diff --git a/specs/ecc-proof.md b/specs/ecc-proof.md
index 83fe10036..b76f1ed68 100644
--- a/specs/ecc-proof.md
+++ b/specs/ecc-proof.md
@@ -1,52 +1,36 @@
 # Ecc Proof
 
-[Elliptic Curve Digital Signature Algorithm]: https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm
-
-According to the [Elliptic Curve Digital Signature Algorithm] (ECDSA), the signatures `(r,s)` are calculated via ECDSA from `msg_hash` and a `public_key` using the formula
-
-`(r,s)=ecdsa(msg_hash, public_key)`
-
-The `public_key` is obtained from `private_key` by mapping the latter to an elliptic curve (EC) point. The `r` is the x-component of an EC point, and the same EC point's y-component will be used to determine the recovery id `v = y%2` (the parity of y). Given the signature `(v, r, s)`, the `public_key` can be recovered from `(v, r, s)` and `msg_hash` using `ecrecover`.
-
+EccCircuit supports three ECC operations which are addition, multiplication and pairing. This circuit provides the correctness of `EccTable`.
 
 ## Circuit behavior
 
-SigTable built inside zkevm-circuits is used to verify signatures. It has the following columns:
-- `msg_hash`: Advice Column, the Keccak256 hash of the message that's signed;
-- `sig_v`: Advice Column, the recovery id, either 0 or 1, it should be the parity of y;
-- `sig_r`: Advice Column, the signature's `r` component;
-- `sig_s`: Advice Column, the signature's `s` component;
-- `recovered_addr`: Advice Column, the recovered address, i.e. the 20-bytes address that must have signed the message;
-- `is_valid`: Advice Column, indicates whether or not the signature is valid or not upon signature verification.
+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
+- `outx`: x-coordinate of output
+- `outy`: y-coordinate of output
+- `is_valid`: Indicates whether the operation is valid or not.
 
 Constraints on the shape of the table is like:
 
-| 0 op_type | 1 input_1     | 2 input_2     | 3 output      | 4 is_valid |
-| --------- | ------------- | ------------- | ------------- |  ---------- |
-|   $tag    | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} |    bool     |  
-
-* tag: ADD, MUL and PAIRING
+| 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    |  
 
-The Sig Circuit aims at proving the correctness of SigTable. This mainly includes the following type of constraints:
-- checking that the signature is obtained correctly. This is done by the ECDSA chip, and the correctness of `v` is checked separately;
-- checking that `msg_hash` is obtained correctly from Keccak hash function. This is done by lookup to Keccak table;
+- tag: `Add`, `Mul` and `Pairing`
 
 
 ## Constraints
 
-`assign_ecdsa` method takes the signature data and uses ECDSA chip to verify its correctness. The verification result `sig_is_valid` will be returned. The recovery id `v` value will be computed and verified.
-
-`sign_data_decomposition` method takes the signature data and the return values of `assign_ecdsa`, and returns the cells for byte decomposition of the keys and messages in the form of `SignDataDecomposed`. The latter consists of the following contents:
-- `SignDataDecomposed`
-    - `pk_hash_cells`: byte cells for keccak256 hash of public key;
-    - `msg_hash_cells`: byte cells for `msg_hash`;
-    - `pk_cells`: byte cells for the EC coordinates of public key;
-    - `address`: RLC of `pk_hash` last 20 bytes;
-    - `is_address_zero`: check if address is zero;
-    - `r_cells`, `s_cells`: byte cells for signatures `r` and `s`.
+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`.
 
-The decomposed sign data are sent to `assign_sign_verify` method to compute and verify their RLC values and perform Keccak lookup checks. 
 
 ## Code
 
-Please refer to `src/zkevm-specs/sig_circuit.py`
\ No newline at end of file
+Please refer to `src/zkevm-specs/ecc_circuit.py`
\ No newline at end of file
diff --git a/specs/tables.md b/specs/tables.md
index 4109b938e..553420e4e 100644
--- a/specs/tables.md
+++ b/specs/tables.md
@@ -383,10 +383,10 @@ NOTE:
 
 ## Elliptic Curve Table
 
-Proved by the Elliptic Curve circuit.
+Proved by the ecc_circuit. The circuit verifies the correctness of ECC operations.
 
-| 0 op_type | 1 input_a     | 2 input_b     | 3 output      | 4 is_valid |
-| --------- | ------------- | ------------- | ------------- |  ---------- |
-|   $tag    | $value{Lo,Hi} | $value{Lo,Hi} | $value{Lo,Hi} |    bool     |  
+| 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    |  
 
-- **tag**: supports `Add`, `Mul` and `Pairing`
+- tag: supports `Add`, `Mul` and `Pairing`
diff --git a/src/zkevm_specs/evm_circuit/table.py b/src/zkevm_specs/evm_circuit/table.py
index abe3003e3..ee1b39d48 100644
--- a/src/zkevm_specs/evm_circuit/table.py
+++ b/src/zkevm_specs/evm_circuit/table.py
@@ -555,6 +555,7 @@ class SigTableRow(TableRow):
     sig_r: Word
     sig_s: Word
     recovered_addr: FQ
+    is_valid: FQ
 
 
 @dataclass(frozen=True)
diff --git a/src/zkevm_specs/util/ec.py b/src/zkevm_specs/util/ec.py
index be1d93d81..876ee5103 100644
--- a/src/zkevm_specs/util/ec.py
+++ b/src/zkevm_specs/util/ec.py
@@ -33,10 +33,6 @@ def to_le_bytes(self) -> bytes:
     def to_be_bytes(self) -> bytes:
         return self.to_int_value().to_bytes(32, "big")
 
-    def add(self, other: WrongFieldInteger) -> int:
-        # Python will extend the size if it exceeds 32bytes. So, don't need to take care overflow here.
-        return self.to_int_value() + other.to_int_value()
-
 
 class Secp256k1BaseField(WrongFieldInteger):
     """