The Nutanix SSL certificate implementation supports two types of private keys: ECDSA (Elliptic Curve Digital Signature Algorithm) and RSA (Rivest–Shamir–Adleman). ECDSA is a type of elliptic curve cryptography which is widely used for its efficiency and security, while RSA is one of the oldest and most widely used asymmetric encryption algorithms. These key types ensure robust security for data transmission using SSL certificates.