For any SHA-family of algorithms (including Keccak) except for SHA1, would it be theoretically possible for there to exist a pre-image a
whose hash digest b
is the pre-image to the hash digest c
which is the pre-image to a
thus completing a circle (i.e. circular hash or collision of pre-image a
with the digest a
)?
${{hash(A)\to B}}$, ${{hash(B)\to C}}$ , ${{hash(C)\to A}}$
Given the use of XOR and bit-rotations, as well as padding and pre-processing and the many steps involved in hash functions such as SHA256 or SHA512, would it be possible for the above circular hash scenario to exist? (despite the unlikelihood of it being found)
P.S. candidate values include an all-zero string for pre-image or digest, or any valid-length output (i.e. 256, 512).