## Cryptology ePrint Archive: Report 2009/275

Algebraic Attacks specialized to $\mathbb{F}_2$ (Diplomarbeit)

Thomas Dullien

Abstract: This thesis studies the ring of boolean functions. A simple algorithm that performs similarly to the euclidian algorithm is derived, and it's performance for solving multivariate boolean equation systems is evaluated. Furthermore, the Raddum-Semaev equation system solving algorithm is put into geometric context, and the pseudo-euclidian algorithm is generalized to multivariate polynomial rings over arbitrary finite fields.

Category / Keywords: secret-key cryptography / algebraic attacks, multivariate polynomials, boolean functions

Publication Info: Diplomarbeit, submitted Summer 2008