In this second talk, the speaker explained the concept of Linear Recurrence Relations and results on existence of minimal polynomials of sequences over finite fields, showing how they can be used to compute the local inverses of maps and sequences. The inverse computation utilises only the black box map operation and solving a Hankel linear system of equations over the field. The maximal rank of the Hankel system is the Linear Complexity of the sequence.

Illustrations were shown for applications to stream cipher cryptanalysis, RSA inversion, RSA private key computation, the Quadratic Residue problem, and the Discrete Log problem over finite fields. The talk concluded with a list of further problems and applications of the approach.