From [KPS] Network Security: Private Communications in a Public World, Problem 5.4-

In 5.2.4.2 Hashing Large Messages, we described a hash algorithm in which a constant was successively encrypted with blocks of the message. We showed that you could find two messages with the same hash value in about 232 operations. So we suggested doubling the hash size by using the message twice, first in forward order to make up the first half of the hash, and then in reverse order for the second half of the hash. Assuming a 64-bit encryption block, how could you find two messages with the same hash value in about 232 iterations? Hint: consider blockwise palindromic messages.