Non-full-active Super-Sbox Analysis: Applications to ECHO and Grøstl
In this paper, we present non-full-active Super-Sbox analysis which can detect non-ideal properties of a class of AES-based permutations with a low complexity. We apply this framework to SHA-3 round-2 candidates ECHO and Grøstl. The first application is for the full-round (8-round) ECHO permutation, which is a building block for 256-bit and 224-bit output sizes. By combining several observations specific to ECHO, our attack detects a non-ideal property with a time complexity of 2182 and 237 amount of memory. The complexity, especially in terms of the product of time and memory, is drastically reduced from the previous best attack which required 2512×2512. Note that this result does not impact the security of the ECHO compression function nor the overall hash function. We also show that our method can detect non-ideal properties of the 8-round Grøstl-256 permutation with a practical complexity, and finally show that our approach improves a semi-free-start collision attack on the 7-round Grøstl-512 compression function. Our approach is based on a series of attacks on AES-based hash functions such as rebound attack and Super-Sbox analysis. The core idea is using a new differential path consisting of only non-full-active states.