Describe the algorithm for establishing an HTTPS connection.

An HTTPS connection is established via the TLS (Transport Layer Security) protocol over TCP. The process is roughly as follows:

1. The client initiates a TCP connection to the server on port 443.
2. The client sends a "ClientHello" to the server with supported TLS versions, cipher suites, and a random number.
3. The server responds with a "ServerHello", selecting encryption parameters and sending its certificate (usually X.509), containing the public key.
4. The client verifies the certificate: trust chain, validity period, domain match.
5. The client generates a secret (pre-master secret), encrypts it with the server's public key, and sends it.
6. Both parties compute the shared secret (master secret) based on the pre-master secret and random numbers.
7. Keys for encryption and MAC for symmetric encryption are generated from the master secret.
8. The client and server exchange Finished messages, confirming the successful setup of parameters.
9. After this, all traffic is encrypted and protected.

This is roughly how the TLS handshake occurs, ensuring confidentiality and authentication.