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A Mathematical Framework for the Problem of Security for Cognition in Neurotechnology

Bryce Allen Bagley, Claudia K Petritsch

TL;DR

This paper develops Cognitive Neurosecurity, a mathematical framework which enables such description and analysis by drawing on methods and results from multiple fields, and presents descriptions of the algorithmic problems faced by attackers attempting to violate privacy and autonomy, and defenders attempting to obstruct such attempts.

Abstract

The rapid advancement in neurotechnology in recent years has created an emerging critical intersection between neurotechnology and security. Implantable devices, non-invasive monitoring, and non-invasive therapies all carry with them the prospect of violating the privacy and autonomy of individuals' cognition. A growing number of scientists and physicians have made calls to address this issue, but applied efforts have been relatively limited. A major barrier hampering scientific and engineering efforts to address these security issues is the lack of a clear means of describing and analyzing relevant problems. In this paper we develop Cognitive Neurosecurity, a mathematical framework which enables such description and analysis by drawing on methods and results from multiple fields. We demonstrate certain statistical properties which have significant implications for Cognitive Neurosecurity, and then present descriptions of the algorithmic problems faced by attackers attempting to violate privacy and autonomy, and defenders attempting to obstruct such attempts.

A Mathematical Framework for the Problem of Security for Cognition in Neurotechnology

TL;DR

This paper develops Cognitive Neurosecurity, a mathematical framework which enables such description and analysis by drawing on methods and results from multiple fields, and presents descriptions of the algorithmic problems faced by attackers attempting to violate privacy and autonomy, and defenders attempting to obstruct such attempts.

Abstract

The rapid advancement in neurotechnology in recent years has created an emerging critical intersection between neurotechnology and security. Implantable devices, non-invasive monitoring, and non-invasive therapies all carry with them the prospect of violating the privacy and autonomy of individuals' cognition. A growing number of scientists and physicians have made calls to address this issue, but applied efforts have been relatively limited. A major barrier hampering scientific and engineering efforts to address these security issues is the lack of a clear means of describing and analyzing relevant problems. In this paper we develop Cognitive Neurosecurity, a mathematical framework which enables such description and analysis by drawing on methods and results from multiple fields. We demonstrate certain statistical properties which have significant implications for Cognitive Neurosecurity, and then present descriptions of the algorithmic problems faced by attackers attempting to violate privacy and autonomy, and defenders attempting to obstruct such attempts.
Paper Structure (34 sections, 35 equations, 2 figures)

This paper contains 34 sections, 35 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Projective Holographic Cognition
  4. Results
  5. Distance Statistics of Cogit Vectors
  6. Measurement Statistics
  7. Operational Dynamic Analysis
  8. Readout Attacks
  9. Model-Aware Defense
  10. Model-Agnostic Defense
  11. Alteration Attacks
  12. Conclusions
  13. Hyperdimensional Computing Algebras
  14. Why Hyperdimensional Computing?
  15. Required Features
  16. ...and 19 more sections

Figures (2)

  • Figure 1: The Bloch sphere graphically represents qubits -- and thus cogits -- in terms of one angle $\varphi$ corresponding to the phasor component and a second angle $\theta$ corresponding to relative probabilities of a qubit/cogit being measured as $0$ or $1$. The notation $\ket{0}$ and $\ket{1}$ are used to represent the states which exist in superposition in a qubit/cogit. Image credit: Wikimedia Commons.bloch_sphere_wikimedia
  • Figure 2: Visual summary of the general structure of a Hyperdimensional Computing algebra. Colored boxes correspond to individual variables, with different shades -- of orange, green, blue, and purple respectively -- denoting different values. The addition, binding, and dynamics operations convert between individual hypervector. Each darker grey box represents a particular pairing of indices with variables, and permutation rotates these pairings in the manner shown.

Theorems & Definitions (6)

  • Definition 1: State Model-Optimal Noise
  • Definition 2: Dynamics Model-Optimal Noise
  • Definition 3: State Information-Optimal Noise
  • Definition 4: Dynamics Information-Optimal Noise
  • Definition 5: State Model-Optimal Alteration
  • Definition 6: Dynamics Model-Optimal Alteration