Cryptography without assumptions -- seeking an overview
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.