From 16th IEEE Computer Security Foundations Workshop.
IEEE Computer Society.
2003.
Pages 47–61.

We demonstrate that for any well-defined 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 particular system of quadratic Diophantine equations. This result enables formal analysis of protocols that employ primitives such as Diffie-Hellman exponentiation, products, and xor, with a bounded number of role instances, but without imposing any bounds on the size of terms created by the attacker. In the case of xor, the resulting system of Diophantine equations is decidable. In the case of a general Abelian group, decidability remains an open question, but our reduction demonstrates that standard mathematical techniques for solving systems of Diophantine equations are sufficient for the discovery of protocol insecurities.

@InProceedings{MS03,
    AUTHOR = {{J.} Millen and {V.} Shmatikov},
    TITLE = {Symbolic protocol analysis with products and Diffie-Hellman exponentiation},
    YEAR = {2003},
    PAGES = {47--61},
    URL = {http://www.csl.sri.com/papers/csags/},
    BOOKTITLE = {16th {IEEE} Computer Security Foundations Workshop},
    ORGANIZATION = {{IEEE} Computer Society}
}

• csag.ps