after conclusion, the blockchain forwards the deposit and the remuneration to the entitled parties to achieve fair payment. />
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