Algorithm 7 DistanceCompare.

Input:

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

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

${\tau }_e$: the ciphered compare parameter τ;

Output:

$true$ or $false$;

1: Execute $di{s}_e=DistanceCompute\left(X_e,Y_e\right)$;

2: if $di{s}_e-{\tau }_e\le 0$ then return $true$;

3: end if

return $false$;