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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-#?
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  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.

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  • $\begingroup$ 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? $\endgroup$
    – dylan7
    Jul 17, 2015 at 1:14
  • $\begingroup$ Yes. $\:$ My suggestion (now removed) was worse. $\:$ All strongly universal hash families $\hspace{1.27 in}$ are universal hash families. $\;\;\;\;$ $\endgroup$
    – user991
    Jul 17, 2015 at 1:37

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