Computing a Gröbner basis of a polynomial ideal over a Euclidean domain
Journal of Symbolic Computation
Unification in commutative theories, Hilbert's basis theorem, and Gröbner bases
Journal of the ACM (JACM)
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
RTA '91 Proceedings of the 4th International Conference on Rewriting Techniques and Applications
Unification in the Union of Disjoint Equational Theories: Combining Decision Procedures
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Solving linear equations over polynomial semirings
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
A Security Analysis of the Cliques Protocols Suites
CSFW '01 Proceedings of the 14th IEEE workshop on Computer Security Foundations
Analyzing Protocols that use Modular Exponentiation: Semantic Unification
Analyzing Protocols that use Modular Exponentiation: Semantic Unification
Journal of Computer Security - Special issue on ACM conference on computer and communications security, 2001
An NP decision procedure for protocol insecurity with XOR
Theoretical Computer Science
Symbolic protocol analysis with an Abelian group operator or Diffie-Hellman exponentiation
Journal of Computer Security
Higher-Order and Symbolic Computation
A survey of algebraic properties used in cryptographic protocols
Journal of Computer Security
Hierarchical combination of intruder theories
Information and Computation
ACM Transactions on Computational Logic (TOCL)
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
The finite variant property: how to get rid of some algebraic properties
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Limits of the cryptographic realization of dolev-yao-style XOR
ESORICS'05 Proceedings of the 10th European conference on Research in Computer Security
Hierarchical combination of intruder theories
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
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Modular multiplication and exponentiation are common operations in modern cryptography. Unification problems with respect to some equational theories that these operations satisfy are investigated. Two different but related equational theories are analyzed. A unification algorithm is given for one of the theories which relies on solving syzygies over multivariate integral polynomials with noncommuting indeterminates. For the other theory, in which the distributivity property of exponentiation over multiplication is assumed, the unifiability problem is shown to be undecidable by adapting a construction developed by one of the authors to reduce Hilbert's 10th problem to the solvability problem for linear equations over semi-rings. A new algorithm for computing strong Gröbner bases of right ideals over the polynomial ring Z〈X1, . . . , Xn〉 is proposed; unlike earlier algorithms proposed by Baader as well as by Madlener and Reinert which work only for right admissible term orderings with the boundedness property, this algorithm works for any right admissible term ordering. The algorithms for some of these unification problems are expected to be integrated into Naval Research Lab.'s Protocol Analyzer (NPA), a tool developed by Catherine Meadows, which has been successfully used to analyze cryptographic protocols, particularly emerging standards such as the Internet Engineering Task Force's (IETF) Internet Key Exchange [11] and Group Domain of Interpretation [12] protocols. Techniques from several different fields - particularly symbolic computation (ideal theory and Gröebner basis algorithms) and unification theory -- are thus used to address problems arising in state-based cryptographic protocol analysis.