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\section{Introduction}  Key agreement protocols are one of the oldest public key protocols known, dating back to the Diffie-Hellman protocol\cite{Diffie_1976}. In a key agreement protocol, each side selects private values, and exchange public values (key shares); 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 key shares, and derive the same secret value. The security goal is that someone just listening into the exchanged public key shares would find it infeasible to derive that secret value.  Now, Diffie-Hellman would be vulnerable to a Quantum Computer; one research topic is to find alternatives that would be secure in that environment. Several such proposed  alternatives are based on the ring-LWE problem; just problem. From a protocol standpoint, these proposals work largely  like Diffie-Hellman, each side selects private values, one side sends its public value, the other side replies, and then they both compute a shared secret. With Diffie-Hellman, it is perfectly safe to reuse the same public key share for multiple exchanges. For example, Alice might select a private value, and publish the corresponding key share. Then, when Bob, Carol, Dave and Eve want to communicate with Alice, they can take Alice's key share, select their own private values, and then send to Alice their key shares, thus creating a secure connection. In this case, as long as Alice takes some well-known precautions, the connections are independent; Eve gets no advantage on deriving the secret used in the Alice to Bob connection.