Distinguisher and Related-Key Attack on the Full AES-256

In this paper we construct a chosen-key distinguisher and a related-key attack on the full 256-bit key AES. We define a notion of differential q -multicollision and show that for AES-256 q-multicollisions can be constructed in time q·267 and with negligible memory, while we prove that the same task for an ideal cipher of the same block size would require at least $O(q\cdot 2^{\frac{q-1}{q+1}128})$ time. Using similar approach and with the same complexity we can also construct q-pseudo collisions for AES-256 in Davies-Meyer mode, a scheme which is provably secure in the ideal-cipher model. We have also computed partial q-multicollisions in time q·237 on a PC to verify our results. These results show that AES-256 can not model an ideal cipher in theoretical constructions. Finally we extend our results to find the first publicly known attack on the full 14-round AES-256: a related-key distinguisher which works for one out of every 2^{35} keys with 2^{120} data and time complexity and negligible memory. This distinguisher is translated into a key-recovery attack with total complexity of 2^{131} time and 2^{65} memory.