Algebraic cryptanalysis for post-quantum cryptography – POSTCRYPTUM

Among well-established techniques in cryptanalysis, algebraic attacks are methods to describe the scheme as a system of polynomial equations, and consequently reduce its security to the hardness of solving the associated system. The POSTCRYPTUM project aims at designing efficient algebraic
attacks, for several classes of cryptosystems which may be modeled as binary polynomial systems. By using the equivalence between multiplication and the logical AND operator and addition and the XOR operator, Boolean systems may be transformed into logical formulas, which are
treated as a satisfiability problem. This is the starting idea of the POSTCRYPTUM project, whose ambition is to conceive and develop efficient algorithms for solving Boolean formulas coming from cryptanalysis and evaluate the impact of these algorithms on the underlying schemes.
Our main focus will be to study the security of cryptosystems proposed to the NIST standardization competition for post-quantum cryptography.