There could be double-tree PKI, where nodes in the tree are represented by two key pairs in different kinds of key spaces, with the different signatures terminating in two ephemeral key pairs, which are then used for key derivation, and the subsequent secret perhaps concatenated and boosted into a higher key space? The complexity would be mind boggling. And, weaknesses in one half of the tree could translate into a security reduction on the final symmetric key, so it would have to be way over powered to be effective.
Not a simple problem to solve.
Ignoring quantum computing, doubling up algorithms doesn't really protect you against unknown unknowns all that much as there is a good chance that a massive flaw in one of them could apply to the others (since they are all somewhat based on the same "problem").
When you start layering lattice based crypto with traditional crypto the payoff might change and make it more viable.
How would you propose to securely exchange the keys for the several algorithms? If there is enough meta or implied information for you to know what algorithms are used, an attacker would also know what algorithms are in use.
The obstacle isn't lack of randomness or an excess of decipherability but not using a quantum resistant algorithm.
If you're using encryption to keep your data safe (e.g. local files, full disk encryption), then you don't actually need asymmetric encryption.
Additionally... unless you generated all the bytes you are encrypting yourself without transmitting them over a network at any time... e.g. video/pictures you took yourself and then stored to your own encrypted disk, your data could be compromised by quantum-breakable encrypted communication protocols at the time of transmission. I would wager that most data worth surveilling goes over the network at some point using TLS.
Done right, this means quantum won't get you access to dropbox-like stuff. (Dropbox itself probably doesn't work like that, it'll store the symmetric keys server side somehow.)
There's no encryption there at all, except TLS in transit.
Eg think you want to encrypt your logs: with asymmetric encryption you can store the public keys on all your servers, encrypt your logs as you generated them and forget the plain text as soon as possible. You keep your private key hidden away on a secure server, and only use it when you actually want to look at your logs (which doesn't happen all that often).
Contrast with deriving a key using cryptographic primitives, which can accept low-quality randomness (as long as there is sufficient entropy), that can be easily and transparently collected.
But that was never the problem. The problem is, now what? To use this OTP you need to securely deliver pads to everybody you'll ever send a message to. So, OTP is practical for a handful of secret agents who'll receive messages of a few dozen words per year from a single controller, and useless for most of us in the real world.
_This_ problem is why we have public key cryptography.
The only thing that OTP buys you is that you can exchange the pads at your convenience any time before.
With a few GB (a couple bucks in a supermarket will buy a 8GB usb stick) you can communicate in text about 16 thousand books worth of words.
In other words, to deplete the pad you would have to write sixteen thousand books.
I think that's pretty convenient, as far as literally unbreakable encryption goes!
It's just that key-sharing is basically the most complicated and vulnerable part of modern cryptography.
It's really cheap to store ALL phone calls these days, and just "playback" when you get the legal search warrant.
https://wiki.strongswan.org/projects/strongswan/wiki/IKEv2Ci...
http://www.mail-archive.com/cryptography@metzdowd.com/msg123...
https://www.schneier.com/academic/paperfiles/paper-ipsec.pdf
Conclusions
We are of two minds about IPsec. On the one hand, IPsec is far better than any IP security protocol that has come before: Microsoft PPTP, L2TP, etc.
On the other hand, we do not believe that it will ever result in a secure operational system.
It is far too complex, and the complexity has lead to a large number of ambiguities, contradictions, inefficiencies, and weaknesses.
It has been very hard work to perform any kind of security analysis; we do not feel that we fully understand the system, let alone have fully analyzed it.