Lwe-Based Single Noisy Linear Equations for Public Key Over Integer Encryption

In this work, we introduce a novel post-quantum public key encryption scheme over integers, leveraging a hybrid approach that combines large random numbers with the Learning With Errors (LWE) system. The scheme addresses the security challenges posed by quantum computing advancements, aiming to provide a robust solution resistant to quantum-based attacks. By using the unknown random number hardness assumption with enhancements to the traditional LWE framework and operating directly on integers, this approach ensures a high level of cryptographic security while maintaining computational efficiency. Extensive theoretical and experimental analyses demonstrate that the proposed encryption system achieves state-of-the-art performance: encryption execution time as low as$2.45 \times 10^{-5}$seconds, decryption time of$4.47 \times 10^{-5}$seconds, and an integrity check time of$5.30 \times 10^{-5}$seconds. Moreover, the ciphertext size is reduced to only 1330 bits while maintaining a 256 -bit security level, representing a significant reduction in storage requirements compared to conventional lattice-based approaches. These results confirm that our scheme not only provides strong quantum-resistant security guarantees but also delivers excellent efficiency and scalability, making it a viable candidate for secure communications in bandwidth-limited and resource-constrained environments in the quantum era.

• post-quantum cryptography
• public-key encryption
• learning with errors
• lattice-based cryptography
• ciphertext size reduction
• quantum resistance
• resource-constrained environments

• 9 — الصناعة والابتكار والبنية التحتية

• Cryptography and Data Security
• Quantum Information and Cryptography
• Cryptography and Residue Arithmetic
• post-quantum cryptography
• public-key encryption
• learning with errors
• lattice-based cryptography
• ciphertext size reduction
• quantum resistance
• resource-constrained environments
• Artificial Intelligence
• Information Systems
• Computer Science