Commitment to a certain degree polynomial

[Fiono11]

Hello,

Does this scheme allow the commitment to a certain degree d polynomial, or only to a polynomial of at most degree D? In other words, can you verify the degree of the committed polynomial?

Thanks!

[Pratyush]

Just to clarify, you're asking whether, for some d < D, we can commit to a polynomial of degree d and in a manner that makes it verifiable that the resulting commitment is to a polynomial of a degree at most d?

If so, yes, the library supports that. When creating your polynomial, just provide d as the degree bound here:

https://github.com/scipr-lab/poly-commit/blob/77676213c10069b376960ab824ddcc436ac66a67/src/data_structures.rs#L92

[Pratyush]

@Fiono11 does this resolve your issue?

[Fiono11]

Hi! No, I was asking if you can commit to a polynomial of degree d and verify that its degree is exactly d instead of at most d.

[Fiono11]

Btw, can you make a proof evaluation of a point for a given commitment of a polynomial p(x) without sending the evaluation v (as in p(z) = v), but sending instead vG? Thanks!

[3for]

@Fiono11 I think it's possible, just treat the polynomial commitment as an inner product. See this paper Doubly-efficient zkSNARKs without trusted setup, the dot-product proof protocol maybe suitable。