Proof by consistency

Kapur, Deepak; Musser, David R.

doi:10.1016/0004-3702(87)90017-8

Cited by 92 publications

(43 citation statements)

References 4 publications

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“…The idea of proving properties by showing the consistency of a given formula F , i.e, showing that ¬F has no proof, is known as proof by consistency [53], or inductionless induction [58,24]. Note that the formal Coq proofs we shall extract from models of S, using our tool h1mc, are proofs of security for π that work by (explicit) induction over term structure.…”

Section: Related Workmentioning

confidence: 99%

Finite models for formal security proofs

Goubault-Larrecq

2010

JCS

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First-order logic models of security for cryptographic protocols, based on variants of the Dolev-Yao model, are now well-established tools. Given that we have checked a given security protocol π using a given first-order prover, how hard is it to extract a formally checkable proof of it, as required in, e.g., common criteria at the highest evaluation level (EAL7)? We demonstrate that this is surprisingly hard in the general case: the problem is non-recursive. Nonetheless, we show that we can instead extract finite models M from a set S of clauses representing π, automatically, and give two ways of doing so. We then define a model-checker testing M |= S, and show how we can instrument it to output a formally checkable proof, e.g., in Coq. Experience on a number of protocols shows that this is practical, and that even complex (secure) protocols modulo equational theories have small finite models, making our approach suitable. * Partially supported by project PFC ("plateforme de confiance"), pôle de compétitivité System@tic Parisrégion Ile-de-France. Part of this work was done during RNTL project EVA, 2000-2003. 1

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Section: Related Workmentioning

confidence: 99%

Finite models for formal security proofs

Goubault-Larrecq

2010

JCS

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“…Here, an induction scheme explicitly gives the base cases and the step cases, where a step case consists of an obligation and one or more hypotheses. In implicit induction (see, e.g., [33,21,26,24,16,27,34,7,1,37]), no concrete induction scheme is constructed a priori. Instead, an induction scheme is implicitly constructed during the proof attempt.…”

Section: Introductionmentioning

confidence: 99%

Rewriting Induction + Linear Arithmetic = Decision Procedure

Falke¹,

Kapur

2012

Automated Reasoning

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Abstract. This paper presents new results on the decidability of inductive validity of conjectures. For this, a class of term rewrite systems (TRSs) with built-in linear integer arithmetic is introduced and it is shown how these TRSs can be used in the context of inductive theorem proving. The proof method developed for this couples (implicit) inductive reasoning with a decision procedure for the theory of linear integer arithmetic with (free) constructors. The effectiveness of the new decidability results on a large class of conjectures is demonstrated by an evaluation of the prototype implementation Sail2.

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“…The idea of proving properties by showing the consistency of a given formula F , i.e, showing that ¬F has no proof, is known as proof by consistency [41], or inductionless induction [45,19]. Note that the formal Coq proofs we shall extract from models of S, using our tool h1mc, are proofs of security for π that work by (explicit) induction over term structure.…”

Section: Introductionmentioning

confidence: 99%

Towards Producing Formally Checkable Security Proofs, Automatically

Goubault-Larrecq¹

2008

2008 21st IEEE Computer Security Foundations Symposium

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Proof by consistency

Cited by 92 publications

References 4 publications

Finite models for formal security proofs

Finite models for formal security proofs

Rewriting Induction + Linear Arithmetic = Decision Procedure

Towards Producing Formally Checkable Security Proofs, Automatically

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