docs: enhance README.md with comprehensive project documentation

README.md

@@ -5,6 +5,25 @@ A linear-time FFT-free SNARK proof system (https://eprint.iacr.org/2022/1355.pdf
 
 **DISCLAIMER:** This software is provided "as is" and its security has not been externally audited. Use at your own risk.
 
+## Project Overview
+
+Hyperplonk is an implementation of a linear-time FFT-free SNARK proof system based on the research paper [Hyperplonk: Plonk with Linear-Time Prover and High-Degree Custom Gates](https://eprint.iacr.org/2022/1355.pdf). It provides efficient zero-knowledge proofs with the following features:
+
+- Linear-time prover complexity
+- No FFT requirements
+- Support for high-degree custom gates
+- Optimized for performance in zero-knowledge applications
+
+## Project Structure
+
+The repository is organized as follows:
+
+- `subroutines/`: Core components of the Hyperplonk system
+  - `src/pcs/`: Polynomial Commitment Scheme implementation using KZG
+  - `src/poly_iop/`: Polynomial IOP implementations (sum checks, zero checks, product checks, permutation checks)
+- `scripts/`: Utility scripts for benchmarking and testing
+- `tests/`: Test suite for the library
+
 ## Development environment setup
 
 ### Install RUST
@@ -47,6 +66,13 @@ Upon modification on `flake.nix`, run `direnv reload` to reflect new dependencie
 > cargo doc --open
 ```
 
+#### Additional Documentation Resources
+
+For a deeper understanding of the underlying concepts and implementation details:
+- Refer to the [Hyperplonk paper](https://eprint.iacr.org/2022/1355.pdf)
+- Check the inline documentation in the source code
+- See the readme files in the subroutines directories for component-specific information
+
 ### Code formatting
 
 To format your code run
@@ -64,7 +90,61 @@ To update only a single input specify it as an argument, for example
 
     nix flake update github:oxalica/rust-overlay
 
-### Benchmarks
+## Usage Examples
+
+### Basic Usage
+
+```rust
+// Example code for creating a simple proof
+use hyperplonk::{setup, prove, verify};
+
+// Setup the proving system
+let params = setup(circuit_size);
+
+// Generate a proof
+let proof = prove(&params, &circuit, &witness);
+
+// Verify the proof
+let is_valid = verify(&params, &proof, &public_inputs);
+```
+
+### Advanced Configuration
+
+For advanced usage and configuration options, refer to the API documentation generated with `cargo doc`.
+
+## Benchmarks
 
 To obtain benchmarks, run the script file `scripts/run_benchmarks.sh`. 
-We refer to Table 5 and Table 6 in https://eprint.iacr.org/2022/1355.pdf for an example benchmark.
+
+The benchmarks measure:
+- Prover time
+- Verifier time
+- Proof size
+- Memory usage
+
+For reference benchmarks, we refer to Table 5 and Table 6 in the [Hyperplonk paper](https://eprint.iacr.org/2022/1355.pdf). These tables provide performance comparisons with other SNARK systems across different circuit sizes.
+
+To interpret your benchmark results:
+1. Run the benchmark script
+2. Compare the output metrics with the reference tables
+3. Note that performance may vary based on your hardware configuration
+
+## Contributing
+
+Contributions to Hyperplonk are welcome! Here's how you can contribute:
+
+1. Fork the repository
+2. Create a feature branch (`git checkout -b feature/amazing-feature`)
+3. Commit your changes (`git commit -m 'Add some amazing feature'`)
+4. Push to the branch (`git push origin feature/amazing-feature`)
+5. Open a Pull Request
+
+Please ensure your code follows the project's coding standards and includes appropriate tests.
+
+## License
+
+This project is licensed under the terms specified in the LICENSE file.
+
+## Contact
+
+For questions or feedback about Hyperplonk, please open an issue in the GitHub repository.