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How is the generator point G chosen in the secp256k1 curve used in Bitcoin?

Bitcoin Stack Exchange

Bitcoin News / Bitcoin Stack Exchange 154 Views

We don't know. The secp256k1 curve (and the corresponding generator) was defined and standardized by people at Certicom. I know people have inquired about its origins, but it appears those involved are simply not around anymore.

There is however an unsuual property that may give a hint about how it was constructed. If the point is multiplied by the multiplicative inverse of 2 (so effectively undoing a doubling operation), one gets the point with X coordinate 0x3b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63, an unfathomably small number (only 166 bits in size). Perhaps the generator was constructed by hashing some simple input, feeding it through a 160-bit hash function, prefixing it with 0x3b, constructing the point with the result as X coordinate, and then doubling it.

That said, it is believed that the choice of generator is irrelevant for security properties of schemes that only use one generator (like ECDSA, BIP340 Schnorr signatures, ECDH, ...).


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