One of the world’s top cryptographers believes that Satoshi Nakamoto chose Bitcoin’s (BTC) elliptic curve either for its efficiency or because it may offer a secret backdoor.
A Bitcoin public key is created by applying elliptic-curve cryptography to the private key. One can easily create a public key from the private key, but it is impossible to go in the reverse direction. Unless, of course, Bitcoin’s elliptic curve is compromised.