Cryptography without assumptions -- seeking an overview Suppose $P = NP$ and a fast linear-time algorithm for SAT appears tomorrow.  Suddenly RSA is insecure, much of our modern communication system is broken, and we need to reconsider how to keep secrets from each other. 

Question: Is there a good single reference (or short list) to gain a big-picture view of what is possible in crypto (and in the allied field of "security") without intractability assumptions? This could save civilization one day, and would also be nice to peruse in the meantime. 

Discussion: Most of the cryptographic tasks we now study (OWFs, PRGs, PKE) are provably impossible in the $P = NP$ world (a world dubbed "Algorithmica" in an influential essay by Impagliazzo), but some things remain possible: communication with a one-time pad; distributed secret sharing; private info retrieval; and some other nice things.
(Certain kinds of physical mechanisms such as locked boxes, devices implementing oblivious transfer, and quantum states can also come in handy.  Of course there is always some kind of physical assumption about who can see what information.)

One can distinguish between information-theoretic security (which works against a computationally unbounded adversary) and "unconditional" security (which may require a bounded adversary, but still shows security under no unproven assumptions).  I'm most interested in the info-theoretic case.  

For starters, here is one bibliography of information-theoretic security (which, for my purposes, is unmanageably long and disparate).
The key phrases you are probably looking for are "information-theoretic cryptography" and "quantum cryptography".  Searching the literature on these topics will turn up lots of work of the sort you are looking for.  Some example highlights below:


For confidentiality: the one-time pad, the Wyner wiretap channel, secret sharing, quantum key exchange, etc.
For integrity and authentication: universal hash functions.
For anonymity: anonymous communication (e.g., DC nets, onion-based schemes, p2p networks based upon rapidly mixing random walks), distance bounding protocols.
For security based upon physical assumptions: PUFs (physically unclonable functions), integrity codes (Capkun et al.), quantum cryptography, security using TPMs or tamper-resistant hardware.


There are lots of papers on those topics; too many to summarize all the results in the literature.