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I am reading this paper "The security of Hidden Field Equations (HFE)"
and at the end of the page 4 the author wrote:

Thus, after all, this belief about every attack being kind of ”completely puzzled by the irreducible randomness of answers to all possible questions”, maybe it is not necessary at all to achieve security ?

I know what is irreducible randomness but sincerily I do not understand that sentence.

Could you explain me please what that sentence means?

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    $\begingroup$ Honestly, I don't understand it either. Maybe it needs more context (I haven't actually read the paper), or maybe something got lost in translation? $\endgroup$ – Ilmari Karonen Mar 3 '16 at 18:15
  • $\begingroup$ @juaninf: Could you explain what irreducible randomness is? I certainly don't know what it is. $\endgroup$ – kodlu Mar 3 '16 at 22:07
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I think the key to comprehending this passage is the first sentence of the paragraph it is in, which refers to a "random oracle paradigm". From wikipedia, a random oracle is essentially a black-box function; deterministic and repeatable, yet its output is indistinguishable from random noise. The random oracle paradigm is defining the security of a cryptographic primitive by comparing it to a random oracle, i.e. does it leak any information about its function such that its output can be distinguished from random noise. This, the paper argues, is a reasonable standard for symetric primitives, but unreasonable for asymmetric ones. The crux of their argument is, in essence, secure symmetric primitives have very complex internal function, but asymmetric primitives are comparable very simple. Thus, as the sentence you provide very unclearly states, it is unreasonable to think that an attacker would have no knowledge of the internal function of asymmetric primitives, and so it is not necessary that an asymetric primitive's output leak no information about its function, i.e. indistinguishable from random noise, for it to be secure.

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