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103
Deciding knowledge in security protocols under equational theories
 In Proc. 31st International Colloquium on Automata, Languages and Programming (ICALP’04), volume 3142 of LNCS
, 2004
"... Abstract. The analysis of security protocols requires precise formulations of the knowledge of protocol participants and attackers. In formal approaches, this knowledge is often treated in terms of message deducibility and indistinguishability relations. In this paper we study the decidability of th ..."
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Cited by 109 (9 self)
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Abstract. The analysis of security protocols requires precise formulations of the knowledge of protocol participants and attackers. In formal approaches, this knowledge is often treated in terms of message deducibility and indistinguishability relations. In this paper we study the decidability of these two relations. The messages in question may employ functions (encryption, decryption, etc.) axiomatized in an equational theory. Our main positive results say that, for a large and useful class of equational theories, deducibility and indistinguishability are both decidable in polynomial time. 1
Intruder deductions, constraint solving and insecurity decision in presence of exclusive or
, 2003
"... We present decidability results for the verification of cryptographic protocols in the presence of equational theories corresponding to xor and Abelian groups. Since the perfect cryptography assumption is unrealistic for cryptographic primitives with visible algebraic properties such as xor, we exte ..."
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Cited by 90 (12 self)
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We present decidability results for the verification of cryptographic protocols in the presence of equational theories corresponding to xor and Abelian groups. Since the perfect cryptography assumption is unrealistic for cryptographic primitives with visible algebraic properties such as xor, we extend the conventional DolevYao model by permitting the intruder to exploit these properties. We show that the ground reachability problem in NP for the extended intruder theories in the cases of xor and Abelian groups. This result follows from a normal proof theorem. Then, we show how to lift this result in the xor case: we consider a symbolic constraint system expressing the reachability (e.g., secrecy) problem for a finite number of sessions. We prove that such constraint system is decidable, relying in particular on an extension of combination algorithms for unification procedures. As a corollary, this enables automatic symbolic verification of cryptographic protocols employing xor for a fixed number of sessions.
Deciding the security of protocols with DiffieHellman exponentiation and products in exponents
, 2003
"... ..."
A survey of algebraic properties used in cryptographic protocols
 JOURNAL OF COMPUTER SECURITY
"... Cryptographic protocols are successfully analyzed using formal methods. However, formal approaches usually consider the encryption schemes as black boxes and assume that an adversary cannot learn anything from an encrypted message except if he has the key. Such an assumption is too strong in general ..."
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Cited by 69 (20 self)
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Cryptographic protocols are successfully analyzed using formal methods. However, formal approaches usually consider the encryption schemes as black boxes and assume that an adversary cannot learn anything from an encrypted message except if he has the key. Such an assumption is too strong in general since some attacks exploit in a clever way the interaction between protocol rules and properties of cryptographic operators. Moreover, the executability of some protocols relies explicitly on some algebraic properties of cryptographic primitives such as commutative encryption. We give a list of some relevant algebraic properties of cryptographic operators, and for each of them, we provide examples of protocols or attacks using these properties. We also give an overview of the existing methods in formal approaches for analyzing cryptographic proto
New Decidability Results for Fragments of FirstOrder Logic and Application to Cryptographic Protocols
, 2003
"... We consider a new extension of the Skolem class for firstorder logic and prove its decidability by resolution techniques. We then extend this class including the builtin equational theory of exclusive or. Again, we prove the decidability of the class by resolution techniques. ..."
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Cited by 54 (18 self)
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We consider a new extension of the Skolem class for firstorder logic and prove its decidability by resolution techniques. We then extend this class including the builtin equational theory of exclusive or. Again, we prove the decidability of the class by resolution techniques.
The CLAtse Protocol Analyser
, 2006
"... This paper presents an overview of the CLAtse tool, an efficient and versatile automatic analyser for the security of cryptographic protocols. CLAtse takes as input a protocol specified as a set of rewriting rules (IF format, produced by the AVISPA compiler), and uses rewriting and constraint sol ..."
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Cited by 51 (5 self)
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This paper presents an overview of the CLAtse tool, an efficient and versatile automatic analyser for the security of cryptographic protocols. CLAtse takes as input a protocol specified as a set of rewriting rules (IF format, produced by the AVISPA compiler), and uses rewriting and constraint solving techniques to model all reachable states of the participants and decide if an attack exists w.r.t. the DolevYao intruder. Any statebased security property can be modelled (like secrecy, authentication, fairness, etc...), and the algebraic properties of operators like xor or exponentiation are taken into account with much less limitations than other tools, thanks to a complete modular unification algorithm. Also, useful constraints like typing, inequalities, or shared sets of knowledge (with set operations like removes, negative tests, etc...) can also be analysed.
LTL model checking for security protocols
 In 20th IEEE Computer Security Foundations Symposium (CSF20
, 2007
"... Most model checking techniques for security protocols make a number of simplifying assumptions on the protocol and/or on its execution environment that prevent their applicability in some important cases. For instance, most techniques assume that communication between honest principals is control ..."
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Cited by 44 (7 self)
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Most model checking techniques for security protocols make a number of simplifying assumptions on the protocol and/or on its execution environment that prevent their applicability in some important cases. For instance, most techniques assume that communication between honest principals is controlled by a DolevYao intruder, i.e. a malicious agent capable to overhear, divert, and fake messages. Yet we might be interested in establishing the security of a protocol that relies on a less unsecure channel (e.g. a confidential channel provided by some other protocol sitting lower in the protocol stack). In this paper we propose a general model for security protocols based on the setrewriting formalism that, coupled with the use of LTL, allows for the specification of assumptions on principals and communication channels as well as complex security properties that are normally not handled by stateoftheart protocol analysers. By using our approach we have been able to formalise all the assumptions required by the ASW protocol for optimistic fair exchange as well as some of its security properties. Besides the previously reported attacks on the protocol, we report a new attack on a patched version of the protocol. 1.
A RewritingBased Inference System for the NRL Protocol Analyzer and its MetaLogical Properties
, 2005
"... The NRL Protocol Analyzer (NPA) is a tool for the formal specification and analysis of cryptographic protocols that has been used with great effect on a number of complex reallife protocols. One of the most interesting of its features is that it can be used to reason about security in face of attem ..."
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Cited by 41 (20 self)
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The NRL Protocol Analyzer (NPA) is a tool for the formal specification and analysis of cryptographic protocols that has been used with great effect on a number of complex reallife protocols. One of the most interesting of its features is that it can be used to reason about security in face of attempted attacks on lowlevel algebraic properties of the functions used in a protocol. Indeed, it has been used successfully to either reproduce or discover a number of such attacks. In this paper we give for the first time a precise formal specification of the main features of the NPA inference system: its grammarbased techniques for invariant generation and its backwards reachability analysis method. This formal specification is given within the wellknown rewriting framework so that the inference system is specified as a set of rewrite rules modulo an equational theory describing the behavior of the cryptographic algorithms involved. We then use this formalization to prove some important metalogical properties about the NPA inference system, including the soundness and completeness of the search algorithm and soundness of the grammar generation algorithm. The formalization and soundness and completeness theorems not only provide also a better understanding of the NPA as it currently operates, but provide a modular basis which can be used as a starting point for increasing the types of equational theories it can handle.
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 41 (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
On the Complexity of Equational Horn Clauses
"... Security protocols employing cryptographic primitives with algebraic properties are conveniently modeled using Horn clauses modulo equational theories. We consider clauses corresponding to the class H3 of Nielson, Nielson and Seidl. We show that modulo the theory ACU of an associativecommutative s ..."
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Cited by 34 (2 self)
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Security protocols employing cryptographic primitives with algebraic properties are conveniently modeled using Horn clauses modulo equational theories. We consider clauses corresponding to the class H3 of Nielson, Nielson and Seidl. We show that modulo the theory ACU of an associativecommutative symbol with unit, as well as its variants like the theory XOR and the theory AG of Abelian groups, unsatisfiability is NPcomplete. Also membership and intersectionnonemptiness problems for the closely related class of oneway as well as twoway tree automata modulo these equational theories are NPcomplete. A key technical tool is a linear time construction of an existential Presburger formula corresponding to the Parikh image of a contextfree language. Our algorithms require deterministic polynomial time using an oracle for existential Presburger formulas, suggesting efficient implementations are possible.