Invariant-Based Cryptography: Toward a General Framework

TL;DR

This paper introduces a generalized framework for invariant-based cryptography, expanding the use of algebraic invariants as core mechanisms for secure symmetric cryptographic schemes.

Contribution

It broadens the invariant-based approach to include multiple classes of algebraic invariants, providing new symmetric schemes and analyzing their security properties.

Findings

Invariant-based schemes achieve security comparable to traditional models.

New symmetric schemes based on polynomial roots and algebraic identities.

Framework establishes invariant-based design as a versatile cryptographic approach.

Abstract

We develop a generalized framework for invariant-based cryptography by extending the use of structural identities as core cryptographic mechanisms. Starting from a previously introduced scheme where a secret is encoded via a four-point algebraic invariant over masked functional values, we broaden the approach to include multiple classes of invariant constructions. In particular, we present new symmetric schemes based on shifted polynomial roots and functional equations constrained by symmetric algebraic conditions, such as discriminants and multilinear identities. These examples illustrate how algebraic invariants -- rather than one-way functions -- can enforce structural consistency and unforgeability. We analyze the cryptographic utility of such invariants in terms of recoverability, integrity binding, and resistance to forgery, and show that these constructions achieve security levels comparable to the original oscillatory model. This work establishes a foundation for invariant-based design as a versatile and compact alternative in symmetric cryptographic protocols.