Provably Secure Area Verification Based On The Bounded Retrieval Model

Location-based services have grown rapidly in recent years,secure location verification is essential.Currently,substantial efforts have been made on position-based cryptography,however,area-based cryptographic protocols has not been involved in this field to use the geographical area of a party as its only credential.The goal of area-based cryptography is to use the geographical area of a party as its only credential to achieve some cryptographic tasks,such as area-based encryption,area-based key exchange.Constructing an area veri-fication protocol is the cornerstone of achieving other area-based cryptographic protocols.Area verification should have the property that if there is a user at the designated area,then at the end of the protocol,the verifier can verify whether the user exists in the designated area.This thesis investigates secure area verification in the bounded retrieval model against col-luding adversaries,where the goal is to verify if a user is located within the designated area.Firstly,the system model of the area verification protocol is constructed,the adversary attack model is analyzed and the security difinition is given.Secondly,this thesis designs a secure area verification protocol in 2-dimensions and then constructs a secure area-based group key exchange protocol on the basis of it.Thirdly,the thesis proves the security of the proposed protocol.The security theorem of the area verification protocol can be proved by using the provable security theory.And then the thesis proves the security of the area-based GKE pro-tocol according to the the security objectives that the protocol required.Subsequently,the thesis analyzes the error problem of the protocol.The thesis discusses the variation of er-ror values and analyzes the protocol configuration strategies suitable for different users with the different topological positions of the verifier.Finally,the performance of the area-based GKE protocol is compared with the existing typical GKE protocol.The area verifivation protocol proposed in this thesis adopts BRM model,which can not only verify the user's regional information,but also resist the collusion attack of multiple adversaries,and can provide a cryptographically secure area authentication service.The area-based GKE protocol based on the area verification protocol enables users located in the area to efficiently calculate the shared group session key and implement secure group communication.