Finding Intruder Knowledge with Cap-Matching

  • Erin Hanna
  • Christopher LynchEmail author
  • David Jaz Myers
  • Corey Richardson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11565)


Given two terms s and t, a substitution \(\sigma \) matches s onto t if \(s\sigma = t\). We extend the matching problem to handle \(\mathbf{Cap }\)-terms, which are constructed of function symbols from the signature and a \(\mathbf{Cap }\) operator which represents an unbounded number of applications of function symbols from the signature to a set of \(\mathbf{Cap }\)-terms. A \(\mathbf{Cap }\)-term represents an infinite number of terms. A \(\mathbf{Cap }\)-substitution maps variables to \(\mathbf{Cap }\)-terms and represents an infinite number of term substitutions. \(\mathbf{Cap }\) matching is the problem of, given a term s and a \(\mathbf{Cap }\)-term T, find a set of \(\mathbf{Cap }\)-substitutions which represents the set of substitutions that matches s onto all the terms t represented by T. We give a sound, complete and terminating algorithm for \(\mathbf{Cap }\)-matching, which has been implemented in Maude. We show how the \(\mathbf{Cap }\)-matching problem can be used to find all the messages learnable by an active intruder in a cryptographic protocol, where the \(\mathbf{Cap }\) operator represents all the possible functions that can be performed by the intruder.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Erin Hanna
    • 1
  • Christopher Lynch
    • 2
    Email author
  • David Jaz Myers
    • 3
  • Corey Richardson
    • 4
  1. 1.Department of MathematicsEastern UniversitySt. DavidsUSA
  2. 2.Department of Computer ScienceClarkson UniversityPotsdamUSA
  3. 3.Department of MathematicsJohns Hopkins UniversityBaltimoreUSA
  4. 4.O(1) LabsSan FranciscoUSA

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