Gaussian Mechanism Sigma

Problem

Return the noise standard deviation for the Gaussian mechanism that satisfies (epsilon, delta)-differential privacy:

sigma = sqrt(2 * ln(1.25 / delta)) * sensitivity / epsilon

Assume delta is small and positive.

Hint

A smaller delta demands more noise.

case 1

in: [1,1,0.00001]

expected: 4.844805262605389

case 2

in: [1,0.1,0.00001]

expected: 48.44805262605389

case 3

in: [2,0.5,0.000001]

expected: 21.195210107401895

case 4

in: [1,1,0.1]

expected: 2.247544724497493

Starter codePython

import math
def gaussian_sigma(sensitivity, epsilon, delta):
    # Your code here
    pass

4 test cases · run your code against them in the editor