Abstract : Algebraic cryptanalysis has become unavoidable in the cryptanalysis and design of schemes in cryptography. In the first part, I explain what is a good algebraic modeling, and how we can estimate the complexity of solving a polynomial system with Gröbner basis. In the second part, I present different algebraic modelings for the decoding problem in rank metric code-based cryptography, and their complexity analysis.

Keywords : Gröbner bases; algebraic attack; rank decoding problem; minrank problem