International Association
for Cryptologic Research

In this paper, we make attacks on DBL (Double-Block-Length) hash modes of block ciphers with n-bit key and n-bit block. Our preimage attack on MDC-4 scheme requires the time complexity $2^{3n/2}$, which

is significantly improved compared to the previous results. Our collision attack on the hash function of MJH scheme has time complexity less than $2^{124}$ for n = 128. Our preimage attack on the compression functions of MJH scheme find a preimage with time complexity of $2^n$. It is converted to a preimage attack on the hash function with time complexity of $2^{3n/2+1}$. Our preimage attack on the compression functions of MJH scheme find a preimage with time complexity of $2^{3n/2}$. It is converted to a second-preimage attack on the hash function with time complexity of $2^{7n/4+1}$. These attacks are helpful for understanding the security of the hash modes together with their security proofs.