A quantum algorithm to estimate the closeness to the Strict Avalanche criterion in Boolean functions

TL;DR

This paper introduces a quantum algorithm that efficiently estimates how closely a Boolean function satisfies the strict avalanche criterion, requiring fewer oracle queries than classical methods.

Contribution

It presents the first quantum algorithm for estimating SAC closeness with minimal oracle queries, outperforming existing quantum approaches.

Findings

Uses only n queries for n input variables, fewer than classical methods.

Verifies SAC with the fewest quantum oracle calls among existing algorithms.

Requires the fewest samples for a given confidence level.

Abstract

We propose a quantum algorithm (in the form of a quantum oracle) that estimates the closeness of a given Boolean function to one that satisfies the ``strict avalanche criterion'' (SAC). This algorithm requires $n$ queries of the Boolean function oracle, where $n$ is the number of input variables, this is fewer than the queries required by the classical algorithm to perform the same task. We compare our approach with other quantum algorithms that may be used for estimating the closeness to SAC and it is shown our algorithm verifies SAC with the fewest possible calls to quantum oracle and requires the fewest samples for a given confidence bound.