Spartan

Spartan implementation

R1cs

$ A,B,C \in \mathbb F^{m \times n}$ and $Z = (w,1,x) \in \mathbb F^n $

$x \in \mathbb F^l$
$w \in \mathbb F^{n - l - 1}$

Commitment Scheme

For $X = \mathbb F^{n \times m}$ and $M_{ij} \in X$

$Setup(1^λ) \rightarrow pp$

pp

$Γ_1 \leftarrow \mathbb G_1^m$
$H_1 \leftarrow \mathbb G_1$
$Γ_2 \leftarrow \mathbb G_2^n$
$H_2 \leftarrow \mathbb G_2$

$Commit(pp;M_{ij}) \rightarrow (C,S)$

$(C,S) := (C,(r_{rows},r_{fin},V))$ for

$r_{rows} \leftarrow \mathbb F^n$
$r_{fin} \leftarrow \mathbb F$
$H_T \leftarrow e(H_1,H_2)$
$V_i \leftarrow Commit_{Pedersen}((Γ_1,H_1);M_{ij},r_{rows,i})$
$C \leftarrow Commit_{AFGHO}((Γ_2,H_T);V,r_{fin})$