Abstract
We give diagrammatic tools to reason about information flow within encrypted communication. In particular, we are interested in deducing where information flow (communication or otherwise) has taken place, and fully accounting for all possible paths.
The core mathematical concept is using a single categorical diagram to model the underlying mathematics, the epistemic knowledge of the participants, and (implicitly) the potential or actual communication between participants. A key part of this is a ‘correctness’ or ‘consistency’ criterion that ensures we accurately & fully account for the distinct routes by which information may come to be known (i.e. communication and / or calculation).
We demonstrate how this formalism may be applied to answer questions about communication scenarios where we have the partial information about the participants and their interactions. Similarly, we show how to analyse the consequences of changes to protocols or communications, and to enumerate the distinct orders in which events may have occurred.
We use various forms of Diffie-Hellman key exchange as an illustration of these techniques. However, they are entirely general; an extended version of this paper [8] provides similar analyses of other protocols.
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Notes
- 1.
Although it is standard to assume that Eve is an adversary to Alice and Bob, the tools themselves take a more agnostic approach. Our aim is to study information flow generally; we may be more concerned about information flow to Eve, but the models themselves treat her equally to the other participants.
- 2.
We assume an implicit, fixed, embedding in order not to have to consider the graph embedding or graph isomorphism problem. In practice, this embedding is immediate from the interpretation.
- 3.
I would like to thank various members of the Oxford school for the folklore that the ‘classical communication’ in these protocols – although often implicit – should properly be thought of as 2-categorical structure. It is pleasing to be able to claim that the same applies to implicit communication in classical protocols!.
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Acknowledgements
I have had the good fortune to encounter several cryptographically-minded category theorists, and category-curious cryptographers. Thanks are due to Chris Heunen (Edinburgh), Delaram Kahrobaei (York), Dusko Pavlovic (Hawaii), and Noson Yanofsky (New York). Thanks are also due to Morgan Hines, for help in finding the regular polyhedra in three or more dimensions associated with the protocols in [8].
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Hines, P.M. (2020). A Diagrammatic Approach to Information Flow in Encrypted Communication. In: Eades III, H., Gadyatskaya, O. (eds) Graphical Models for Security. GraMSec 2020. Lecture Notes in Computer Science(), vol 12419. Springer, Cham. https://doi.org/10.1007/978-3-030-62230-5_9
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