Date of Award


Document Type


Degree Name

Master of Science (MS)


Mathematical Sciences

First Advisor

Joe Near


Group key exchange protocols are used to establish session keys, which can then be used as encryption keys to set up secure channels of communication, between more than two parties simultaneously. Many different group key exchange protocols exist and require security proofs in order to determine the strength of the protocol and answer the following questions: does the protocol provide authentication, and if so, to what degree? Does the protocol provide key secrecy? In this thesis we examine a particular group key exchange protocol that we call the \textit{vector space projection protocol} as first described in “A Group Key Establishment Scheme” by Guzey, Kurt, and Ozdemir, and show using a particular type of security proof — the game based security model — that the protocol as described does not achieve key secrecy. We show that there are at least four adversaries with non-negligible probabilities of winning the key secrecy security game, which indicates that this key exchange protocol is not one that should be implemented.



Number of Pages

42 p.