Talk by Elisa Gorla, Université de Neuchâtel
Multivariate cryptography belongs to post-quantum cryptography, which is the branch of cryptography that is supposed to remain secure even in the presence of a quantum computer. After introducing public-key cryptography and motivating the need for studying post-quantum cryptography, I will discuss the role played by commutative algebra techniques in multivariate cryptography. The security of multivariate cryptographic primitive relies on the hardness of computing the solutions of multivariate polynomial systems over finite fields. Since we can compute the solutions of a polynomial system from its Gröbner basis, bounds on the complexity of Gröbner bases computations provide bounds on the security of the corresponding multivariate cryptographic primitives. In the talk, I will introduce and discuss some algebraic invariants which play a role in these security estimates and motivate their importance in this applied setting
