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Jon Sterling (Feb 10 2022 at 12:02):Bob Harper and I have released a new manuscript applying category theory and topos theory to type-based security in programming languages.
Title: Sheaf semantics of termination-insensitive noninterference
Authors: Jonathan Sterling and Robert Harper
Abstract:
We propose a new sheaf semantics for secure information flow over a space of abstract behaviors, based on synthetic domain theory: security classes are open/closed partitions, types are sheaves, and redaction of sensitive information corresponds to restricting a sheaf to a closed subspace. Our security-aware computational model satisfies termination-insensitive noninterference automatically, and therefore constitutes an intrinsic alternative to state of the art extrinsic/relational models of noninterference. Our semantics is the latest application of Sterling and Harper's recent re-interpretation of phase distinctions and noninterference in programming languages in terms of Artin gluing and topos-theoretic open/closed modalities. Prior applications include parametricity for ML modules, the proof of normalization for cubical type theory by Sterling and Angiuli, and the cost-aware logical framework of Niu et al. In this paper we employ the phase distinction perspective twice: first to reconstruct the syntax and semantics of secure information flow as a lattice of phase distinctions between "higher" and "lower" security, and second to verify the computational adequacy of our sheaf semantics vis-à-vis an extension of Abadi et al.'s dependency core calculus with a construct for declassifying termination channels.
PDF: https://www.jonmsterling.com/papers/sterling-harper:2022.pdf
There may still be typos.
Jon Sterling (Apr 19 2022 at 16:34):Update: this paper is now accepted to FSCD '22!