A Taxonomy of Cryptographic Irreversibility: The Bateson Framework and a Novel Hybrid Sponge-LWE Construction

We introduce the Bateson Framework, a conceptual model that provides a taxonomy for computational irreversibility based on two fundamental sources: information loss (degeneracy) and injected uncertainty (ambiguity). This model allows for a clear classification of existing primitives, such as hash functions (high-degeneracy) and LWE-based schemes (high-ambiguity). Our primary contribution is to demonstrate that this taxonomy is not merely descriptive but generative. We present illustrative instantiations based on the Learning with Errors (LWE) assumption and cryptographic sponges, analyzing their security and practical limitations. Crucially, we introduce a novel hybrid construction that simultaneously leverages both degeneracy and ambiguity by composing a cryptographic sponge with an LWE scheme, showcasing the power of the unified approach for designing robust cryptographic primitives.