franco
@francos.eth
I wonder if you could recast cryptography in categorical language: Instead of “groups, rings and fields + probabilistic Turing machines”, you work with objects that stand for resources (channels, keys, random beacons, OT-boxes, etc.) and morphisms that stand for protocols transforming those resources.
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franco
@francos.eth
Sequential and parallel composition of protocols are captured by the two compositions in a symmetric monoidal category. Security is phrased as the existence of a simulator that makes a real-world diagram commute with an ideal-world one, so that “anything an adversary can do here, it could also do there”.
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franco
@francos.eth
Some papers I found (haven't read and probably goes way over my head): - Categorical Composable Cryptography: https://arxiv.org/abs/2105.05949 - Abstract / Constructive Cryptography: https://crypto.ethz.ch/publications/files/MauRen11.pdf
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franco
@francos.eth
You get: - Composability for free: once morphisms are secure, any string diagram built from them is secure by functoriality. - Unified classical/quantum view: same graphical language covers AES-based MPC and entanglement-based QKD. - Abstraction from machines: you reason at the algebraic level. concrete PPT machines enter only when you instantiate objects. - Tooling potential: rewriting systems for string diagrams can automate large chunks of laborious proofs.
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franco
@francos.eth
I still believe category theory is the best framework we have to reason about things in general. I'm not a cryptographer but this feels more intuitive than the current Universal-Composability model or game-based proofs and sequences of games frameworks for reasoning about cryptographic security.
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