Algorithm 6 DistanceCompute.

Input:

$X_e$: the ciphertext of a querier’s location X;

$Y_e$: the ciphertext of a publisher’s location Y;

Output:

${dis}_e$: the ciphertext of the distance between X and Y;

1: Obtain $m^{\prime }=m·W^s$ and $x^{\prime }=x+W^s$ from the $Y_e^I$ ;

2: Compute ${K^{\prime }}_Y=m^{\prime }·g^{x^{\prime }}\mathrm{mod}n$;

3: Compute ${dis}_e=\sqrt{{\displaystyle \sum _{i=1}^3}{\left(x_{ei}-y_{ei}·{K^{\prime }}_Y\right)}^2}$;

return ${dis}_e$;