Invariant-Based Cryptography

TL;DR

This paper introduces a novel symmetric cryptographic scheme leveraging invariants of discrete oscillatory functions, providing a secure, self-verifying mechanism for authentication and communication.

Contribution

It presents a new cryptographic approach based on functional invariants, with detailed framework, security analysis, and practical applications.

Findings

Scheme encodes secrets via invariant-preserving identities.

Security relies on structural coherence, not algebraic inversion.

Framework includes analytic, modular, and security analysis components.

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.