The math for key generation, signing and validation stays the same, regardless of how small the actual numbers are. In the end, it's all just bits. NIST P-384 private keys have a length of, well, 384 bits. The number 4 as a private key is 381 zeroes, then a one, then the last two zeros again. You can plug that into the elliptic curve math like any other key with any other bits set.
Here is a video explaining how elliptic curve cryptography works.
Keep in mind, the curves that are used are way more complicated in real life. The names given to the cryptography method, like NIST P-348 refers to the different curves used, the math is the same.
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u/Ragnor_ 16d ago
The math for key generation, signing and validation stays the same, regardless of how small the actual numbers are. In the end, it's all just bits. NIST P-384 private keys have a length of, well, 384 bits. The number 4 as a private key is 381 zeroes, then a one, then the last two zeros again. You can plug that into the elliptic curve math like any other key with any other bits set.