Unconditional authentication I have a few questions regarding universal-hash functions:


Is there a way universal hash functions can be used to provide unconditional authentication in the way the OTP provides unconditional security? 
Assuming a TRNG is used how could this be combined to form a perfect cryptosystem, assuming PSK's  are secured? 
Is there unconditional non-repudiation(acceptance by third-party) to go along with this? 
And lastly, why are these hash functions not used as a SHA-#?
$\;\;\;$ Sure. $\:$ The simplest way is to OTP-encrypt the

$\;\;\;$ output of an almost xor-universal hash family.
$\;\;\;$ That could be used for encrypt-then-MAC, where

$\;\;\;$ the MAC is applied to an ordered pair that indicates

$\;\;\;$ [the message number or how far into the pad to start] and the OTP ciphertext.

$\;\;\;$ (Presumably, the pairing function would be $\;\;\; \langle x,\hspace{-0.03 in}y\hspace{-0.03 in}\rangle \: \mapsto \; $prefixfree$(x)\hspace{.04 in}||\hspace{.04 in}y \:\:\:\:$.)
$\;\;\;$ Yes.
$\;\;\;$ The tightest way I'm aware of to get provable universality while still hopefully being

$\;\;\;$ second-preimage resistant is the trivial construction that just concatenates an output

$\;\;\;$ from a universal hash family with the output from a standard cryptographic hash function.