1 research outputs found
On the influence of the algebraic degree of on the algebraic degree of
We present a study on the algebraic degree of iterated permutations seen as multivari-
ate polynomials. Our 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 non-injective 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