Perfect Secrecy Check

Problem

Return True when the channel p(c|m), passed as pcm[m][c], equals the ciphertext prior pc for every message and ciphertext within a tolerance of 1e-9. That equality is exactly Shannon's condition for perfect secrecy.

Hint

The ciphertext distribution must not depend on the message at all.

Test cases

case 1

in: [[[0.5,0.5],[0.5,0.5]],[0.5,0.5]]

expected: true

case 2

in: [[[1,0],[0.5,0.5]],[0.5,0.5]]

expected: false

case 3

in: [[[0.25,0.75],[0.25,0.75]],[0.25,0.75]]

expected: true

case 4

in: [[[1,0],[1,0]],[1,0]]

expected: true

Starter codePython

def perfect_secrecy_holds(pcm, pc):
    # Your code here
    pass

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