An Efficient and Privacy-Preserving Multiuser Cloud-Based LBS Query Scheme

Algorithm 1

APSE scheme.

APSE Scheme

Key: a invertible matrix .

Tuple Encryption Function : Consider an LBS data which will be stored in a cloud server.

(1) Create a -dimensional point .

(2) The encrypted data .

Query Encryption Function  : Consider an LBS query .

(1) Generate a random number .

(2) Create a -dimensional point .

(3) The encrypted query .

Distance Comparison Operator  :

Let and be the encrypted data of and respectively. To determine whether is nearer to a

query than is, the system checks whether , where is the encrypted point of .

Decryption Function  : Consider an encrypted data .

The original data , where is a matrix which projects on the first dimensions

and where is the identity matrix.