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I am reading this paper "The security of Hidden Field Equations (HFE)"
and at the end of the page 3 the author wrote:

The random oracle paradigm would be to ignore that the function formulae exist.

I know what is the random oracle paradigm but sincerily I do not understand why the
"The random oracle paradigm would be to ignore that the function formulae exist."
Could you explain me please what that sentence means?

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Random oracles are used in cryptographic proofs as a way to abstract away a complex function, making the analysis easier (ie "ignore the actual function, and model it as a random oracle instead").

In the paragraphs before the sentence you highlighted, they propose to measure the "complexity" of an equation / function by the degree of its multivariate polynomial representation over $GF(2)$.

In the context of the surrounding paragraphs, I would interpret that sentence to mean

The random oracle paradigm abstracts away the complexity of the function, which renders our complexity metric useless.

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  • $\begingroup$ it is my poor english? or there is help of the author to confuse everybody? $\endgroup$ – juaninf Mar 2 '16 at 21:01
  • $\begingroup$ No, I agree with you that the sentence could have been better worded. $\endgroup$ – Mike Ounsworth Mar 2 '16 at 21:05

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