[EXT] Solving Polynomial Equation Systems without Gröbner Bases

  • Name:

    [EXT] Solving Polynomial Equation Systems without Gröbner Bases

  • Venue:

    252 / BBB

  • Date:

    2026-10-06

  • Speaker:

    Akin Ünal

  • Time:

    15:45

  • Solving Polynomial Systems over multiple Variables is a core aspect of Algebraic Cryptanalysis, and many other symbolic calculations.
    A typical approach is to compute a degrevlex GB of the system, transform it to a lexicographic GB and apply the Shape-Lemma.
    Can we do without GBs?

    I will show here an approach that only utilizes Macaulay Matrices and Stickelberger's theorem.
    This approach has the advantage that it descends well to quotients of polynomial rings (assuming that a GB of the defining ideal is known).