  In Conspiracy Santa, a variant of Secret Santa, a group of people offer each
other Christmas gifts, where each member of the group receives a gift from the
other members of the group. To that end, the members of the group form
conspiracies, to decide on appropriate gifts, and usually divide the cost of
each gift among all participants of that conspiracy. This requires to settle
the shared expenses per conspiracy, so Conspiracy Santa can actually be seen as
an aggregation of several shared expenses problems. First, we show that the
problem of finding a minimal number of transaction when settling shared
expenses is NP-complete. Still, there exist good greedy approximations. Second,
we present a greedy distributed secure solution to Conspiracy Santa. This
solution allows a group of n people to share the expenses for the gifts in such
a way that no participant learns the price of his gift, but at the same time
notably reduces the number of transactions to 2 $\times$ n + 1 with respect to
a na{\"i}ve aggregation of n $\times$ (n -- 2). Furthermore, our solution does
not require a trusted third party, and can either be implemented physically
(the participants are in the same room and exchange money using envelopes) or,
over Internet, using a cryptocurrency.
