A distinguisher for SHA256 using Bitcoin (mining faster along the way)

The post analyzes Bitcoin mining data and the sparsity of SHA-256 inputs selected by difficulty, finding that valid blocks exhibit systematic bias in 32-bit nonce fields (especially bits 5–7), resulting in fewer set bits than random expectation and a skewed histogram. It claims this bias enables a distinguisher between SHA-256 and a random 256-bit permutation with ~2^80 evaluations and proposes a practical mining heuristic—skipping nonces with bits 5–7 set—to reduce hashing while retaining a disproportionate share of valid solutions.