On-Curve / Off-Curve

In elliptic curve cryptography, a point is 'on-curve' if it satisfies the curve equation (e.g., Ed25519) and can serve as a valid public key with a corresponding private key. An 'off-curve' point does not lie on the curve and has no associated private key. Solana Program Derived Addresses (PDAs) are deliberately generated as off-curve points by appending a bump seed, guaranteeing that no private key exists and only the owning program can sign for the address.