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(There are other emergencies that could bring us to this point. One is a fire, which could result from machinery shorting. Another is a toxic ammonia leak. But these are even more unlikely.)
The objective is a tall order. The quantum-resistant cryptographic data needed to transparently publish TLS certificates is roughly 40 times bigger than the classical cryptographic material used today. Today’s X.509 certificates are about 64 bytes in size, and comprise six elliptic curve signatures and two EC public keys. This material can be cracked through the quantum-enabled Shor’s algorithm. Certificates containing the equivalent quantum-resistant cryptographic material are roughly 2.5 kilobytes. All this data must be transmitted when a browser connects to a site.