Invariant-Based Cryptography: Toward a General Framework

2025-05-12

AI Summary

This work addresses the overreliance of conventional cryptography on one-way functions by proposing a generic algebraic-invariant-based cryptographic framework that replaces one-way functions with structural identities for key encapsulation and message authentication. Methodologically, it systematically extends the four-point algebraic invariant scheme, introducing novel symmetric constructions—including shift polynomial roots, discriminants, and multilinear identities—integrated with polynomial root encoding, functional equation constraints, and structural consistency verification. The framework achieves balanced guarantees in recoverability, integrity binding, and forgery resistance, attaining security strength comparable to the oscillation model while substantially reducing computational and storage overhead. Its primary contribution is establishing an “invariant-driven” paradigm for lightweight symmetric cryptography, yielding compact, provably secure, and structurally grounded cryptographic primitives tailored for resource-constrained environments.

Technology Category

• Machine Learning: Structured Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Security and Privacy: Applications of cryptography
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Extending structural identities for invariant-based cryptography
• Developing symmetric schemes using algebraic invariants
• Analyzing invariants' cryptographic utility and security levels

Innovation

• Extends structural identities as core cryptographic mechanisms
• Uses algebraic invariants for structural consistency and unforgeability
• Develops symmetric schemes with shifted polynomial roots