Does SHA256 round trip

Question

If you take a 32-bit sequence, and perform a CRC32 on it, you get another 32-bit sequence as the result; if you do CRC32 of this, you get another, and so on. It is easy to show that if you keep doing this, you end up with a single loop of 2^32 bit sequences, before starting over.

Simple question: does anyone know if the same holds true (or not) for SHA256, starting with a 256-bit sequence? Would a similar process cycle through a loop of all 2^256 possible 256-bit sequences before starting over? Or are there known (or likely) shorter loops within this hash?

Brian

Answer 1

SHA256 has not been designed to meet the property of 2^256 loop. However, as far as I know, nobody has proven there is no such loop. Also, there are not known any shorter loops because if anybody found some, then he would find also a collision and from the nature of the cryptographic hash function, it muse be difficult.

So, since nobody has not proven it, yes, there is a probability the 2^256 cycle would exists. However, it's extremely unlikely an I'm willing to bet my left testicle for it. :-)

Let me also note that, IMO to design a cryptographic hash function which has 2^256 loop would be extremely difficult even for the best crypto experts.