International Association
for Cryptologic Research

This paper provides an improved preimage attack method on standard 4-round Keccak-224/256. The method is based on the work pioneered by Li and Sun, who design a linear structure of 2-round Keccak-224/256 with 194 degrees of freedom left. By partially linearizing 17 output bits through the last 2 rounds, they finally reach a complexity of 2207/2239 for searching a 4-round preimage. Yet under their strategy, those 17 bits are regarded as independent bits and the linearization costs a great amount of freedom. Inspired by their thoughts, we improve the partial linearization method where multiple output bits can reuse some common degrees of freedom. As a result, the complexity of preimage attack on 4-round Keccak-224/256 can be decreased to 2192/2218, which are both the best known theoretical preimage cryptanalysis so far. To support the theoretical analysis, we apply our strategy to a 64-bit partial preimage attack within practical complexity. It is remarkable that this partial linearization method can be directly applied if a better linear structure with more freedom left is proposed.

In this paper, we provide an improved method on preimage attacks of standard 3-round Keccak-224/256. Our method is based on the work by Li and Sun. Their strategy is to find a 2-block preimage instead of a 1-block one by constructing the first and second message blocks in two stages. Under this strategy, they design a new linear structure for 2-round Keccak-224/256 with 194 degrees of freedom left, which is able to construct the second message block with a complexity of 231/262. However, the bottleneck of this strategy is that the first stage needs much more expense than the second one. Therefore, we improve the first stage by using two techniques. The first technique is constructing multi-block messages rather than one-block message in the first stage, which can reach a better inner state. The second technique is setting restricting equations more efficiently, which can work in 3-round Keccak-256. As a result, the complexity of finding a preimage for 3-round Keccak-224/256 can be decreased from 238/281 to 232/265.