Invariant-Based Cryptography

2025-05-08

AI Summary

Traditional symmetric encryption relies on algebraic hardness assumptions and lacks intrinsic structural self-verifiability. Method: This paper proposes a novel symmetric encryption scheme based on functional invariants of discrete oscillatory functions. It constructs a four-point algebraic identity with hidden parameters, encoding secret integers as structurally consistent functional invariants; security stems from the inherent geometric and algebraic consistency of the identity—not invertibility or computational assumptions. Contribution/Results: It introduces functional invariants as a new cryptographic primitive, enabling keyless ciphertext validity verification—a first for self-verifying encryption. The scheme features modular parameter design, an index recovery algorithm, hash-binding analysis, and a rigorously provable security framework. Experiments demonstrate lightweight implementation, forgery resistance, compactness, high efficiency, and strong verifiability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under controlled parameterization. Security arises not from algebraic inversion but from structural coherence: the transmitted values satisfy an invariant that is computationally hard to forge or invert without knowledge of the shared secret. We develop the full analytic and modular framework, prove exact identities, define index-recovery procedures, and analyze security assumptions, including oscillator construction, hash binding, and invertibility conditions. The result is a compact, self-verifying mechanism suitable for secure authentication, parameter exchange, and lightweight communication protocols.

Problem

• Develops symmetric cryptography using discrete oscillatory function invariants
• Ensures security via structural coherence, not algebraic inversion
• Provides framework for secure authentication and lightweight protocols

Innovation

• Symmetric scheme using functional invariants
• Four-point algebraic identity encoding
• Structural coherence ensures security