# Unconditional authentication

I have a few questions regarding functions:

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

1. $\;\;\;$ Sure. $\:$ The simplest way is to OTP-encrypt the
$\;\;\;$ output of an almost xor-universal hash family.

2. $\;\;\;$ 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$(x)\hspace{.04 in}||\hspace{.04 in}y \:\:\:\:$.)

3. $\;\;\;$ Yes.

4. $\;\;\;$ 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.

• So a universal hash function is not cryptographically secure (pre/second/collision resistant). Is it actually multiple hash functions together so could not become a SHA? In addition after looking this up I found a paper that said to MAC-THEN-ENCRYPT would provide unconditional security. researchgate.net/publication/… , is your suggestion better? In addition why strongly universal is there not an actually universal family? – dylan7 Jul 17 '15 at 1:14
• Yes. $\:$ My suggestion (now removed) was worse. $\:$ All strongly universal hash families $\hspace{1.27 in}$ are universal hash families. $\;\;\;\;$ – user991 Jul 17 '15 at 1:37