Cryptanalysis of double-block-length hash modes MDC-4 and MJH

We give some attacks on the DBL hashmodesMDC-4 and MJH. Our preimage attack on the MDC-4 hash function requires the time complexity O(2^3n/2) for the block length n of the underlying block cipher, which significantly improves the previous results. Our collision attack on the MJH hash function has a time complexity less than 2¹²⁴ for n = 128. Our preimage attack on the the MJH compression function finds a preimage with the time complexity of 2 ⁿ. It is converted to a preimage attack on the hash function with the time complexity of O(2^3n/2). As far as we know, any cryptanalytic result for MJH has not been published before. Our results are helpful for understanding the security of the hash modes together with their security proofs.