Cryptanalysis of MDC-2

We provide a collision attack and preimage attacks on the MDC-2 construction, which is a method (dating back to 1988) of turning an $n$-bit block cipher into a $2n$-bit hash function. The collision attack is the first below the birthday bound to be described for MDC-2 and, with $n=128$, it has complexity $2^{124.5}$, which is to be compared to the birthday attack having complexity $2^{128}$.

The preimage attacks constitute new time/memory trade-offs; the most efficient attack requires time and space about $2^n$, which is to be compared to the previous best known preimage attack of Lai and Massey (Eurocrypt '92), having time complexity $2^{3n/2}$ and space complexity $2^{n/2}$, and to a brute force preimage attack having complexity $2^{2n}$.