An application of Combinatorics in Cryptography

Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse system that are 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 a new method for solving such sparse systems. It turns out that a combinatorial MaxMinMax problem provides bounds on the case where the average computational complexity of their method is maximum. We focus on this MaxMinMax problem and present results over finite and infinite fields.