Invariant-Based Cryptography (Part II): New Schemes, New Invariants, Generalized Framework

I’ve just published a follow-up to my earlier work on invariant-based symmetric cryptography — this time shifting from proofs to principles, from a single construction to a flexible paradigm.

What’s new?

• Two fresh symmetric schemes built around algebraic invariants:

→ One uses polynomial discriminants,

→ The other exploits the projective cross-ratio from geometry.

• A recipe for turning these invariants into cryptographic puzzles, challenge-response protocols, and session keys — all without revealing secrets.

• Extensions from simple rings to finite fields, matrix algebras, and coordinate rings — the idea generalizes far beyond its original form.

• A session-mode pseudorandom generator derived from invariant structure — stateless, forward-secure, and safe even with weak entropy.

Full preprint: [https://zenodo.org/records/15392345](https://zenodo.org/records/15392345)

Would love to hear your thoughts or criticisms — especially if you’re into algebraic methods, lightweight protocols, or symmetric alternatives to group-based crypto.