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    $\begingroup$ For anyone reading this: If you want strong security, I strongly recommend against creating your own schemes or modifiying existing ones. $\endgroup$ Commented Apr 13, 2016 at 10:09
  • $\begingroup$ The user didn't seem to want very strong security as he/she explicitly stated in the topic title that he was after cryptographic (or non-cryptographic) hashing functions. Having said this, yes by doing what I suggested you could actually weaken md5, but I don't think it would be to a state of complete breaking (the round functions are non-linear and are kinda algebraically ugly to treat nicely) - however - I didn't NOT fully studied this so I can't be sure. $\endgroup$ Commented Apr 13, 2016 at 10:16
  • $\begingroup$ Yes, I am clearly looking for some scheme that has been peer reviewed and shown to work in the above setting (most certainly, if such a scheme exists, it will be an algorithm family parameterized by the word size on which the operations work). $\endgroup$ Commented Apr 13, 2016 at 10:33