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There is actually no strong reason SHA1 would not have worked also, hashcash relies only on the hash partial preimage resistance property (security up to hash-size, 160-bit with SHA1) and not birthday collision hardness (security up to 80-bit), so the SHA1 hash is big enough.Bitcoin is anyway built to 128-bit security because 256-bit ECDSA is used, which also offers 128-bit security.The attack on SHA1 and in principle other hashes of similar design like SHA256, was also the motivation for the NIST SHA3 design competition which is still ongoing.Once the NIST SHA3 contest has finalised, bitcoin might in the future consider adopting hashcash-SHA3 as a security upgrade (eg a single invocation of SHA3 vs a double invocation of SHA256).Never the less SHA256 is the correct and more conservative choice because even SHA1 has started to show some weakenesses, though only in birthday collision, not in 2nd-preimage.

It takes a lot of memory, but there are memory-time tradeoffs.Hashcash was also used by Hal Finney's bitcoin precursor RPOW as a way to mine coins.Wei Dai's B-money Proposal, and Nick Szabo's similar Bit Gold proposal bitcoin precursors, also were proposed in the context of hashcash mining.A comparable attack on SHA256 does not exist so far, however as the design of SHA256 is similar to SHA1 it is probably defensive for applications to use double SHA256.And this is what bitcoin does, it is not necessary given hashcash reliance on preimage security, but it is a defensive step against future cryptanalytic developments.

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