Question about 1-of-many proofs

#1

I am reading both the papers on one-of-many proofs (mainly this one: https://eprint.iacr.org/2014/764.pdf) and trying to implement the protocol as in section 3 (see figure 2).

The paper specifies computing the polynomial coefficients p_i_k, but I cannot find any explanation for how those coefficients are to be calculated. Can anyone help me understand this?

Thanks!

#2

Look at the line above the equation (1) on page 9. For each i \in {0,...N-1}, the polynomial P_i(X) = \prod_{j=1}^n f_{j, i_j}. So you can compute each polynomal after constructing the f_i_j matrix as is described in the paper

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#3

Indeed! It seems so obvious upon re-reading :man_facepalming:

Thanks @ajivanyan!

#4

You may want to take a look at this instead which updates the scheme a little bit and is the one in use in Zcoin. https://eprint.iacr.org/2015/643

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#5

Thanks! That is very helpful.