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\section{Attack variants}  One issue is that the \cite{Ding_2012} variant of the protocol has Alice adding an add a second  error vector to the computed $V$ vector before doing the reconciliation; this would add in errors to our tests. This an error that Eve cannot control. Eve  can be handled either compensate for this  by either  running multiple probes (and averaging out the error), or by increasing the $j, k$ values (to attempt to magnify the signal over the fixed noise level). In addition, the test (as written) assumes that Eve gets only a single bit per probe (that is, she can test whether her guess of the shared secret was accurate or not). If Alice sends the first encrypted message, then it is possible that Eve might probe several bits per attempt. That is, she might arrange to have several coefficients be near a Quadrant border, and she would be able to compute the shared secrets for each setting of the bits under test, and see which version matches the encrypted data she sees from Alice).