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I have been reading a paper about accumulators (title of the paper: "Universal Accumulators with Efficient Nonmembership Proofs"). It mentions "auxiliary information" about a function, which I couldn't quite understand. Can anyone explain the term in this context?

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This will vary from construction to construction, but for the purposes of the scheme outlined in the paper where the function is $$f_N(g,x):=g^x\pmod N$$ (or similar) the auxiliary information is the prime factorisation of $N$ (see the second bullet of Construction 1) or equivalently the value of the Euler $\phi$-function of $N$ (see the first bullet of Construction 2).

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