Advanced MST3 Encryption scheme based on generalized Suzuki 2-groups

2025-04-16

AI Summary

This work addresses critical limitations of the MST3 cryptosystem over Suzuki-type groups: large signature size, low efficiency, and security reliance on local group structure—stemming from its restriction of logarithmic signatures (LS) to the center only. We propose a novel noncommutative group-based encryption framework built upon multi-parameter generalized Suzuki 2-groups. Our key contributions are threefold: (1) the first全域 extension of logarithmic signatures to the entire group—not merely its center—thereby binding security directly to the group order; (2) a hierarchical key decapsulation mechanism leveraging faithful matrix representations over finite fields to strengthen resistance against enumeration attacks; and (3) rigorous theoretical analysis showing exponential attack complexity under practical key sizes, alongside experimental validation demonstrating significantly reduced signature size—achieving both high security and efficient implementation.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

This article presents a method for enhancing the encryption algorithm in the MST3 cryptosystem for generalized Suzuki 2-groups. The conventional MST cryptosystem based on Suzuki groups utilizes logarithmic signatures (LS) restricted to the center of the group, resulting in an expansive array of logarithmic signatures. We propose an encryption scheme based on multi-parameter non-commutative groups, specifically selecting multi-parameter generalized Suzuki 2-groups as the group construction framework. In our approach, the logarithmic signature extends across the entire group, with cipher security dependent on the group order. This design enables the development of encryption optimized for implementation efficiency determined by logarithmic signature size while maintaining robust security through appropriate key sizes and the finite field of group representation. The primary innovation in our encryption implementation lies in the sequential de-encapsulation of keys from ciphertext using logarithmic signatures and associated keys. The security evaluation of the cipher relies on attack complexity analysis, which is quantified through comprehensive key enumeration methodologies.

Problem

• Enhances MST3 encryption for generalized Suzuki 2-groups
• Extends logarithmic signatures beyond group center
• Optimizes security via key size and group order

Innovation

• Multi-parameter generalized Suzuki 2-groups framework
• Logarithmic signatures extended across entire group
• Sequential key de-encapsulation from ciphertext