Apply Vivek's Latex edits

Co-authored-by: Vivek Arte <46618816+vivek-arte@users.noreply.github.com>

Author: AntoineRondelet

zips/draft-approval.rst

@@ -26,7 +26,7 @@ The terms "Asset" and "ZSA" in this document are to be interpreted as described
 Abstract
 ========
 
-This ZIP proposes transaction user controls - a mechanism allowing recipients of shielded funds to actively participate in the transfer of Assets by approving or rejecting incoming transactions.
+This ZIP specifies user controls for transactions - a mechanism allowing recipients of shielded funds to actively participate in the transfer of Assets by approving or rejecting incoming transactions.
 
 Motivation
 ==========
@@ -79,9 +79,9 @@ Given the Orchard address of the recipient of the output note of an Orchard Acti
 2. The recipient executes the following steps:
     - $m \gets H(OrchardActionDescription)$
     - $r \overset{R}{\leftarrow} \mathbb{Z}_{r_{\mathbb{P}}}$, where $\mathbb{Z}_{r_{\mathbb{P}}}$ is the scalar field of Pallas [#protocol-pallas-vesta]_, and where $\overset{R}{\leftarrow}$ denotes a variable assignment uniformly at random from a given set.
-    - $u \gets [r]g_d$, a Pallas point
+    - $u \gets [r] \mathsf{g_d}$
     - $C \gets H(g_d, pk_d, u, m) \mod r_{\mathbb{P}}$, an element of Pallas' scalar field, and where $H$ is a secure hash function (e.g. SHA256 or Blake2)
-    - $s \gets r + C * ivk \mod r_{\mathbb{P}}$, an element of Pallas' scalar field
+    - $s \gets r + C \cdot ivk \mod r_{\mathbb{P}}$, an element of Pallas' scalar field
     - $\sigma_{approval} \gets (u, s)$
 
 , and sends $\sigma_{approval}$ to the sender (off-chain).
@@ -96,18 +96,18 @@ In other words, we want to prove that the approval signature is generated by the
 Doing so means that only the recipient of the note created in the Orchard Action can approve the payment.
 
 To achieve this, we look into the key structure of Zcash Orchard.
-We know that the Orchard address is of the form: $d | pk_d$.
+We know that the Orchard address is of the form: $(\mathsf{d}, \mathsf{pk_d})$.
 These 2 fields, the diversifier and the diversified address, are used by the sender when sending notes.
 
-Looking at the Orchard key components derivations, we know that $pk_d$ is derived as:
-$pk_d := KAOrchard.DerivePublic(ivk, g_d) = [ivk]g_d$, see [#protocol-orchard-keys]_ and [#protocol-key-agreement]_
+Looking at the Orchard key components derivations, we know that $\mathsf{pk_d}$ is derived as:
+$\mathsf{pk_d} =mathsf{KAOrchard.DerivePublic}(\mathsf{ivk}, \mathsf{g_d}) = [\mathsf{ivk}]\mathsf{g_d}$ [#protocol-orchard-keys]_```
 
-Given that $ivk$ is derived from the spending key of the recipient of the funds, we can prove that the recipient of the funds in an Orchard Action is approving the receipt of the funds, by using a proof of knowledge of $ivk$.
-Such proof of knowledge of $ivk$ can be obtained by using the Non-Interactive Schnorr Protocol. 
+Given that $\mathsf{ivk}$ is derived from the spending key of the recipient of the funds, we can prove that the recipient of the funds in an Orchard Action is approving the receipt of the funds, by using a proof of knowledge of $\mathsf{ivk}$.
+Such proof of knowledge of $\mathsf{ivk}$ can be obtained by using the Non-Interactive Schnorr Protocol. 
 
-In fact, such proof of knowledge of $ivk$ can be obtained by using a Schnorr Signature on the Action (the message) with $ivk$ as signing/secret key and $g_d$ as group generator.
+In fact, such proof of knowledge of $\mathsf{ivk}$ can be obtained by using a Schnorr Signature on the Action (the message) with $\mathsf{ivk}$ as signing/secret key and $\mathsf{g_d}$ as group generator.
 
-**Note:** Zcash Orchard already uses a Schnorr-based signature scheme instantiated with the Pallas curve (see RedPallas [#protocol-redpallas]_).
+**Note:** Zcash Orchard already uses a Schnorr-based signature scheme instantiated with the Pallas curve, $\mathsf{RedPallas}$ [#protocol-redpallas]_.
 As of NU6, RedPallas is used to instantiate $SpendAuthSig^{Orchard}$ and $BindingSig^{Orchard}$.
 
 Modifications to the Orchard Statement/Circuit