Abstract
We present a study on the algebraic degree of iterated permutations seen as multivariate polynomials. The main result shows that this degree depends on the algebraic degree of the inverse of the permutation which is iterated. This result is also extended to noninjective balanced vectorial functions where the relevant quantity is the minimal degree of the inverse of a permutation expanding the function. This property has consequences in symmetric cryptography since several attacks or distinguishers exploit a low algebraic degree, like higher order differential attacks, cube attacks, and cube testers, or algebraic attacks. Here, we present some applications of this improved bound to a higher degree variant of the block cipher KN, to the block cipher Rijndael-256 and to the inner permutations of the hash functions ECHO and JH.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.