Cryptographic Applications of High Dimensional Manifold Collapse
Year: 2025
Type: article
Abstract: Traditional cryptographic methodologies predominantly depend upon careful management of cryptographic keys, involving secure storage, controlled transmission, and regular maintenance of sensitive private keys. The Rosario-Wang Proof-of-Knowledge (PoK) system represents a significant evolution beyond conventional cryptographic paradigms by eliminating the dependency on persistent stored keys. Instead, it employs an innovative cryptographic architecture that integrates manifold-to-projection holographic reductions with cognitive XOR operations to securely authenticate knowledge and membership without disclosing underlying secrets.This paper provides a detailed exposition of the Rosario-Wang Proof and the underlying Cypher Primitive, introducing a novel form of agentic computation. This advanced approach leverages sophisticated mathematical techniques drawn from Hilbert-space manifold projections, principles derived from holographic theory and dimensional collapse, hidden morphisms, quantum mechanical formalisms, and cognitive science frameworks. The Rosario Cypher, constructed upon these primitives, implements a dynamic and interactive proof-of-knowledge system specifically designed for probabilistic verification of private membership within high-dimensional information spaces. Within this advanced cryptographic context, eigenvalue sets are holographically projected onto lower-dimensional manifolds—specifically hyperplane leaves—through entropy-driven manifold reduction. Cryptographic accumulators are utilized within the verification protocol to logically aggregate verification outcomes via conjunctive operations (logical AND). This cumulative Boolean aggregation results in a deterministic cryptographic proof thus ensuring a robust and reliable verification of secret membership.Agent interaction within the Rosario-Wang protocol involves cognitively recognizing an encoded secret positioned within the manifold projection. By applying a cognitive XOR verification process, agents securely participate in the proof-of-knowledge ceremony without explicitly revealing their underlying secrets. This cognitive XOR mechanism demonstrates the practical utility of the Rosario-Wang Primitive, vividly illustrating how principles from manifold geometry, quantum theory, and cognitive sciences can be effectively synthesized into a cryptographically secure, computationally efficient, and operationally robust authentication framework suitable for contemporary academic research and industrial deployment.
Author: ROSARIO, FRANK DYLAN
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893460191
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