Can Two Different Private Keys Generate the Same Public Key?
Theoretically, yes, but only if the private keys differ by a multiple of the base point's order (n). Since the private key is mathematically constrained to be a number between 1 and n-1, any number outside this range will wrap around, effectively generating the same public key.
However, in practice, all legitimate private keys are chosen within this range, ensuring a unique one-to-one mapping. Therefore, for all practical purposes in cryptocurrency, a unique private key generates a unique public key.
Glossar
Unique Private Key
Definition ⎊ A unique private key is a large, randomly generated secret number that forms the core component of an asymmetric cryptographic key pair.
Private Key
Ownership ⎊ The private key is the definitive proof of non-custodial ownership over the associated cryptocurrency or the collateral securing a derivative position.
Private Keys
Ownership ⎊ Private Keys are the secret cryptographic credentials that mathematically prove ownership and grant exclusive control over associated cryptocurrency addresses and the assets they secure.