1. What have the authors contributed in "Linear-time zero-knowledge proofs for arithmetic circuit satisfiability∗" ?
First, the authors give a zero-knowledge proof for arithmetic circuit satisfiability in an ideal linear commitment model where the prover may commit to secret vectors of field elements, and the verifier can receive certified linear combinations of those vectors.. Second, the authors show that the ideal linear commitment proof can be instantiated using error-correcting codes and non-interactive commitments.
read more
2. What is the way to get a linear-time public-coin commitment scheme?
if the authors instantiate the hash function with the one by Applebaum et13al. [AHI+17], which is public coin, the authors obtain a linear-time public-coin statistically hiding commitment scheme.
read more
3. What is the way to get a linear-time computable commitment?
Using the lineartime computable pseudorandom number generators of Ishai et al. [IKOS08] the authors get linear-time computable statistically binding commitments.
read more
4. What is the communication complexity of proofs with unconditional soundness?
The communication complexity of their proofs with unconditional soundness is only O(N) field elements, while their arguments with computational soundness have sub-linear communication of poly(λ) √
read more
![Fig. 5: Vectors vτ organized in matrix V are encoded row-wise as matrix E = ẼC(V ;R). The vertical line in the right matrix and vector denotes concatenation of matrices respectively vectors. The prover commits to each column of E. When the prover given q wants to reveal the linear combination v(q) = qV she also reveals r(q) = qR. The verifier now asks for openings of 2λ columns J = {j1, . . . , j2λ} in E and verifies for these columns that qE|J = ẼC(v(q); r(q))|J . To avoid revealing any information about EC(V ), we must ensure that ∀j ∈ [n] : j ∈ J ⇒ j + n /∈ J . If the spot checks pass, the verifier believes that v(q) = qV .](/figures/fig-5-vectors-vt-organized-in-matrix-v-are-encoded-row-wise-2v55c3sj.webp)
