Invariant-Based Cryptography: A Symmetric Scheme with Algebraic Structure and Deterministic Recovery

I’ve developed a new symmetric cryptographic construction based on algebraic invariants defined over masked oscillatory functions with hidden rational indices. Instead of relying on classical group operations or LWE-style hardness, the scheme ensures integrity and unforgeability through structural consistency: a four-point identity must hold across function evaluations derived from pseudorandom parameters.

Key features:

\- Compact, self-verifying invariant structure

\- Deterministic recovery of session secrets without oracle access

\- Pseudorandom masking via antiperiodic oscillators seeded from a shared key

\- Hash binding over invariant-constrained tuples

\- No exposure of plaintext, keys, or index

The full paper includes analytic definitions, algebraic proofs, implementation parameters, and a formal security game (Invariant Index-Hiding Problem, IIHP).

Might be relevant for those interested in deterministic protocols, zero-knowledge analogues, or post-classical primitives.

Preprint: [https://doi.org/10.5281/zenodo.15368121](https://doi.org/10.5281/zenodo.15368121)

Happy to hear comments or criticism.