fix functions description

neps/nep-0488.md

@@ -36,29 +36,29 @@ we must efficiently verify BLS signatures based on BLS12-381, as these are the s
 
 In this NEP, we propose to add the following host functions:
 
-- ***bls12381_g1_sum —*** computes the sum of signed points from $G_1$ on an elliptic curve. This function is useful for aggregating public keys in the BLS signature scheme. It can be employed for simple addition in $G_1$. It is kept separate from the `multiexp` function due to gas cost considerations.
-- ***bls12381_g2_sum —*** computes the sum of signed points from $G_2$ on an elliptic curve. This function is useful for aggregating signatures in the BLS signature scheme. 
-- ***bls12381_g1_multiexp —*** calculates $\sum g_i s_i$ for points $g_i \in G_1$ and scalars $s_i$. This operation can be used to multiply a group element by a scalar. 
-- ***bls12381_g2_multiexp —*** calculates $\sum g_i s_i$ for points $g_i \in G_2$ and scalars $s_i$. 
+- ***bls12381_p1_sum —*** computes the sum of signed points from $E(F_p)$ elliptic curve. This function is useful for aggregating public keys in the BLS signature scheme. It can be employed for simple addition in $E(F_p)$. It is kept separate from the `multiexp` function due to gas cost considerations.
+- ***bls12381_p2_sum —*** computes the sum of signed points from $E'(F_{p^2})$ elliptic curve. This function is useful for aggregating signatures in the BLS signature scheme. 
+- ***bls12381_p1_multiexp —*** calculates $\sum g_i s_i$ for points $g_i \in E(F_p)$ and scalars $s_i$. This operation can be used to multiply a group element by a scalar. 
+- ***bls12381_p2_multiexp —*** calculates $\sum g_i s_i$ for points $g_i \in E'(F_{p^2})$ and scalars $s_i$. 
 - ***bls12381_map_fp_to_g1 —*** maps base field elements into $G_1$ points. It does not perform the mapping of byte strings into field elements.
 - ***bls12381_map_fp2_to_g2 —*** maps extension field elements into $G_2$ points.  This function does not perform the mapping of byte strings into extension field elements, which would be needed to efficiently map a message into a group element. We are not implementing the `hash_to_field`[^60] function because the latter can be executed within a contract and various hashing algorithms can be used within this function.
-- ***bls12381_decompress_g1 —*** decompresses points from $G_1$ provided in a compressed form. Certain protocols offer points on the curve in a compressed form (e.g., the light client updates in Ethereum 2.0), and decompression is a time-consuming operation. All the other functions in this NEP only accept decompressed points for simplicity and optimized gas consumption.
-- ***bls12381_decompress_g2 —*** decompresses points from $G_2$ provided in a compressed form.
+- ***bls12381_p1_decompress —*** decompresses points from $E(F_p)$ provided in a compressed form. Certain protocols offer points on the curve in a compressed form (e.g., the light client updates in Ethereum 2.0), and decompression is a time-consuming operation. All the other functions in this NEP only accept decompressed points for simplicity and optimized gas consumption.
+- ***bls12381_p2_decompress —*** decompresses points from $E'(F_{p^2})$ provided in a compressed form.
 - ***bls12381_pairing_check —*** verifies that $\prod e(p_i, q_i) = 1$, where $e$ is a pairing operation and $p_i \in G_1 \land q_i \in G_2$. This function is used to verify BLS signatures or zkSNARKs. 
 
 Functions required for verifying BLS signatures[^59]:
 
-- bls12381_g1_sum
-- bls12381_g2_sum
+- bls12381_p1_sum
+- bls12381_p2_sum
 - bls12381_map_fp2_to_g2
-- bls12381_decompress_g1
-- bls12381_decompress_g2
+- bls12381_p1_decompress
+- bls12381_p2_decompress
 - bls12381_pairing_check
 
 Functions required for verifying zkSNARKs:
 
-- bls12381_g1_sum
-- bls12381_g1_multiexp
+- bls12381_p1_sum
+- bls12381_p1_multiexp
 - bls12381_pairing_check
 
 Both zkSNARKs and BLS signatures can be implemented alternatively by swapping $G_1$ and $G_2$. 
@@ -495,7 +495,7 @@ The encoding rules for curve points and field elements align with the standards
 
 ### Host functions
 
-#### bls12381_g1_sum
+#### bls12381_p1_sum
 
 ***Description:***
 
@@ -585,13 +585,13 @@ Edge cases:
 ***Annotation:***
 
 ```rust
-pub fn bls12381_g1_sum(&mut self, 
+pub fn bls12381_p1_sum(&mut self, 
                        value_len: u64, 
                        value_ptr: u64, 
                        register_id: u64) -> Result<u64>;
 ```
 
-#### bls12381_g2_sum
+#### bls12381_p2_sum
 
 ***Description:***
 
@@ -620,18 +620,18 @@ The ERROR_CODE is returned.
 
 ***Test cases:***
 
-The test cases are identical to those of `bls12381_g1_sum`, with the only alteration being the substitution of points from $G_1$ and $E(F_p)$ with points from $G_2$ and $E'(F_{p^2})$.
+The test cases are identical to those of `bls12381_p1_sum`, with the only alteration being the substitution of points from $G_1$ and $E(F_p)$ with points from $G_2$ and $E'(F_{p^2})$.
 
 ***Annotation:***
 
 ```rust
-pub fn bls12381_g2_sum(&mut self, 
+pub fn bls12381_p2_sum(&mut self, 
                        value_len: u64, 
                        value_ptr: u64, 
                        register_id: u64) -> Result<u64>;
 ```
 
-#### ***bls12381_g1_multiexp***
+#### ***bls12381_p1_multiexp***
 
 ***Description:***
 
@@ -686,7 +686,7 @@ Edge cases:
 
 <ins>Tests for sum of two points</ins>
 
-These are identical test cases to those in the `bls12381_g1_sum` section.
+These are identical test cases to those in the `bls12381_p1_sum` section.
 
 - Generate random points P and Q, then compare the results with the sum function.
 
@@ -706,20 +706,20 @@ These are identical test cases to those in the `bls12381_g1_sum` section.
 
 <ins>Tests for error cases</ins>
 
-The same test cases as those in the `bls12381_g1_sum` section will be applied.
+The same test cases as those in the `bls12381_p1_sum` section will be applied.
 
 ***Annotation:***
 
 ```rust
-pub fn bls12381_g1_multiexp(
+pub fn bls12381_p1_multiexp(
         &mut self,
         value_len: u64,
         value_ptr: u64,
         register_id: u64,
 ) -> Result<u64>;
 ```
 
-#### ***bls12381_g2_multiexp***
+#### ***bls12381_p2_multiexp***
 
 ***Description:***
 
@@ -755,12 +755,12 @@ The ERROR_CODE is returned.
 
 ***Test cases:***
 
-The test cases are identical to those for `bls12381_g1_multiexp`, except that the points from $G_1$ and $E(F_p)$ are replaced with points from $G_2$ and $E'(F_{p^2})$
+The test cases are identical to those for `bls12381_p1_multiexp`, except that the points from $G_1$ and $E(F_p)$ are replaced with points from $G_2$ and $E'(F_{p^2})$
 
 ***Annotation:***
 
 ```rust
-pub fn bls12381_g2_multiexp(
+pub fn bls12381_p2_multiexp(
         &mut self,
         value_len: u64,
         value_ptr: u64,
@@ -978,7 +978,7 @@ pub fn bls12381_pairing_check(&mut self,
                               register_id: u64) -> Result<u64>;
 ```
 
-#### bls12381_decompress_g1
+#### bls12381_p1_decompress
 
 ***Description:***  The function decompresses compressed points from $E(F_p)$. It takes an arbitrary number of points $p_i \in E(F_p)$ in compressed format as input and outputs the same number of points from $E(F_p)$ in decompressed format. Further details about the decompressed and compressed formats are available in the Curve Points Encoding section.
 
@@ -1024,13 +1024,13 @@ The ERROR_CODE is returned.
 ***Annotation:***
 
 ```rust
-pub fn bls12381_decompress_g1(&mut self, 
+pub fn bls12381_p1_decompress(&mut self, 
                               value_len: u64, 
                               value_ptr: u64, 
                               register_id: u64) -> Result<u64>;
 ```
 
-#### bls12381_decompress_g2
+#### bls12381_p2_decompress
 
 ***Description:*** The function decompresses compressed points from $E'(F_{p^2})$. It takes an arbitrary number of points $p_i \in E'(F_{p^2})$ in compressed format as input and outputs the same number of points from $E'(F_{p^2})$ in decompressed format. For more information about the decompressed and compressed formats, refer to the Curve Points Encoding section.
 
@@ -1048,12 +1048,12 @@ The ERROR_CODE is returned.
 
 ***Test cases:***
 
-The same test cases as `bls12381_decompress_g1`, but with points from $G_2$, and the input length should be divisible by 96.
+The same test cases as `bls12381_p1_decompress`, but with points from $G_2$, and the input length should be divisible by 96.
 
 ***Annotation:***
 
 ```rust
-pub fn bls12381_decompress_g2(&mut self, 
+pub fn bls12381_p2_decompress(&mut self, 
                               value_len: u64, 
                               value_ptr: u64, 
                               register_id: u64) -> Result<u64>;