During the TLS handshake process, there are multiple running hashes kept of the handshake data.
For TLS records, there's a MAC at the end of each record. The MAC is based on HMAC, the most efficient implemenation involves priming two hash states with the MAC secret in advance. So with send and receive, every TLS connection already has four open hash states.
You're right though that most implementations seem to buffer a full record's data too. One could probably avoid this overhead when sending TLS (if you knew a minimum length in advance).
Comments
During the TLS handshake process, there are multiple running hashes kept of the handshake data.
For TLS records, there's a MAC at the end of each record. The MAC is based on HMAC, the most efficient implemenation involves priming two hash states with the MAC secret in advance. So with send and receive, every TLS connection already has four open hash states.
You're right though that most implementations seem to buffer a full record's data too. One could probably avoid this overhead when sending TLS (if you knew a minimum length in advance).