Ferdinand motivates and introduces the concepts used in signature based Gröbner basis computation algorithms, like the widely celebrated F₅. Omitted proofs can be found in the literature mentioned in the video and listed below. If you have questions, feel free to write him at ferdinand (at) asdm (dot) gmbh.

Faugère, J.C.: A new efficient algorithm for computing Gröbner bases without reduction to zero (F₅). In: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation. pp. 75–83 (2002)

Cox, D.A., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer Science & Business Media (2013)

Eder, C., Faugère, J.C.: A survey on signature-based algorithms for computing Gröbner bases. Journal of Symbolic Computation 80, 719–784 (2017)

Ferdinand Sauer explains how the FGLM Gröbner basis term order change algorithm works.

Ferdinand Sauer gives an introductory presentation to attacking arithmetization-oriented ciphers using Gröbner basis methods.


Created 3 months, 3 weeks ago.

3 videos

Category Science & Technology

We do mathematics, information theory, computer science, and cryptography.