A Combinatorial Problem Related to Sparse Systems of Equations

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.