fix Motivation section

neps/nep-0488.md

@@ -37,15 +37,15 @@ 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 —*** sum the signed points from $G_1$ on an elliptic curve. This function is useful for the aggregation of public keys in BLS Signature. It can be used for simple addition in $G_1$. Separate from the multiexp function due to the gas cost.
-- ***bls12381_g2_sum —*** sum the signed points from $G_2$ on an elliptic curve. This function is useful for the aggregation of signatures in BLS Signature. It can be used for simple addition in $G_2$. Separate from the multiexp function due to the gas cost.
-- ***bls12381_g1_multiexp —*** for points $g_i \in G_1$ and scalars $s_i$ calculate $\sum g_i s_i$. It can be used to multiply a group element by a scalar. 
-- ***bls12381_g2_multiexp —*** for points $g_i \in G_2$ and scalars $s_i$ calculate $\sum g_i s_i$. It can be used to multiply a group element by a scalar.
-- ***bls12381_map_fp_to_g1 —*** maps base field element into the $G_1$ point. It does not perform mapping of the byte string into field elements.
-- ***bls12381_map_fp2_to_g2 —*** maps extension field element into the $G_2$ point. It does not perform mapping of the byte string into extension field elements. We require this function to efficiently map a message into a group element. We don't implement hash_to_field[^60] function, because it can be done inside a contract and different hashing algorithms can be used.
-- ***bls12381_decompress_g1 —*** decompresses the points from $G_1$ provided in the compressed form. Some protocols provide points on the curve in the compressed form (e.g., the light client updates in Ethereum 2.0), and decompressing is a time-consuming operation. All the other functions in this NEP accept only decompressed points to be simple and to have optimized gas consumption.
+- ***bls12381_g1_sum —*** sum the signed points from $G_1$ on an elliptic curve. This function is useful for aggregating public keys in BLS Signature. 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 —*** sum the signed points from $G_2$ on an elliptic curve. This function is useful for aggregating signatures in BLS Signature. 
+- ***bls12381_g1_multiexp —*** for points $g_i \in G_1$ and scalars $s_i$ calculate $\sum g_i s_i$. This operation can be utilized to multiply a group element by a scalar. 
+- ***bls12381_g2_multiexp —*** for points $g_i \in G_2$ and scalars $s_i$ calculate $\sum g_i s_i$. 
+- ***bls12381_map_fp_to_g1 —*** maps a base field element into the $G_1$ point. It does not perform the mapping of the byte string into field elements.
+- ***bls12381_map_fp2_to_g2 —*** maps an extension field element into the $G_2$ point. It does not perform the mapping of the byte string into extension field elements. We need this function to efficiently map a message into a group element. We are not implementing the hash_to_field[^60] function because it can be executed within a contract and various hashing algorithms can be applied.
+- ***bls12381_decompress_g1 —*** decompresses the points from $G_1$ provided in the compressed form. Certain protocols offer points on the curve in 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 the points from $G_2$ provided in the compressed form.
-- ***bls12381_pairing_check —*** verifying that $\prod e(p_i, q_i) = 1$, where $e$ is a pairing operation and $p_i \in G_1 \land q_i \in G_2$. Used to verify BLS signatures or zkSNARKs. 
+- ***bls12381_pairing_check —*** verifying 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]:
 
@@ -66,8 +66,9 @@ Both zkSNARKs and BLS signatures can be implemented alternatively by swapping G1
 Therefore, all functions have been implemented for both G1 and G2.
 
 An analogous proposal, EIP-2537[^15], exists in Ethereum. 
-The functions here have been designed considering compatibility with Ethereum's proposal. 
-This design approach aims to ensure future ease in supporting corresponding precompiles for Aurora[^24].
+The functions here have been designed with compatibility 
+with Ethereum's proposal in mind. This design approach aims 
+to ensure future ease in supporting corresponding precompiles for Aurora[^24].
 
 ## Specification