Sketch serialization subcircuit subdirectory

msm/src/lib.rs

@@ -11,6 +11,7 @@ pub mod precomputed_srs;
 pub mod proof;
 pub mod prover;
 pub mod verifier;
+pub mod serialization;
 
 /// Domain size for the MSM project, equal to the BN254 SRS size.
 pub const DOMAIN_SIZE: usize = 1 << 15;

msm/src/serialization/README.md

@@ -0,0 +1,34 @@
+## Kimchi Foreign Field gate serialization subcircuit
+
+The 15/16 bulletproof challenges will be given as 88 limbs, the encoding used by Kimchi.
+A circuit would be required to convert into 15 bits limbs that will be used for the MSM algorithm.
+We will use one row = one decomposition.
+
+We have the following circuit shape:
+
+| $b_{0}$ | $b_{1}$ | $b_{2}$ | $c_{0}$ | $c_{1}$ | ... | $c_{16}$ | $b_{2, 0}$ | $b_{2, 1}$ | ... | $b_{2, 19}$ |
+| ------- | ------- | ------- | ------- | ------- | --- | -------- | ---------  | ---------  | --- | ----------- |
+| ...     | ...     | ...     | ...     | ...     | ... | ...      | ...        |  ...       | ... | ...         |
+| ...     | ...     | ...     | ...     | ...     | ... | ...      | ...        |  ...       | ... | ...         |
+
+We can suppose that $b_{2}$ is only on 80 bits as the input is maximum
+$BN254(\mathbb{F}_{scalar})$, which is 254 bits long.
+We will decompose $b_{2}$ in chunks of 4 bits:
+
+$$b_{2} = \sum_{i = 0}^{19} b_{2, i} 2^{4 i}$$
+
+And we will add the following constraint:
+
+1. For the first 180 bits:
+
+$$b_{0} + b_{1} 2^88 + b_{2, 0} * 2^{88 * 2} - \sum_{j = 0}^{11} c_{j} 2^{15 j} = 0$$
+
+2. For the remaining 75 bits:
+
+$$c_{12} + c_{13} * 2^{15} + c_{14} 2^{15 * 2} + c_{15} 2^{15 * 3} + c_{16} 2^{15 * 4} = \sum_{j = 1}^{19} b_{2, j} * 2^{4 j}$$
+
+with additional lookups.
+
+$b_{0}$, $b_{1}$ and $b_{2}$ are the decomposition on 88 bits given by the
+foreign field gate in Kimchi. The values $c_{0}$, $\cdots$, $c_{16}$ are the limbs
+required for the MSM circuit. Each limbs $c_{i}$ will be on 15 bits.

msm/src/serialization/columns.rs

@@ -0,0 +1,35 @@
+use crate::columns::ColumnIndexer;
+use crate::LIMBS_NUM;
+use crate::columns::Column;
+use kimchi::circuits::expr::ConstantExpr;
+use kimchi::circuits::expr::Expr;
+
+/// Columns for the circuit splitting the bulletproof challenges in limbs used
+/// by the MSM.
+pub enum DecompositionColumnIndexer {
+    KimchiLimbs(usize),
+    MSMLimbs(usize),
+    IntermediateKimchiLimbs(usize),
+}
+
+impl ColumnIndexer for DecompositionColumnIndexer {
+    fn ix_to_column(self) -> Column {
+        match self {
+            DecompositionColumnIndexer::KimchiLimbs(i) => {
+                assert!(i < 3);
+                Column::X(i)
+            }
+            DecompositionColumnIndexer::MSMLimbs(i) => {
+                assert!(i < LIMBS_NUM);
+                Column::X(3 + i)
+            }
+            DecompositionColumnIndexer::IntermediateKimchiLimbs(i) => {
+                assert!(i < 3 + LIMBS_NUM);
+                Column::X(3 + LIMBS_NUM + i)
+            }
+        }
+    }
+}
+
+pub type DecompositionExpr<F> = Expr<ConstantExpr<F>, Column>;
+

msm/src/serialization/mod.rs

@@ -0,0 +1 @@
+pub mod columns;