Differentially Private Mobile Crowd Sensing Considering Sensing Errors

. 2020 May 14;20(10):2785. doi: 10.3390/s20102785

Algorithm 1 Anonymization Algorithm.

Input: $m i n v_{o r g}$ , $m a x v_{o r g}$ , $m i n v_{r e p}$ , $m a x v_{r e p}$ , $m i n σ_{o r g}$ , $m a x σ_{o r g}$ , $ϵ$ .

Output: Report value v and standard deviation $σ$ of sensing error

1:
Obtain sensed value v and standard deviation $σ$ of sensing error
2:
if the standard deviation is considered as private information then
3:
$ϵ \leftarrow ϵ / 2$
4:
end if
5:
$v \leftarrow \min (\max (m i n v_{o r g}, v), m a x v_{o r g})$ /* If v is smaller than $m i n v_{o r g}$ (or larger than $m a x v_{o r g}$ ), v is set to $m i n v_{o r g}$ (or $m a x v_{o r g}$ ).*/
6:
$v \leftarrow v + L a p ((m a x v_{o r g} - m i n v_{o r g}) / ϵ)$ /* The global sensitivity is $m a x v_{o r g} - m i n v_{o r g}$ .*/
7:
$v \leftarrow \min (\max (m i n v_{r e p}, v), m a x v_{r e p})$ /* If v is smaller than $m i n v_{r e p}$ (or larger than $m a x v_{r e p}$ ), v is set to $m i n v_{r e p}$ (or $m a x v_{r e p}$ ).*/
8:
if the standard deviation is considered as private information then
9:
$σ \leftarrow \min (\max (m i n σ_{o r g}, σ), m a x σ_{o r g})$ /* If $σ$ is smaller than $m i n σ_{o r g}$ (or larger than $m a x σ_{o r g}$ ), $σ$ is set to $m i n σ_{o r g}$ (or $m a x σ_{o r g}$ ).*/
10:
$σ \leftarrow σ + L a p ((m a x σ_{o r g} - m i n σ_{o r g}) / ϵ)$ /* The global sensitivity is $m a x σ_{o r g} - m i n σ_{o r g}$ .*/
11:
end if
12:
Report v and $σ$ .