Uploaded November 2024 | Updated September 2026, 3 weeks ago
Topos Institute Colloquium, 7th of November 2024.
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Mathematical security proofs are crucial in the field of cryptography: they allow us to base the theoretical security of a particular protocol on a set of simply-stated assumptions. However, a major challenge (in both education and research) is managing the complexity of these proofs. Fully rigorous security proofs can occupy a lot of space even when the underlying ideas are relatively simple. In the subfield of quantum cryptography, which incorporates quantum states and processes, this challenge has additional complications.
Visual reasoning helps illuminate proofs in cryptography, and in some cases, visual reasoning can actually serve as a replacement for symbolic reasoning. In this talk I will discuss how picture-proofs, based on categorical quantum mechanics, can be incorporated into quantum cryptography.
References:
- Breiner, Spencer, Carl A. Miller, and Neil J. Ross. "Graphical methods in device-independent quantum cryptography." Quantum 3 (2019): 146. arXiv:1705.09213
- Breiner, Spencer, Amir Kalev, and Carl Miller. "Parallel Self-Testing of the GHZ State with a Proof by Diagrams." 15th International Conference on Quantum Physics and Logic. Electronic Proceedings in Theoretical Computer Science (EPTCS), 2018. arXiv:1806.04744
Topos Institute Colloquium, 7th of November 2024.
———
Mathematical security proofs are crucial in the field of cryptography: they allow us to base the theoretical security of a particular protocol on a set of simply-stated assumptions. However, a major challenge (in both education and research) is managing the complexity of these proofs. Fully rigorous security proofs can occupy a lot of space even when the underlying ideas are relatively simple. In the subfield of quantum cryptography, which incorporates quantum states and processes, this challenge has additional complications.
Visual reasoning helps illuminate proofs in cryptography, and in some cases, visual reasoning can actually serve as a replacement for symbolic reasoning. In this talk I will discuss how picture-proofs, based on categorical quantum mechanics, can be incorporated into quantum cryptography.
References:
- Breiner, Spencer, Carl A. Miller, and Neil J. Ross. "Graphical methods in device-independent quantum cryptography." Quantum 3 (2019): 146. arXiv:1705.09213
- Breiner, Spencer, Amir Kalev, and Carl Miller. "Parallel Self-Testing of the GHZ State with a Proof by Diagrams." 15th International Conference on Quantum Physics and Logic. Electronic Proceedings in Theoretical Computer Science (EPTCS), 2018. arXiv:1806.04744
![[DOTS Lectures] 2. More categories of systems](https://i.ytimg.com/vi/zv10Vgl3Shc/mqdefault.jpg "[DOTS Lectures] 2. More categories of systems
Part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.")
