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This paper shows how several ring-LWE based key exchange protocols can be broken, under the assumption that the same key share is used for multiple exchanges. This indicates that, if these key exchange protocols are used, then it will be necessary for a fresh key share be generated for each exchange, and that these key exchange protocols cannot be used as a drop in replacement which uses Diffie-Hellman static key shares.  \section{Introduction}  Key agreement protocols are one of the oldest public key protocols known, dating back to the Diffie-Hellman protocol protocol\cite{Diffie_1976}. In a key agreement protocol, each side selects private values, and exchange public values; in most such protocols, each side sends a single message. Then, both side do computations based on their private values and the other side's public values, and derive the same secret value. The security goal is that someone just listening into the exchanged public values would find it infeasible to derive that secret value.  ...