As a practical matter, revocation on the Web is handled mostly by centrally distributed revocation lists (CRLsets, CRLite, etc. [0]), so all you really need is:
(1) A PQ-secure way of getting the CRLs to the browser vendors.
(2) a PQ-secure update channel.
Neither of these require broad scale deployment.
However, the more serious problem is that if you have a setting where most servers do not have PQ certificates, then disabling the non-PQ certificates means that lots of servers can't do secure connections at all. This obviously causes a lot of breakage and, depending on the actual vulnerability of the non-PQ algorithms, might not be good for security either, especially if people fall back to insecure HTTP.
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As a practical matter, revocation on the Web is handled mostly by centrally distributed revocation lists (CRLsets, CRLite, etc. [0]), so all you really need is:
(1) A PQ-secure way of getting the CRLs to the browser vendors. (2) a PQ-secure update channel.
Neither of these require broad scale deployment.
However, the more serious problem is that if you have a setting where most servers do not have PQ certificates, then disabling the non-PQ certificates means that lots of servers can't do secure connections at all. This obviously causes a lot of breakage and, depending on the actual vulnerability of the non-PQ algorithms, might not be good for security either, especially if people fall back to insecure HTTP.
See: https://educatedguesswork.org/posts/pq-emergency/ and https://www.chromium.org/Home/chromium-security/post-quantum...
[0] The situation is worse for Apple.