doc: add nicer example on landing to doc index.

Author: mmaker

src/lib.rs

@@ -13,17 +13,26 @@
 //!
 //! ---
 //!
-//! ## Key Features
-//!
-//! - **Composable**: Combine multiple proofs into compound statements
-//! - **Generic**: Works with any cryptographic group supporting the required operations
-//! - **Flexible Hashing**: Multiple hash function backends for different use cases
-//! - **Non-Interactive Ready**: Support for Fiat–Shamir transformation
-//!
-//! ---
-//!
 //! ## Basic Usage
 //!
+//! ```rust
+//! # use curve25519_dalek::ristretto::RistrettoPoint;
+//! # use curve25519_dalek::scalar::Scalar;
+//! # use group::Group;
+//!
+//! let mut instance = sigma_rs::LinearRelation::new();
+//! let mut rng = rand::thread_rng();
+//! let witness = vec![Scalar::random(&mut rng), Scalar::random(&mut rng)];
+//!
+//! let [var_x, var_r] = instance.allocate_scalars();
+//! let [var_G, var_H] = instance.allocate_elements();
+//! instance.allocate_eq(var_G * var_x + var_H * var_r);
+//! instance.set_elements([(var_G, RistrettoPoint::generator()), (var_H, RistrettoPoint::random(&mut rng))]);
+//! instance.compute_image(&witness);
+//! let narg_string: Vec<u8> = instance.into_nizk(b"your session identifier").unwrap().prove_batchable(&witness, &mut rng).unwrap();
+//! println!("{}", hex::encode(narg_string));
+//! ```
+//!
 //! The library provides building blocks for creating zero-knowledge proofs:
 //!
 //! 1. Define your mathematical relation using [`LinearRelation`]

src/tests/test_validation_criteria.rs

@@ -181,12 +181,10 @@ mod instance_validation {
         let mut rng = rand::thread_rng();
         let mut linear_relation = LinearRelation::new();
 
-
         let [x_var, y_var] = linear_relation.allocate_scalars();
         let [Z_var, A_var, B_var, C_var] = linear_relation.allocate_elements();
         linear_relation.append_equation(Z_var, x_var * A_var + y_var * B_var + C_var);
 
-
         let [x, y] = [Scalar::random(&mut rng), Scalar::random(&mut rng)];
         let Z = G::identity();
         let A = G::random(&mut rng);
@@ -252,7 +250,7 @@ mod proof_validation {
         assert!(nizk.verify_batchable(&proof).is_ok());
 
         // Test bitflips at various positions
-        for pos in 0 .. proof.len() {
+        for pos in 0..proof.len() {
             let original_byte = proof[pos];
 
             // Flip each bit in the byte