Why does SHA-256d (double SHA-256) in Bitcoin have a constrained message schedule in the second hash?

Bitcoin mining uses SHA-256d: SHA-256(SHA-256(data)).

I recently discovered experimentally (IACR ePrint 2026/109079) that the second SHA-256 application has a structurally constrained message schedule:

  • The second hash always receives exactly 32 bytes (the first hash output) + fixed Merkle-Damgård padding
  • This makes W[8-15] in the second hash always constant (0x80000000... + length encoding)
  • Only 30 unique carry patterns exist in the second hash vs theoretical 2^64
  • Measurable cross-hash anti-correlation: 9.56σ (confirmed real, scales as √N)

My questions:

  1. Was this structural property of SHA-256d considered when Bitcoin adopted double-SHA-256? Or was it chosen purely for length-extension attack resistance?

  2. Is there any documentation of this constrained W-schedule effect in Bitcoin's design rationale?

  3. Does this property have any known implications for Bitcoin's security model beyond length-extension resistance?

The correlation is not exploitable (r=0.03, <0.1% variance explained), but it is a measurable deviation from ideal independence of the two hash applications.



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