Proving termination with multiset orderings

The primary authentication method for a user account is rarely the only way to access that account. Accounts can often be accessed through other accounts, using recovery methods, password managers, or single sign-on. This increases each account's attack surface, giving rise to subtle security problems. These problems cannot be detected by considering each account in isolation, but require analyzing the links between a user's accounts. Furthermore, to accurately assess the security of accounts, the physical world must also be considered. For example, an attacker with access to a physical mailbox could obtain credentials sent by post.Despite the manifest importance of understanding these interrelationships and the security problems they entail, no prior methods exist to perform an analysis thereof in a precise way. To address this need, we introduce account access graphs, the first formalism that enables a comprehensive modeling and analysis of a user's entire setup, incorporating all connections between the user's accounts, devices, credentials, keys, and documents. Account access graphs support systematically identifying both security vulnerabilities and lockout risks in a user's accounts. We give analysis algorithms and illustrate their effectiveness in a case study, where we automatically detect significant weaknesses in a user's setup and suggest improvement options. CCS CONCEPTS• Security and privacy → Formal security models; Authentication.

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“…Note that this multiset ordering is specialized to our needs and differs from standard multiset orderings [5].…”

Section: A Multiset-based Scoring Schemementioning

confidence: 99%

User Account Access Graphs

Hammann

Radomirović

Sasse

et al. 2019

Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security

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“…Note that since J is finite, it follows that there are only finitely many n with non-zero multiplicity in μ( J). Hence, we can use the multiset ordering construction of Dershowitz & Manna (1979) to derive a well-founded ordering ≺ on μ( J) in terms of the < ordering on natural numbers. We now proceed to the main intermediate result in our proof of logical completeness, where we show that the set of formula reduction steps possible from a given configuration accounts for all satisfying valuations of that configuration.…”

Section: Logical Completenessmentioning

confidence: 99%

Contextual equivalence for inductive definitions with binders in higher order typed functional programming

Lakin¹,

Pitts²

2013

J. Funct. Prog.

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Correct handling of names and binders is an important issue in meta-programming. This paper presents an embedding of constraint logic programming into the αML functional programming language, which provides a provably correct means of implementing proof search computations over inductive definitions involving names and binders modulo α-equivalence. We show that the execution of proof search in the αML operational semantics is sound and complete with regard to the model-theoretic semantics of formulae, and develop a theory of contextual equivalence for the subclass of αML expressions which correspond to inductive definitions and formulae. In particular, we prove that αML expressions, which denote inductive definitions, are contextually equivalent precisely when those inductive definitions have the same model-theoretic semantics. This paper is a revised and extended version of the conference paper (Lakin, M. R. & Pitts, A. M. (2009) Resolving inductive definitions with binders in higher-order typed functional programming. InProceedings of the 18th European Symposium on Programming (ESOP 2009), Castagna, G. (ed), Lecture Notes in Computer Science, vol. 5502. Berlin, Germany: Springer-Verlag, pp. 47–61) and draws on material from the first author's PhD thesis (Lakin, M. R. (2010)An Executable Meta-Language for Inductive Definitions with Binders. University of Cambridge, UK).

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“…χ defines a well-founded ordering, with the standard ordering on natural numbers, extended lexicographically to triples for backtrack values and by multiset extension (Dershowitz & Manna, 1979) for resumptions.…”

Section: Terminationmentioning

confidence: 99%

A functional toolkit for morphological and phonological processing, application to a Sanskrit tagger

Huet¹

2005

J. Funct. Prog.

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We present the Zen toolkit for morphological and phonological processing of natural languages. This toolkit is presented in literate programming style, in the Pidgin ML subset of the Objective Caml functional programming language. This toolkit is based on a systematic representation of finite state automata and transducers as decorated lexical trees. All operations on the state space data structures use the zipper technology, and a uniform sharing functor permits systematic maximum sharing as dags. A particular case of lexical maps is specially convenient for building invertible morphological operations such as inflected forms dictionaries, using a notion of differential word. As a particular application, we describe a general method for tagging a natural language text given as a phoneme stream by analysing possible euphonic liaisons between words belonging to a lexicon of inflected forms. The method uses the toolkit methodology by constructing a non-deterministic transducer, implementing rational rewrite rules, by mechanical decoration of a trie representation of the lexicon index. The algorithm is linear in the size of the lexicon. A coroutine interpreter is given, and its correctness and completeness are formally proved. An application to the segmentation of Sanskrit by sandhi analysis is demonstrated.

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Proving termination with multiset orderings

Cited by 95 publications

References 2 publications

User Account Access Graphs

User Account Access Graphs

Contextual equivalence for inductive definitions with binders in higher order typed functional programming

A functional toolkit for morphological and phonological processing, application to a Sanskrit tagger

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