There has been ongoing discussion in the

Internet Engineering Task Force (IETF)
about how to protect internet traffic against future quantum computers. So far,
that work has focused on key exchange as the most urgent problem; now,

a new IETF working group is looking at adopting post-quantum cryptography
for authentication and certificate transparency as well. The main challenge to
doing so is the increased size of
certificates - around 40 times larger. The techniques that the working group is
investigating
to reduce that overhead could have efficiency benefits for traditional
certificates as well.

https://lwn.net/Articles/1060941/
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