The following is taken from BIP-330 (aka Erlay):
A short ID sketch with capacity c consists of a sequence of c field elements. The first is the sum of all short IDs in the set, the second is the sum of the 3rd powers of all short IDs, the third is the sum of the 5th powers etc., up to the last element with is the sum of the (2c-1)th powers.
Why is it that the first c odd powers are picked instead of the first c? How is it that we can reconstruct those c elements from their first c odd power sums? It is more or less straightforward using Newton’s identities if we had their first c, but it is not obvious to me how to do so with just the odd ones.
