Reversing Eight Rounds of SHA-256

This paper demonstrates a method to deterministically reverse the first eight rounds (iterations) of the SHA-256 compression function. By tracking the propagation of a single message schedule word through the internal state and expressing its effect algebraically across rounds, we isolate and recover its original value from the final state. The results indicate that for eight rounds of SHA-256, the function remains fully invertible, with each round preserving enough structural information to reconstruct the original input. When reduced to eight rounds, SHA-256 no longer satisfies the criteria of a one-way function, but instead exhibits behavior more akin to a reversible transformation. The reversibility framework introduced here may also extend to SHA-512.