  We study the question of how to shuffle $n$ cards when faced with an opponent
who knows the initial position of all the cards {\em and} can track every card
when permuted, {\em except} when one takes $K< n$ cards at a time and shuffles
them in a private buffer "behind your back," which we call {\em buffer
shuffling}. The problem arises naturally in the context of parallel mixnet
servers as well as other security applications. Our analysis is based on
related analyses of load-balancing processes. We include extensions to
variations that involve corrupted servers and adversarially injected messages,
which correspond to an opponent who can peek at some shuffles in the buffer and
who can mark some number of the cards. In addition, our analysis makes novel
use of a sum-of-squares metric for anonymity, which leads to improved
performance bounds for parallel mixnets and can also be used to bound
well-known existing anonymity measures.
