Research On The Verifiable Modular Index Outsourcing Calculation Algorithm With Privacy Protection In The Cloud Environment

With the rapid development of information technology,how to deal with massive data has become a hotspot of current research.Especially for users with limited resources,how to cope with massive data has become a difficult problem to be solved.Cloud computing,equipped with powerful centralized configurable resources,provides a new solution to this problem--outsourcing computing.Users entrust complex computing tasks to cloud servers who have powerful resources with a pay-as-you-go manner,with the aim of reducing their local overhead.Even though outsourcing computing brings considerable convenience,it also raises huge security risks.On the one hand,during the outsourcing process,users' data may be leaked or may be stolen by unauthorized entities,resulting in the disclosure of users' private information.On the other hand,outsourcing means that the user transfers direct control of the data to the cloud servers,which are usually not completely trusted and may falsify the result and return it to the user.Therefore,how to ensure the privacy of data and the correctness of results is the key issue to be solved in outsourcing computing.Since the modular exponentiation computing is one of the most basic and expensive calculations in cryptography,how to effectively solve the modular exponentiation calculation has become one of the important problems in the field of current outsourcing computing.This thesis focuses on secure outsourcing of modular exponentiation among outsourcing computing.Finally,our specific work is completed as follows:(1)To avoid the security problems in the two-server based solutions,this thesis proposes a secure and verifiable single-server based modular exponentiation outsourcing scheme,called MExp.Our scheme is based on single server model which avoids the “collusion attack” problem.Moreover,by adopting a new logical division method,MExp also ensures the privacy security of the base and exponent in users' outsourced data.In addition,MExp can detect wrong calculation results returned by the cloud server with a probability of 1,ensuring that the user can fully verify the outsourcing calculation results.The final security analysis and simulation experiments prove that MExp can achieve security,verifiability and high efficiency.(2)To solve the large-scale modular exponentiation computing outsourcing problem,this thesis proposes a secure batch processing scheme M2 Exp for modular exponential computing.Compared with MExp,the proposal can not only reduce users' overhead of modular exponentiation computing but also efficiently solve the computation problem of multiple modular exponentiations.Moreover,while guaranteeing the privacy of outsourced data,M2 Exp is still able to detect the error of the result returned by cloud server with the probability of 1,which achieves the fully verifiable of computing results.Security analysis shows that M2 Exp satisfies data privacy security,and simulation experiments show that M2 Exp has good performance in terms of verifiability and efficiency.(3)Considering the fact that modular exponential computation is one of the most basic and expensive operations in cryptography and has been widely used in encryption or signature algorithms,we apply the proposed MExp algorithm and M2 Exp algorithm to some typical cryptographic schemes.Finally,we realize the security outsourcing of Cramer-Shoup encryption and attribute-based encryption of ciphertext strategy(CP-ABE),as well as the Schnorr blind signature and attribute-based signature(ABS)of signature algorithm.It provides an effective solution to the problem of high computational cost of modular exponent that users may encourted when encrypt or sign.