Vulnerability and leakage measures¶

qif.measure

Each submodule implements a family of measures, with functions following the same naming scheme. For a prior \(\pi\) and a channel \(C\) (see Channels):

prior(pi): The prior vulnerability \(V(\pi)\) (or uncertainty \(U(\pi)\)) of the secret.
posterior(pi, C): The posterior vulnerability \(V[\pi\triangleright C]\), that is the expected vulnerability of the posterior distributions, weighted by their probability: \(\sum_y p(y)\, V(p_{X|y})\) (similarly for \(U\)).
add_leakage(pi, C), mult_leakage(pi, C): The additive and multiplicative leakage, \(V[\pi\triangleright C] - V(\pi)\) and \(V[\pi\triangleright C] / V(\pi)\). For uncertainty measures the order is reversed, \(U(\pi) - U[\pi\triangleright C]\) and \(U(\pi) / U[\pi\triangleright C]\), so that leakage is always non-negative (additive) or at least \(1\) (multiplicative).
add_capacity, mult_capacity: The maximum leakage over a class of priors and/or gain functions.
strategy(pi, C): An optimal strategy of the adversary: an array with the best action for each observation \(y\).

Measures parametrized by a gain or loss function (for instance g_vuln) take it as an extra first argument.