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Symbolic protocol analysis with products and DiffieHellman exponentiation
, 2003
"... We demonstrate that for any welldefined cryptographic protocol, the symbolic trace reachability problem in the presence of an Abelian group operator (e.g., multiplication) can be reduced to solvability of a decidable system of quadratic Diophantine equations. This result enables complete, fully aut ..."
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Cited by 36 (0 self)
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We demonstrate that for any welldefined cryptographic protocol, the symbolic trace reachability problem in the presence of an Abelian group operator (e.g., multiplication) can be reduced to solvability of a decidable system of quadratic Diophantine equations. This result enables complete, fully automated formal analysis of protocols that employ primitives such as DiffieHellman exponentiation, multiplication, andxor, with a bounded number of role instances, but without imposing any bounds on the size of terms created by the attacker. 1
Symbolic protocol analysis with an abelian group operator or DiffieHellman exponentiation
 Journal of Computer Security
, 2005
"... We demonstrate that for any welldefined cryptographic protocol, the symbolic trace reachability problem in the presence of an Abelian group operator (e.g., multiplication) can be reduced to solvability of a decidable system of quadratic Diophantine equations. This result enables complete, fully aut ..."
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Cited by 14 (1 self)
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We demonstrate that for any welldefined cryptographic protocol, the symbolic trace reachability problem in the presence of an Abelian group operator (e.g., multiplication) can be reduced to solvability of a decidable system of quadratic Diophantine equations. This result enables complete, fully automated formal analysis of protocols that employ primitives such as DiffieHellman exponentiation, multiplication, and xor, with a bounded number of role instances, but without imposing any bounds on the size of terms created by the attacker. 1
A Combinatory Logic Approach to Higherorder Eunification
 in Proceedings of the Eleventh International Conference on Automated Deduction, SpringerVerlag LNAI 607
, 1992
"... Let E be a firstorder equational theory. A translation of typed higherorder Eunification problems into a typed combinatory logic framework is presented and justified. The case in which E admits presentation as a convergent term rewriting system is treated in detail: in this situation, a modifi ..."
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Cited by 9 (3 self)
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Let E be a firstorder equational theory. A translation of typed higherorder Eunification problems into a typed combinatory logic framework is presented and justified. The case in which E admits presentation as a convergent term rewriting system is treated in detail: in this situation, a modification of ordinary narrowing is shown to be a complete method for enumerating higherorder Eunifiers. In fact, we treat a more general problem, in which the types of terms contain type variables. 1 Introduction Investigation of the interaction between firstorder and higherorder equational reasoning has emerged as an active line of research. The collective import of a recent series of papers, originating with [Bre88] and including (among others) [Bar90], [BG91a], [BG91b], [Dou92], [JO91] and [Oka89], is that when various typed calculi are enriched by firstorder equational theories, the validity problem is wellbehaved, and furthermore that the respective computational approaches to ...
Assertion checking over combined abstraction of linear arithmetic and uninterpreted functions
 In ESOP, volume 3924 of LNCS
, 2006
"... Abstract. This paper presents results on the problem of checking equality assertions in programs whose expressions have been abstracted using combination of linear arithmetic and uninterpreted functions, and whose conditionals are treated as nondeterministic. We first show that the problem of asser ..."
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Cited by 7 (4 self)
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Abstract. This paper presents results on the problem of checking equality assertions in programs whose expressions have been abstracted using combination of linear arithmetic and uninterpreted functions, and whose conditionals are treated as nondeterministic. We first show that the problem of assertion checking for this combined abstraction is coNPhard, even for loopfree programs. This result is quite surprising since assertion checking for the individual abstractions of linear arithmetic and uninterpreted functions can be performed efficiently in polynomial time. Next, we give an assertion checking algorithm for this combined abstraction, thereby proving decidability of this problem despite the underlying lattice having infinite height. Our algorithm is based on an important connection between unification theory and program analysis. Specifically, we show that weakest preconditions can be strengthened by replacing equalities by their unifiers, without losing any precision, during backward analysis of programs. 1
Negation in Combining Constraint Systems
 Communications of the ACM
, 1998
"... In a recent paper, Baader and Schulz presented a general method for the combination of constraint systems for purely positive constraints. But negation plays an important role in constraint solving. E.g., it is vital for constraint entailment. Therefore it is of interest to extend their results to t ..."
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Cited by 3 (0 self)
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In a recent paper, Baader and Schulz presented a general method for the combination of constraint systems for purely positive constraints. But negation plays an important role in constraint solving. E.g., it is vital for constraint entailment. Therefore it is of interest to extend their results to the combination of constraint problems containing negative constraints. We show that the combined solution domain introduced by Baader and Schulz is a domain in which one can solve positive and negative "mixed" constraints by presenting an algorithm that reduces solvability of positive and negative "mixed" constraints to solvability of pure constraints in the components. The existential theory in the combined solution domain is decidable if solvability of literals with socalled linear constant restrictions is decidable in the components. We also give a criterion for ground solvability of mixed constraints in the combined solution domain. The handling of negative constraints can be signific...
Unification in an Algebra With Choice and Action Prefix.
, 1994
"... This paper contains a unification algorithm for a restricted process algebra with as only operators nondeterministic choice and unary action prefixoperators, and with infinite processes. Termination is ensured by using a modified version of a method for syntactic unification described in [Col84a] a ..."
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This paper contains a unification algorithm for a restricted process algebra with as only operators nondeterministic choice and unary action prefixoperators, and with infinite processes. Termination is ensured by using a modified version of a method for syntactic unification described in [Col84a] and [Col84b]. The algorithm contains a procedure to remove nonmost general solutions. Key words and phrases: unification, process algebra. Contents 1 Introduction 2 2 Algebra and theory 5 2.1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.2 The theory : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.3 The model P : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 3 The algorithm UnPref 10 3.1 Introduction and definitions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 3.2 The rules : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 3.3 The algo...