# The propagation game: on simulatability, correlation matrices, and probing security

## TL;DR

This paper formalizes the concept of simulatability in side-channel security using categorical and matrix-based approaches, offering new theoretical insights and tools for analyzing probing security.

## Contribution

It introduces a categorical formalization of simulatability, revisits existing definitions, and explores probabilistic and spectral methods to enhance security analysis tools.

## Key findings

- Revisits probe isolating non-interference with categorical formalization
- Provides a new, less contrived definition of simulatability
- Explores probabilistic and spectral approaches to security analysis

## Abstract

This work is intended for researchers in the field of side-channel attacks, countermeasure analysis, and probing security. It reports on a formalization of simulatability in terms of categorical properties, which we think will provide a useful tool in the practitioner toolbox. The formalization allowed us to revisit some existing definitions (such as probe isolating non-interference) in a simpler way that corresponds to the propagation of \textit{erase morphisms} in the diagrammatic language of \prop{} categories. From a theoretical perspective, we shed light into probabilistic definitions of simulatability and matrix-based spectral approaches. This could mean, in practice, that potentially better tools can be built. Readers will find a different, and perhaps less contrived, definition of simulatability, which could enable new forms of reasoning. This work does not cover any practical implementation of the proposed tools, which is left for future work.