  Constant function market makers (CFMMs) such as Uniswap, Balancer, Curve, and
mStable, among many others, make up some of the largest decentralized exchanges
on Ethereum and other blockchains. Because all transactions are public in
current implementations, a natural next question is if there exist similar
decentralized exchanges which are privacy-preserving; i.e., if a transaction's
quantities are hidden from the public view, then an adversary cannot correctly
reconstruct the traded quantities from other public information. In this note,
we show that privacy is impossible with the usual implementations of CFMMs
under most reasonable models of an adversary and provide some mitigating
strategies.
