A Combinatorial Problem Related to Sparse Systems of Equations

TL;DR

This paper explores a linear algebra variation of a combinatorial MaxMinMax problem related to solving sparse systems of equations, which are crucial in cryptanalysis for retrieving keys or plaintexts.

Contribution

It introduces a new linear algebra perspective to the MaxMinMax problem, advancing understanding of the complexity of solving sparse systems in cryptanalysis.

Findings

Provides bounds on the computational complexity of sparse systems

Initiates a study of a linear algebra variation of MaxMinMax

Connects combinatorial problems with cryptanalysis applications

Abstract

Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then the system is solved to retrieve either a key or a plaintext. Raddum and Semaev proposed new methods for solving such sparse systems. It turns out that a combinatorial MaxMinMax problem provides bounds on the average computational complexity of sparse systems. In this paper we initiate a study of a linear algebra variation of this MaxMinMax problem.