In Jim Posen's note, the protocol ends with the verifier querying each polynomial M_i at
4/24/2024Multiple Sumcheck claims can be batched together by running the protocol over a random-linear combination of the input claims. The existing implementation of ppSNARK already includes this functionality, though we augmented it to handle instances defined over fewer variables.
12/13/2023Let’s assume our R1CS shape has 2^n variables, \ell public inputs (including the initial 1, or u), and 2^m constraints, where \ell < 2^n. Take N = \max\{2^{n+1}, 2^m\} as the size of the public parameters.
12/13/2023Lagrange Polynomial basics For $0 \leq i < 2^n$, define it's bit representation as $(i_0,\ldots, i_{n-1})$ such that $$ i = \sum_{k=0}^{n-1} i_k \cdot 2^{n-k-1} $$ Note that for $n' < n$, if $i <2^{n'}$ then its bit representation will look like $(0,\ldots,0,i_{n'-n},\ldots, i_{n-1})$, with $n-n'$ zeros in front. The Lagrange polynomials over ${0,1}^n$ are indexed by $0\leq i<2^n$, where $$ \begin{aligned}
11/26/2023or
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