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**2011/503**

**Title:**

On the influence of the algebraic degree of F^{−1} on the algebraic degree of G \circ F

**Authors:**
Christina Boura, Anne Canteaut

**Abstract:**

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.

**ePrint:**
https://eprint.iacr.org/2011/503

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