This extended abstract proposes a general construction for fast and secure nm-bit collision-resistant compression functions based on error-correcting codes and m-bit collision-resistant compression functions. This leads to simple and practical hash function constructions based on block ciphers such as DES and AES. Under reasonable assumptions about the underlying compression function and/or block cipher, it is proved that the new hash functions are collision resistant. The constructions allow for a large degree of internal parallelism.