What is "auxiliary information" in context of cryptographic accumulators?

pe flag

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?

ru flag

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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