What are public-key 

encryption algorithms? 

What are Public-Key Encryption Algorithms?

Public-key cryptography (asymmetric) uses encryption algorithms like RSA and Elliptic Curve Cryptography (ECC) to create the public and private keys. These algorithms are based on the intractability of certain mathematical problems. Problems that can be solved in theory (e.g., given infinite time), but which in practice take too long for their solutions to be useful are known as intractable problems.

With asymmetric encryption it is computationally easy to generate public and private keys, encrypt messages with the public key, and decrypt messages with the private key. However, it is extremely difficult (or impossible) for anyone to derive the private key based only on the public key.