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The DO transforms the spatial data points and indexes them.
However, Hilbert R-trees do not expose the complete ordering of spatial data points.
The Hilbert curve is used to transform the location of spatial data points.
The original spatial data points coordinates are hidden using the Hilbert space-filling curve and grouped in packets.
The search performance of the DISC index is faster-than-linear with regard to the number of spatial data points.
The index construction process at the DO is initiated with static 2−D spatial data points in the space.
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In order to update a spatial data point in DISC, the data owner first needs to issue an update request.
Insert: The new spatial data point to be inserted is sent in an encrypted format by the DO to the CSP.
In the first loop (Lines 1 4), each spatial data point d i in D is normalized to [0,1]2 and then its Hilbert cell value is computed using the Hilbert transformation function, F HSK, based on the Hilbert Space Key.
Each LHV in the nodes is the Hilbert value and is represented by 4 bytes (an integer), and each spatial data point consists of x and y coordinates in double precision (16 bytes).
Table 1 List of Notations used Notation Description DO Data owner CSP Cloud service provider TU Trusted user D 2D spatial data point set F HSK Hilbert transformation function H Hilbert cell value K OPE Order-preserving encryption key K AES Advanced encryption standard key LHV Largest Hilbert value nodeCapacity(n L ) Node Capacity of a leaf node QR Query Hilbert value set R Query result set.
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