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It's a simple sequence of opcodes: https://en.bitcoin.it/wiki/Script The code has been thoroughly audited by many people with substantial experience. Finding an important flaw in Bitcoin would be a major feather in any Whitehat's cap, and a major skull on the mantle for any blackhat.

Script adds extreme flexibility to Bitcoin, allowing the complete decentralization of services which would otherwise require trusted servers like escrow. It is statically validated and purposefully not turing complete. For extra conservativeness scripts not matching a set of standard forms are ignored by the unmodified reference software until transactions show up in blocks.

This is important because its what makes it possible to build other safe distributed transaction systems on top of Bitcoin... it's also what will allow Bitcoin to backwards compatibly upgrade its signing primitives if ECDSA begins looking weak.

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