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Consider from the Bitcoin white paper a graphic that includes dotted arrows, labeled "sign" and "verify":

enter image description here

What does it mean to "sign" and "verify", as outlined in this paper? Are the terms "private key" and "public key" used in the same way that they are in the RSA encryption algorithm?

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Yes. It means "sign" and "verify" exactly as in a public key system such as RSA. Bitcoin doesn't introduce new cryptographic primitives or notions; it simply combines existing ones in a novel way. So you would simply use a public key system such as RSA to implement those operations in Bitcoin. The actual algorithm used is ECDSA, but this predates Bitcoin by quite a while. Arguably the "break-through" in Bitcoin is a clever mix of existing cryptographic techniques and aligning incentives.

Another clever aspect is that Bitcoin solves a different problem than what cryptographers traditionally viewed as "digital cash". That is, Bitcoin doesn't meet all the desiderata that one would hope "digital cash" would have, but clearly it's a pretty effective solution to the colloquial meaning of "digital cash".

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  • $\begingroup$ Do you know what the "hash" designates in the picture? Is it just a label of the previous transaction? If so, how is it generated (within the context of RSA)? $\endgroup$ – George Jan 7 '18 at 4:17
  • $\begingroup$ It's a cryptographic hash function with inputs the previous transaction and the new owner's public key. Any cryptographic hash could be used but presumably Bitcoin as currently implemented uses SHA256 which it also uses for the proof of work. This has nothing to do with the public key cryptosystem (which also isn't RSA in the current implementation of Bitcoin). All of these cryptographic algorithms are black boxes as far as the abstract Bitcoin protocol is concerned. $\endgroup$ – Derek Elkins Jan 7 '18 at 4:56

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