Update README.md

Signed-off-by: David Osipov <[email protected]>

Author: DavidOsipov

README.md

@@ -1,6 +1,6 @@
 # Post-Quantum Secure Feldman's Verifiable Secret Sharing
 
-[![Version](https://img.shields.io/badge/version-0.7.0--Alpha-blue)](https://github.com/davidosipov/feldman-vss-pq)
+[![Version](https://img.shields.io/badge/version-0.7.4a0-blue)](https://github.com/davidosipov/feldman-vss-pq)
 [![License](https://img.shields.io/badge/license-MIT-green)](LICENSE)
 ![Python Version](https://img.shields.io/badge/python-3.8+-blue.svg)
 [![Tests](https://github.com/davidosipov/feldman-vss-pq/actions/workflows/tests.yml/badge.svg)](https://github.com/davidosipov/feldman-vss-pq/actions/workflows/tests.yml)
@@ -9,43 +9,44 @@
 
 This library provides a Python implementation of Feldman's Verifiable Secret Sharing (VSS) scheme, designed with **post-quantum security** in mind.  It builds upon Shamir's Secret Sharing, adding mathematical verification to ensure the integrity of distributed shares, and uses hash-based commitments to resist quantum attacks.
 
-
 ## ATTENTION:
 
 This code was developed with the assistance of AI language models and has been supervised by a product manager (non-cryptographer and non-developer).  **The code has not undergone a formal security audit.** While every effort has been made to implement best practices for security and performance, it is **strongly recommended not to use this code in a production environment** without a thorough independent security review by qualified cryptography experts.  Use at your own risk.
 
-
 **Key Features:**
 
 *   **Post-Quantum Security:** Employs hash-based commitments (using BLAKE3 or SHA3-256) and large prime fields (minimum 4096 bits) to provide resistance against quantum computers.  No reliance on discrete logarithm problems.
-*   **Verifiable Secret Sharing:**  Allows participants to verify the correctness of their shares, ensuring that the dealer has distributed shares of a valid secret.
+*   **Verifiable Secret Sharing:** Allows participants to verify the correctness of their shares, ensuring that the dealer has distributed shares of a valid secret.
 *   **Fault Injection Countermeasures:** Includes redundant computation and checksum verification to mitigate fault injection attacks.
 *   **Efficient Batch Verification:** Optimized for verifying multiple shares simultaneously.
-*   **Serialization and Deserialization:**  Provides secure serialization and deserialization of commitment data, including checksums for integrity checks.
+*   **Serialization and Deserialization:** Provides secure serialization and deserialization of commitment data, including checksums for integrity checks and handling of extra entropy for low-entropy secrets.
 *   **Integration with Shamir's Secret Sharing:** Designed for seamless integration with a standard Shamir Secret Sharing implementation (specifically, it provides a helper function `create_vss_from_shamir`).
 *   **Zero-Knowledge Proofs:** Includes methods to generate and verify zero-knowledge proofs of polynomial knowledge and dual-commitment proofs (for integration with Pedersen VSS).
-*   **Byzantine Fault Tolerance:** Robust handling of malicious participants, including detection of equivocation and inconsistent shares.
-*   **Share Refreshing:** Implements an optimized version of Chen & Lindell's Protocol 5 for securely refreshing shares without changing the underlying secret, with enhancements for asynchronous environments.
+*   **Byzantine Fault Tolerance:** Robust handling of malicious participants, including detection of equivocation, inconsistent shares, and adaptive quorum-based detection during share refreshing.
+*   **Share Refreshing:** Implements an optimized version of Chen & Lindell's Protocol 5 for securely refreshing shares without changing the underlying secret, with enhancements for asynchronous environments and improved Byzantine fault tolerance.
 *   **Constant-Time Operations:** Utilizes constant-time comparison and exponentiation where appropriate to mitigate timing side-channel attacks.
-*   **Optimized Cyclic Group Operations:** Features an enhanced cyclic group implementation with caching and precomputation for improved performance.
+*   **Optimized Cyclic Group Operations:** Features an enhanced cyclic group implementation with a thread-safe LRU caching and precomputation for improved performance.
 *   **Comprehensive Error Handling:** Includes custom exceptions for security, parameter, verification, and serialization errors.
 *   **gmpy2-based Arithmetic:** Leverages the `gmpy2` library for high-performance, arbitrary-precision arithmetic, critical for cryptographic operations.
+*    **Deterministic Hashing:** Uses fixed-size integer representation for commitment generation, to be platform independent.
 
 **Dependencies:**
 
-*   **gmpy2:**  Required for efficient and secure large-number arithmetic.  (`pip install gmpy2`)
+*   **gmpy2:** Required for efficient and secure large-number arithmetic. (`pip install gmpy2`)
 *   **blake3:** (Highly Recommended) For fast and secure cryptographic hashing. (`pip install blake3`)
 *   **xxhash:** (Recommended) For high-performance checksums. (`pip install xxhash`)
 *   **msgpack:** For efficient and secure serialization. (`pip install msgpack`)
 
-If `blake3` is not available, the library will fall back to SHA3-256, but `blake3` is strongly recommended for performance and security.  If `xxhash` is not available, a cryptographic fallback (BLAKE3 or SHA3-256) will be used for checksums.
+If `blake3` is not available, the library will fall back to SHA3-256, but `blake3` is strongly recommended for performance and security. If `xxhash` is not available, a cryptographic fallback (BLAKE3 or SHA3-256) will be used for checksums.
 
 **Installation:**
 
 ```bash
 pip install feldman-vss-pq
 ```
+
 The source code is also available on Github:
+
 ```bash
 git clone https://github.com/davidosipov/feldman-vss-pq.git
 cd feldman-vss-pq
@@ -54,8 +55,8 @@ cd feldman-vss-pq
 **Basic Usage:**
 
 ```python
-from feldman_vss_pq import FeldmanVSS, get_feldman_vss, VSSConfig, CyclicGroup
-from shamir_secret_sharing import ShamirSecretSharing # Assuming you have a Shamir implementation
+from feldman_vss_pq import FeldmanVSS, get_feldman_vss, VSSConfig, CyclicGroup, create_vss_from_shamir
+from shamir_secret_sharing import ShamirSecretSharing  # Assuming you have a Shamir implementation
 
 # Example using a Shamir instance (replace with your actual Shamir implementation)
 shamir = ShamirSecretSharing(5, 3)  # 5 shares, threshold of 3
@@ -74,9 +75,9 @@ is_valid = vss.verify_commitments_with_proof(commitments, proof)
 print(f"Proof Verification: {is_valid}")  # Expected: True
 
 # Verify a share
-share_x, share_y = shares[1]  # Example share
+share_x, share_y = list(shares.items())[0]  # Example share, get first item
 is_share_valid = vss.verify_share(share_x, share_y, commitments)
-print(f"Share Verification: {is_share_valid}") # Expected: True
+print(f"Share Verification: {is_share_valid}")  # Expected: True
 
 # Serialize and deserialize commitments
 serialized = vss.serialize_commitments(commitments)
@@ -88,27 +89,28 @@ new_shares, new_commitments, verification_data = vss.refresh_shares(shares, 3, 5
 # ... further checks with verification_data ...
 
 # --- Example without Shamir ---
-# Example of direct usage (without Shamir)
-from your_module import MersennePrimeField  # Replace with your field implementation
+# Example of direct usage (without Shamir, you need a field implementation)
+
+#  from your_module import MersennePrimeField  # Replace with your field implementation
 
-field = MersennePrimeField(4096) # Using a 4096-bit prime
-vss = get_feldman_vss(field)
-coefficients = [field.random_element() for _ in range(3)]
-commitments = vss.create_commitments(coefficients)
+#  field = MersennePrimeField(4096)  # Using a 4096-bit prime
+#  vss = get_feldman_vss(field)
+#  coefficients = [field.random_element() for _ in range(3)]
+#  commitments = vss.create_commitments(coefficients)
 # ... (rest of the example similar to above)
 ```
 
 **Security Considerations:**
 
-*   **Prime Size:** This library defaults to 4096-bit primes for post-quantum security.  It enforces a minimum of 4096 bits.  Using smaller primes is *strongly discouraged* and will trigger warnings.
-*   **Safe Primes:** The library defaults to using safe primes (where `p` and `(p-1)/2` are both prime) to enhance security.
+*   **Prime Size:** This library defaults to 4096-bit primes for post-quantum security. It enforces a minimum of 4096 bits. Using smaller primes is *strongly discouraged* and will trigger warnings.
+*   **Safe Primes:** The library defaults to using safe primes (where `p` and `(p-1)/2` are both prime) to enhance security.  This can be configured.
 *   **Hash Algorithm:** BLAKE3 is the preferred hash algorithm for its speed and security.
-*   **Entropy:**  The library uses `secrets` for cryptographically secure random number generation.
-*   **Side-Channel Attacks:**  Constant-time operations are used where appropriate to mitigate timing attacks.
+*   **Entropy:** The library uses `secrets` for cryptographically secure random number generation.
+*   **Side-Channel Attacks:** Constant-time operations are used where appropriate to mitigate timing attacks.
 
 **Contributing:**
 
-Contributions are welcome!  Please see [CONTRIBUTING.md](CONTRIBUTING.md) for guidelines.
+Contributions are welcome! Please see [CONTRIBUTING.md](CONTRIBUTING.md) for guidelines (you'll likely want to create this file).
 
 **License:**
 
@@ -117,4 +119,3 @@ This project is licensed under the MIT License - see the [LICENSE](LICENSE) file
 **Author:**
 
 David Osipov ([email protected])
-