VIC-PRO: Vicinity Protection by Concealing Location Coordinates Using Geometrical Transformations in Location Based Services

Abstract

Portable devices today are striding computation potential and memory at par and sometimes even significantly higher than those found in desktop machines. Today’s lifestyle is more mobile than earlier, offices are open cafe houses and people prefer to work from plug and play office spaces. With the exponential growth of mobile technology and its users, a more astute system is in place called ‘location based services’ (LBSs). Since client uses these services out of their dynamic or static working behavior and is required to submit the real location (with query) to get the absolute benefits, it is crucial to layout the systems and frameworks which can protect users from the security and privacy threats by keeping the location information private. Existing defense mechanisms based on trusted third party possesses the significant vulnerability to vicinity identification, which in turn end up identifying the real world identity of the query issuer. In this paper, we present a scheme to preserve location privacy, called VIC-PRO, that fortifies the location privacy of the client alongside vicinity protection using geometrical transformations. We experimentally compare the scheme with other existing mechanisms to demonstrate that VIC-PRO is more efficient, safe against vicinity identification attack, and guarantees better user privacy in an LBS setup.

Appendix: Few Essentials

This section describes the geometric transformations given by [22].

A reflection is a transformation that produces a mirror image of the point.

• 1. Reflection about the line $y=0$, the x axis, is accomplished with the transformation matrix

  $$\begin{aligned} M = \begin{bmatrix} 1&0&0\\ 0&-1&0\\ 0&0&1 \end{bmatrix} \end{aligned}$$

  keeps x value the same, but “flips” the y value of coordinate position

• 2. Reflection about the line $x=0$, the y axis. The matrix for this transformation is

  $$\begin{aligned} M = \begin{bmatrix} -1&0&0\\ 0&1&0\\ 0&0&1 \end{bmatrix} \end{aligned}$$

  “flips” the x value of coordinate position while keeping y the same

• 3. This transformation, referred to as a reflection relative to the coordinate origin, has the matrix representation:

  $$\begin{aligned} M = \begin{bmatrix} -1&0&0\\ 0&-1&0\\ 0&0&1 \end{bmatrix} \end{aligned}$$

  “flip” both the x and y coordinates if a point by reflecting relative to an axis that is perpendicular to the xy plane and passes through the coordinate of origin with the transformation matrix

Final transformation is achieved through, $P' = M \cdot P$

A translation is a transformation applied to a point by repositioning it along a straight line path from one coordinate location to another.

We translate a 2D point by adding translation distances, $t_x$ and $t_y$, to the original (x, y) to move the point to a new position $(x', y')$.

$$\begin{aligned} \begin{bmatrix} x'\\ y'\\ 1 \end{bmatrix} = \begin{bmatrix} 1&0&t_x \\ 0&1&t_y \\ 0&0&1 \end{bmatrix} . \begin{bmatrix} x\\ y\\ 1 \end{bmatrix} \end{aligned}$$

i.e. $P' = T_{(t_x, t_y)} \cdot P$.