private key and public key

Personal rough understanding: two people, A and B, A wants to send an email to B:
1. A encrypts the email with B's public key, and B decrypts it with his own private key, so as to ensure that the email can only be known by B, ensuring security sex.
2. A encrypts the email with his own private key, and B decrypts it with A's public key, so that you can know that the email was sent by A, and ensure the source of the email.

Private key encryption must be decrypted with public key, and vice versa