Abstract

Quantum computing poses a significant threat to existing cryptography systems. Asymmetric algorithms are primarily targeted for tasks such as prime factorization and discrete logarithmic problems using Shor’s algorithm with the help of quantum computers. Symmetric algorithms, while more resistant, are also at risk due to Grover’s algorithm. These advances necessitate the development of post-quantum cryptography (PQC) algorithms to preserve data confidentiality in the emerging quantum era. A novel PQC algorithm was proposed based on polynomial interpolation in the floating-point domain. The method leverages the dynamic and scalable properties of polynomials to create a cryptosystem resistant to both classical and quantum attacks. The algorithm's implementation focuses on optimizing computational efficiency while maintaining robust security. The proposed algorithm underwent extensive performance analysis and was evaluated using the national institute of standards and technology (NIST) statistical test suite, demonstrating its great randomness and security by passing all 15 tests with a 100% success rate and an average P-value of 0.517. Additionally, a comparative evaluation with state-of-the-art PQC methods was conducted, and the 3-polynomial-based cryptography (3-PBC) algorithm demonstrated superior performance. It achieved a faster key generation speed of 163 µs compared to Kyber’s 308 µs, a compact key size of 156 bytes, and significantly reduced encryption/decryption times—1,545 µs and 1,297 µs, respectively—compared to 2,851 µs and 4,359 µs for Hamming Quasi-Cyclic (HQC)-128 cryptography, all while maintaining robust security and randomness characteristics. The results confirm the algorithm’s suitability as a secure and efficient post-quantum solution. Its successful compliance with NIST standards and favourable comparison with existing PQC schemes highlight its potential for real-world adoption.

Keywords

Post-quantum cryptography, Quantum computing, Polynomial interpolation, Security, NIST statistical test suite, Encryption and decryption performance.

Cite this article

Ramachandran RK, Hasija T, Singh B, Kaur A. An emergent paradigm of a post-quantum cryptography leveraging polynomial interpolations in the floating-point domain.International Journal of Advanced Technology and Engineering Exploration.2025;12(131):1-25

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