https://github.com/kayabaNerve/fcmp-ringct/blob/divisor-paper/divisors.pdf posits a 7-multiplicative-constraint proof of scaling with a k
-bit scalar. This technique can be used to prove a Pedersen Commitment opens to a value within a i
-bit range more efficiently than traditional bit commitments.
- Perform a proof of scaling for a
k
-bit scalar and the blinding generatorH
(7 multiplicative constraints). - Perform a proof of scaling for an
i
-bit scalar and the binding generatorG
(7 multiplicative constraints). - Perform an incomplete addition (3 multiplicative constraints).
This makes the proof in total use 17 multiplicative constraints, not the traditional i
. It does require commiting to 2(k+i)
values however, where a vector commitment can have as many items as rows in the IPA multiplied by two, and each vector commitment grows the proof by 4 elements and itself.