A fast cryptographic hash of an input file using multiplication and permutation operations in a parallel processing environment. An example method includes updating an internal state for each of a plurality of packets, the packets being read from an input file. Updating the state for a packet can include injecting the packet into an internal state, mixing the bits of the internal state using multiplication, and shuffling the result of the multiplication so that bits with highest quality are permuted to locations that will propagate most widely in a next multiplication operation. The method also includes performing a reduction on the internal state and repeating the update of the internal state, the reduction, and the injecting a second time. The method may further include finalizing the internal state and storing a portion of the final internal state as a cryptographic hash of the input file.