Single-block collision attack on MD5

Abstract

In 2010, Tao Xie and Dengguo Feng \\cite{cryptoeprint:2010:643} constructed the first single-block collision for MD5 consisting of two 64-byte messages that have the same MD5 hash. 
\nDetails of their attack, developed using what they call an evolutionary approach, has not been disclosed ``for security reasons''.
\nInstead they have posted a challenge to the cryptology community to find a new different single-block collision attack for MD5. 
\nThis paper answers that challenge by presenting a single-block collision attack based on other message differences together with an example colliding message pair.
\nThe attack is based on a new collision finding algorithm that exploits the low number of bitconditions in the first round.
\nIt uses a new way to choose message blocks that satisfy bitconditions up to step 22 and additionally uses three known tunnels to correct bitconditions up to step 25.
\nThe attack has an average runtime complexity equivalent to $2^{49.8}$ calls to MD5's compression function.