Version 1
: Received: 23 September 2024 / Approved: 24 September 2024 / Online: 24 September 2024 (10:06:10 CEST)
How to cite:
Wang, Y.; Li, L.; Zhou, Y.; Zhang, H. A Comprehensive Review of MI-HFE and IPHFE Cryptosystems: Advances in Internal Perturbations for Post-Quantum Security. Preprints2024, 2024091874. https://doi.org/10.20944/preprints202409.1874.v1
Wang, Y.; Li, L.; Zhou, Y.; Zhang, H. A Comprehensive Review of MI-HFE and IPHFE Cryptosystems: Advances in Internal Perturbations for Post-Quantum Security. Preprints 2024, 2024091874. https://doi.org/10.20944/preprints202409.1874.v1
Wang, Y.; Li, L.; Zhou, Y.; Zhang, H. A Comprehensive Review of MI-HFE and IPHFE Cryptosystems: Advances in Internal Perturbations for Post-Quantum Security. Preprints2024, 2024091874. https://doi.org/10.20944/preprints202409.1874.v1
APA Style
Wang, Y., Li, L., Zhou, Y., & Zhang, H. (2024). A Comprehensive Review of MI-HFE and IPHFE Cryptosystems: Advances in Internal Perturbations for Post-Quantum Security. Preprints. https://doi.org/10.20944/preprints202409.1874.v1
Chicago/Turabian Style
Wang, Y., Ying Zhou and Huili Zhang. 2024 "A Comprehensive Review of MI-HFE and IPHFE Cryptosystems: Advances in Internal Perturbations for Post-Quantum Security" Preprints. https://doi.org/10.20944/preprints202409.1874.v1
Abstract
The RSA cryptosystem has long been a fundamental component of contemporary public key in- frastructure. However, recent developments in quantum computing and mathematical theory have introduced signicant challenges to its security. A fully operational quantum computer would allow for the application of Shor's algorithm, enabling the ecient factoring of large integers, thereby com- promising the integrity of RSA and other cryptographic methods dependent on discrete logarithms. Although Grover's algorithm poses a comparatively smaller threat to symmetric encryption systems, it still presents a vulnerability by accelerating key search processes. The looming threat from quan- tum technologies has driven a surge in research aimed at developing quantum-resistant cryptography. These eorts focus on cryptographic techniques grounded in error-correcting codes, lattice structures, and multivariate public key systems, all of which leverage the complexity of NP-hard problemssuch as solving multivariate quadratic equationsto preserve security in a post-quantum world. This pa- per reviews the current progress in quantum-resistant encryption methods, particularly emphasizing the role of robust trapdoor functions. Additionally, it provides a comprehensive analysis of critical multivariate cryptosystem frameworks, such as Matsumoto-Imai, Oil and Vinegar, and Polly Cracker schemes. It also examines advances in lattice-based systems like Kyber and Crystals-Dilithium, which are undergoing assessment by NIST for potential standardization. As quantum computing continues to evolve, the demand for cutting-edge cryptographic solutions to safeguard digital communications grows increasingly pressing.
Keywords
RSA encryption; quantum-resistant cryptography; lattice-based cryptography; multivariate public key cryptosystems; NP-hard problems; quantum computing threats; digital security
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
