  Cryptocurrencies typically aim at preserving the privacy of their users.
Different cryptocurrencies preserve privacy at various levels, some of them
requiring users to rely on strategies to raise the privacy level to their
needs. Among those strategies, we focus on two of them: merge avoidance and
mixing services. Such strategies may be adopted on top of virtually any
blockchain-based cryptocurrency. In this paper, we show that whereas optimal
merge avoidance leads to an NP-hard optimization problem, incentive-compatible
mixing services are subject to a certain class of impossibility results.
Together, our results contribute to the body of work on fundamental limits of
privacy mechanisms in blockchain-based cryptocurrencies.
