Analysis of the NORX Core Permutation

NORX is one of the fifteen authenticated encryption algorithms that have reached the third round of the CAESAR competition. NORX is built using the sponge-based Monkey Duplex construction. In this note we analyze the core permutation F. We show that it has rotational symmetries on different structure levels. This yields simple distinguishing properties for the permutation, which propagate with very high probability or even probability one. We also investigate differential symmetries in NORX at the word level. A new type of truncated differentials called symmetric truncated differentials (STD) is proposed. It is shown that, under the Markov assumption, up to 2.125 rounds of the F function of NORX32 and NORX64 can be distinguished using STD. Finally, we note that our analysis covers only the permutation F and does not immediately threaten the security claims of the designers.