  A conditional version of Sibson's $\alpha$-information is defined using a
simple closed-form "log-expectation" expression, which satisfies important
properties such as consistency, uniform expansion, and data processing
inequalities. This definition is compared to previous ones, which in contrast
do not satisfy all of these properties. Based on our proposal and on a
generalized Fano inequality, we extend the case $\alpha = 1$ of previous works
to obtain sharp universal upper bounds for the probability of success of any
type side-channel attack, particularly when $\alpha = 2$.
