Bit XOR

In this simple example we consider a 1-bit secret h. The protocol produces a random bit r with a given probability p of being 1, and outputs the result of the exclusive disjunction operation between h and r. The attacker knows p and can observe the output, but not r or h. Basically he knows p and whether h = r or not. If p = 0:5 the attacker cannot infer any information about h, thus we have noninterference, i.e. the leakage is 0 bits. If p = 0 or p = 1 then the attacker can determine precisely the value of h, and thus the leakage is 1 bit.

QUAIL can quantify the leakage with arbitrary precision for all p between 0 and 1. The results are shown in the graph below.

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