minor corrections and additions

Author: curiecrypt

prover/README.md

@@ -32,4 +32,5 @@ You can also jump to following sections from following links:
 - Schnorr signature: [Schnorr][crate::docs::schnorr]
 - Ad-hoc threshold multi-signature: [ATMS][crate::docs::atms]
 - Rescue sponge hash function: [Rescue][crate::docs::rescue]
-- I/O specs and encoding: [I/O][crate::docs::encoding_io]
+- I/O specs and encoding: [I/O][crate::docs::encoding_io]
+- Flow of the functionality: [flow][crate::docs::flow]

prover/docs/docs-ecc.md

@@ -1,4 +1,12 @@
 # ECC Preliminaries
+This module includes a brief explanation of the elliptic curve cryptography primitives used in the library.
+- [Basic ECC Toolbox][crate::docs::ecc#basic-ecc-toolbox]
+- [Twisted Edward's Curve][crate::docs::ecc#twisted-edwards-curve]
+  - [EdDSA][crate::docs::ecc#eddsa---edwards-curve-digital-signature-algorithm]
+- [BLS12-381][crate::docs::ecc#bls12-381]
+  - [Pairings][crate::docs::ecc#pairing]
+- [Jubjub][crate::docs::ecc#jubjub]
+
 ## Basic ECC Toolbox
 - $p$: a large prime number.
 - $\mathbb{F}_p$: Finite field over prime $p$.
@@ -32,7 +40,7 @@ where $a, d \in \mathbb{F}_p$ and non-zero.
 $$(x_3, y_3) = \Bigg(\frac{x_1y_2 + y_1x_2}{1 + dx_1x_2y_1y_2}, \frac{y_1y_2 - ax_1x_2}{1 - dx_1x_2y_1y_2}\Bigg).$$
 
 
-### Edward's Curve Digital Signature Algorithm (EdDSA)
+### EdDSA - (Edward's Curve Digital Signature Algorithm)
 Let $B$ be the base point of $E_{E, a, d}$ with order $l$ and $H$ be a hash function with $2b-$bit output size where $2^{b-1} > p$.
 * $keygen$
     * **Input**: Security parameter $\lambda$.

prover/docs/docs-encoding-io.md

@@ -1,5 +1,10 @@
 Encoding and I/O requirements.
 
+This module includes the following:
+- [Commonly used types and structs][crate::docs::encoding_io#commonly-used-types-and-structs]
+- [Functions: I/O][crate::docs::encoding_io#functions-io]
+- [Encoding][crate::docs::encoding_io#encoding]
+
 # Commonly used types and structs
 ## Type Base
 Represents an element of the base field $\mathbb{F}_q$ of the Jubjub elliptic curve construction.

prover/docs/intro.md

@@ -57,6 +57,10 @@ This section includes the basic primitives of elliptic curve cryptography requir
   * Key generation, signing, and verification algorithms of Schnorr signature is given in [here][crate::docs::schnorr].
 * **ATMS:** 
   * We give a brief introduction to [ATMS][crate::docs::atms#atms-ad-hoc-threshold-multi-signatures] and explained the [SNARK-based ATMS with Schnorr setup][crate::docs::atms#snark-based-atms-with-schnorr-setup].
-* **Rescue sponge:** [Rescue][crate::docs::rescue]
-* **Encoding and I/O:** [Encoding and I/O][crate::docs::encoding_io]
-* **Flow:** [Flow][crate::docs::flow]
+* **Rescue sponge:** Rescue prime and Sponge function are explained [here][crate::docs::rescue].
+* **Encoding and I/O:** 
+This [section][crate::docs::encoding_io] contains commonly used types and structs in the library, input and output fields of the crucial functions, and encodings of the field elements.
+  * [Commonly used types and structs][crate::docs::encoding_io#commonly-used-types-and-structs]
+  * [Functions: I/O][crate::docs::encoding_io#functions-io]
+  * [Encoding][crate::docs::encoding_io#encoding]
+* **Flow:** Here we explained the generic [flow][crate::docs::flow] of the functionality.

prover/src/ecc.rs

@@ -1,4 +1,6 @@
 //! Elliptic curve operations.
+//!
+//! See the [Elliptic curve cryptography documentation][crate::docs::ecc].
 use std::fmt::Debug;
 
 use halo2_proofs::{

prover/src/rescue/mod.rs

@@ -1,4 +1,6 @@
 //! Modules for the rescue hash function.
+//!
+//! See the documentation of [Rescue Hash][crate::docs::rescue].
 
 mod primitive;
 mod rescue_counter_mode;

prover/src/signatures/atms.rs

@@ -1,6 +1,8 @@
 //! ATMS verifier.
 //!
 //! We implement a gate that verifies the validity of an ATMS signature given the threshold and public key commitment as Public Inputs.
+//!
+//! Background for SNARK-based ATMS with Schnorr setup can be found [here][crate::docs::atms].
 
 #![doc = include_str!("../../docs/signatures/atms/example.md")]
 

prover/src/signatures/mod.rs

@@ -1,4 +1,7 @@
-//! Schnorr-based Ad-hoc Threshold Multi-signature.
+//! SNARK-based Ad-hoc Threshold Multi-signature with Schnorr setup.
+//!
+//! - See the [documentation][crate::docs] for introduction to ATMS.
+//! - The flow of the functionality is given [here][crate::docs::flow].
 
 pub mod atms;
 pub mod primitive;

prover/src/signatures/schnorr.rs

@@ -27,8 +27,8 @@ pub type AssignedSchnorrSignature = (AssignedEccPoint, ScalarVar);
 /// Type of a Schnorr Signature
 ///
 /// Schnorr signature consists of
-/// - An affine point on jubjub curve: [AffinePoint]
-/// - A [Scalar] which is an element of the scalar field $\mathbb{F}_r$ of the Jubjub curve.
+/// - An affine point on jubjub curve: [AffinePoint][crate::docs::encoding_io#type-affinepoint]
+/// - A [Scalar][crate::docs::encoding_io#type-scalar] which is an element of the scalar field $\mathbb{F}_r$ of the Jubjub curve.
 pub type SchnorrSig = (AffinePoint, Scalar);
 
 /// Configuration for SchnorrVerifierGate
@@ -315,7 +315,8 @@ impl SchnorrVerifierGate {
 
     /// Assign a schnorr signature
     ///
-    /// Assign the [AffinePoint] and [Scalar] of the Schnorr signature
+    /// Assign the [AffinePoint][crate::docs::encoding_io#type-affinepoint] and
+    /// [Scalar][crate::docs::encoding_io#type-scalar] of the Schnorr signature
     /// to [witness_point][crate::ecc::chip::EccChip::witness_point()]
     /// and [witness_scalar_var][crate::ecc::chip::EccChip::witness_scalar_var()] respectively to the `ecc_gate`.
     pub fn assign_sig(