  TLS can resume previous connections via abbreviated resumption handshakes
that significantly decrease the delay and save expensive cryptographic
operations. For that, cryptographic TLS state from previous connections is
reused. TLS version 1.3 recommends to avoid resumption handshakes, and thus the
reuse of cryptographic state, when connecting to a different hostname. In this
work, we reassess this recommendation, as we find that sharing cryptographic
TLS state across hostnames is a common practice on the web. We propose a TLS
extension that allows the server to inform the client about TLS state sharing
with other hostnames. This information enables the client to efficiently resume
TLS sessions across hostnames. Our evaluation indicates that our TLS extension
provides huge performance gains for the web. For example, about 58.7% of the
20.24 full TLS handshakes that are required to retrieve an average website on
the web can be converted to resumed connection establishments. This yields to a
reduction of 44% of the CPU time consumed for TLS connection establishments.
Furthermore, our TLS extension accelerates the connection establishment with an
average website by up to 30.6% for TLS 1.3. Thus, our proposal significantly
reduces the (energy) costs and the delay overhead in the encrypted web.
