Séminaire de Cryptographie

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Eric Schost

Lifting techniques for polynomial system solving.

Through examples taken from point-counting problems or invariant theory, I will give an overview of how lifting techniques (that is, symbolic versions of Newton's iteration) can help us solve polynomial systems.

I will review the key ingredients needed to put this kind of approach to practice, such as degree bounds or efficient arithmetic for polynomials and power series, and hint at the remaining open problems.