MST3 Encryption improvement with three-parameter group of Hermitian function field

2025-04-21

AI Summary

This work addresses the insufficient structural rigidity and resilience against quantum attacks in post-quantum public-key encryption. Methodologically, it introduces a novel framework integrating the automorphism group of Hermitian function fields with non-central logarithmic signature-based three-parameter groups—marking the first fusion of Hermitian function field theory and non-central group structures. The resulting encryption scheme features a staged key-unwrapping mechanism and establishes an explicit mapping model among group strength, attack complexity, and message length, enabling dynamic security-efficiency trade-offs. Contributions include: (i) significantly enhanced resistance against quantum algorithms—including Shor’s, Grover’s, and nonlinear inverse problems under group actions; (ii) efficient decryption for legitimate users; and (iii) configurable security levels and communication overhead. The framework delivers a structurally sound and practically viable paradigm for post-quantum cryptographic systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

This scholarly work presents an advanced cryptographic framework utilizing automorphism groups as the foundational structure for encryption scheme implementation. The proposed methodology employs a three-parameter group construction, distinguished by its application of logarithmic signatures positioned outside the group's center, a significant departure from conventional approaches. A key innovation in this implementation is utilizing the Hermitian function field as the underlying mathematical framework. This particular function field provides enhanced structural properties that strengthen the cryptographic protocol when integrated with the three-parameter group architecture. The encryption mechanism features phased key de-encapsulation from ciphertext, representing a substantial advantage over alternative implementations. This sequential extraction process introduces additional computational complexity for potential adversaries while maintaining efficient legitimate decryption. A notable characteristic of this cryptosystem is the direct correlation between the underlying group's mathematical strength and both the attack complexity and message size parameters. This relationship enables precise security-efficiency calibration based on specific implementation requirements and threat models. The application of automorphism groups with logarithmic signatures positioned outside the center represents a significant advancement in non-traditional cryptographic designs, particularly relevant in the context of post-quantum cryptographic resilience.

Problem

• Enhances encryption using Hermitian function field properties
• Introduces three-parameter group with non-central logarithmic signatures
• Improves post-quantum resilience via automorphism group cryptography

Innovation

• Three-parameter group with Hermitian function field
• Automorphism groups with non-central logarithmic signatures
• Phased key de-encapsulation from ciphertext