Optimizing RSA Algorithm for Polynomial Encryption

Discover effective methods to improve the execution speed of RSA for large polynomials. Uncover the benefits of hybrid encryption techniques. --- This video is based on the question https://stackoverflow.com/q/76908809/ asked by the user 'Aishwarya Menon' ( https://stackoverflow.com/u/16252888/ ) and on the answer https://stackoverflow.com/a/76909173/ provided by the user 'Frank Yellin' ( https://stackoverflow.com/u/6457407/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions. Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: Improving the Execution speed of RSA Algorithm for polynomials with large exponents Also, Content (except music) licensed under CC BY-SA https://meta.stackexchange.com/help/licensing The original Question post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/by-sa/4.0/ ) license, and the original Answer post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/by-sa/4.0/ ) license. If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com. --- Optimizing the RSA Algorithm for Polynomial Encryption In the world of cryptography, securing data through encryption is paramount. The RSA algorithm is one of the most widely used public-key cryptographic protocols, but as you increase the complexity of the data—like polynomials with large exponents—this method can become painfully slow. If you're facing issues with long encryption times, especially as your polynomial degree increases beyond 64, you're not alone. The Problem: Slow Execution Times with RSA You've implemented an RSA algorithm to encrypt coefficients of polynomials, and while it works efficiently for lower degree bounds, performance starts deteriorating as the degree increases. For instance, encrypting polynomials with a degree bound of 64 or higher often exceeds a frustrating one-hour processing time. This raises the question: How can we enhance the encryption speed of RSA for these larger polynomial exponents? The Solution: Embrace Hybrid Encryption Understanding the Shortcomings of Direct RSA Encryption The main issue lies in the fact that you're using RSA to directly encrypt larger payloads. While RSA is excellent for secure key exchange, it is not designed for encrypting large amounts of data due to its time complexity and the exponential growth in processing time with larger key sizes. Implementing a Hybrid Encryption Scheme Rather than relying solely on RSA for encrypting the polynomial coefficients, you should consider a hybrid approach: Generate a Symmetric Key: Create a random symmetric key using a secure algorithm (usually 256 or 512 bits). Encrypt the Symmetric Key with RSA: Use the RSA algorithm to encrypt this generated symmetric key. A key size of 2048 or even 4096 bits is sufficient for strong security. Encrypt the Payload using the Symmetric Key: Encrypt your polynomial coefficients using this symmetric key. Symmetric encryption algorithms, such as AES, are much faster for large data encryption. Transmit Securely: Send both the encrypted symmetric key (using RSA) and the encrypted polynomial coefficients (using symmetric encryption) to the receiving party. Summary of Steps Employ a random symmetric key for data encryption. Use RSA solely to secure the symmetric key. Use efficient symmetric algorithms for large data payloads. Design your messaging protocol carefully to ensure the receiver can validate the key. Benefits of This Method Speed: Encrypting payloads with symmetric algorithms is significantly faster than direct RSA encryption. Scalability: This approach accommodates much larger data sizes without a considerable decline in performance. Security: RSA will still maintain high levels of security for the symmetric keys, while the symmetric encryption secures the bulk of the data efficiently. Conclusion In conclusion, if you're struggling with the execution time of RSA for encrypting large polynomials, the key is to shift your strategy from direct encryption of large payloads to a hybrid encryption model. By combining the strengths of symmetric and asymmetric cryptography, you can ensure secure and efficient processing of polynomial data. By following these guidelines, you should see a substantial improvement in your encryption performance without compromising on security.