the most computationally expensive part of a tls session is the tls handshake, where the tls server (usually a webserver) and the tls client (usually a web browser) agree on a number of parameters that establish the security of the connection. during the tls handshake the server and the client establish session keys (symmetric keys, used for the duration of a given session), but the encryption and signature of the tls handshake messages itself is done using asymmetric keys, which requires more computational power than the symmetric cryptography used for the encryption/decryption of the session data.