  Measuring the information leakage is critical for evaluating the practical
security of cryptographic devices against side-channel analysis.
Information-theoretic measures can be used (along with Fano's inequality) to
derive upper bounds on the success rate of any possible attack in terms of the
number of side-channel measurements. Equivalently, this gives lower bounds on
the number of queries for a given success probability of attack. In this paper,
we consider cryptographic implementations protected by (first-order) masking
schemes, and derive several information-theoretic bounds on the efficiency of
any (second-order) attack. The obtained bounds are generic in that they do not
depend on a specific attack but only on the leakage and masking models, through
the mutual information between side-channel measurements and the secret key.
Numerical evaluations confirm that our bounds reflect the practical performance
of optimal maximum likelihood attacks.
