On Conditional $\alpha$-Information and its Application to Side-Channel Analysis

TL;DR

This paper introduces a new conditional $ ext{α}$-information measure with desirable properties and applies it to derive sharp bounds on the success probability of side-channel attacks, especially for $ ext{α} = 2$.

Contribution

It defines a novel conditional $ ext{α}$-information that satisfies key properties and extends existing bounds to improve side-channel analysis.

Findings

New conditional $ ext{α}$-information with key properties

Extended Fano inequality for $ ext{α} = 1$ and $ ext{α} = 2$

Sharp universal bounds on side-channel attack success probabilities

Abstract

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 $\alpha = 2$.