turkmath.org

The discrete derivative of a function is a simple notion but has many applications in cryptography. Many attacks exploit the properties of derivatives, and consequently the design of cryptographic functions includes requirements on their derivatives. We will give an introduction to this area and then present our results regarding Boolean functions for which the algebraic degree of the derivative is lower than expected. We obtain counting formulae for the number of such functions. Part of this work (joint with Ferruh Ozbudak) was presented last week at the Workshop on Coding and Cryptography in France.