doc: support multi-inputs for pairing

specs/ecc-proof.md

@@ -6,19 +6,22 @@ EccCircuit supports three ECC operations which are addition, multiplication and
 
 EccTable built inside zkevm-circuits is used to verify ECC operations. It has the following columns:
 - `op_type`: Types of ecc operations, `Add`, `Mul` and `Pairing`
-- `px`: x-coordinate of point 1
-- `py`: y-coordinate of point 1
-- `qx`: scalar number if `op_type` is `Mul` otherwise it's x-coordinate of point 2 
-- `qy`: zero if `op_type` is `Mul` otherwise it's y-coordinate of point 2
+- `px`: x-coordinate of point 1 if `op_type` is `Mul` or `Add` otherwise it's zero
+- `py`: y-coordinate of point 1 if `op_type` is `Mul` or `Add` otherwise it's zero
+- `qx`: x-coordinate of point 2 if `op_type` is `Add`. Scalar number if `op_type` is `Mul` otherwise it's zero
+- `qy`: y-coordinate of point 2 if `op_type` is `Add` otherwise it's zero
+- `input_rlc`: rlc of input data if `op_type` is `Pairing` otherwise it's zero
 - `outx`: x-coordinate of output
 - `outy`: y-coordinate of output
 - `is_valid`: Indicates whether the operation is valid or not.
 
+`Pairing` allows multiple input points, and `p` and `q` are not enough to represent multiple points so we introduce `input_rlc` to represent all the input points. Therefore, `input_rlc` is a non-zero value only when `op_type` is `Pairing` otherwise it should be zero.
+
 Constraints on the shape of the table is like:
 
-| 0 op_type | 1 px          | 2 py          | 3 qx          | 2 qy          | 2 outx        | 2 outy        | 4 is_valid |
-| --------- | ------------- | ------------- | ------------- | ------------- | ------------- | ------------- | ---------- |
-|   $tag    | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} |    bool    |  
+| 0 op_type | 1 px          | 2 py          | 3 qx          | 4 qy          | 5 input_rlc   | 6 outx        | 7 outy        | 8 is_valid |
+| --------- | ------------- | ------------- | ------------- | ------------- | ------------- | ------------- | ------------- | ---------- |
+|   $tag    | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} | $input_rlc    | $value{Lo,Hi} | $value{Lo,Hi} |    bool    |  
 
 - tag: `Add`, `Mul` and `Pairing`
 
@@ -27,8 +30,9 @@ Constraints on the shape of the table is like:
 
 This mainly includes the following type of constraints:
 - Checking `op_type` is one of `Add`, `Mul` or `Pairing`.
-- Checking p and q are valid curve points.
-- Checking the correctness amon p, q and out. This is done by `ECCVerifyChip`.
+- Checking p and q are valid curve points if `op_type` is `Add` or `Mul`, and `input_rlc` is zero.
+- Checking `input_rlc` is valid if `op_type` is `Pairing`, and p and q are zero.
+- Checking the correctness among p, q and out. This is done by `ECCVerifyChip`.
 
 
 ## Code

specs/tables.md

@@ -385,8 +385,9 @@ NOTE:
 
 Proved by the ecc_circuit. The circuit verifies the correctness of ECC operations.
 
-| 0 op_type | 1 px          | 2 py          | 3 qx          | 2 qy          | 2 outx        | 2 outy        | 4 is_valid |
-| --------- | ------------- | ------------- | ------------- | ------------- | ------------- | ------------- | ---------- |
-|   $tag    | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} |    bool    |  
+| 0 op_type | 1 px          | 2 py          | 3 qx          | 4 qy          | 5 input_rlc   | 6 outx        | 7 outy        | 8 is_valid |
+| --------- | ------------- | ------------- | ------------- | ------------- | ------------- | ------------- | ------------- | ---------- |
+|   $tag    | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} | $input_rlc    | $value{Lo,Hi} | $value{Lo,Hi} |    bool    |  
 
 - tag: supports `Add`, `Mul` and `Pairing`
+- input_rlc: only has value when `op_type` is `Pairing`