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 $2\cdot n+1$ with respect to a naïve aggregation of $n\cdot (n-2)$. 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.

在“秘密圣诞老人”的变体“阴谋圣诞老人”中，一群人互相提供圣诞节礼物，该小组的每个成员都从该小组的其他成员那里收到礼物。为此，小组成员组成阴谋，以决定合适的礼物，并通常在该阴谋的所有参与者之间分配每种礼物的成本。这需要解决每个阴谋的共享费用，因此，阴谋圣诞老人实际上可以看作是几个共享费用问题的集合。

首先，我们证明了在解决共享费用时找到最小数量的交易的问题是NP完全的。但是，仍然存在良好的贪婪近似。其次，我们向Conspiracy Santa提供一种贪婪的分布式安全解决方案。此解决方案允许n人组成的小组以这样的方式分摊礼物的费用：没有参与者知道他的礼物的价格，但与此同时，交易次数明显减少。$2\cdot ñ+\mathrm{1个}$ 关于天真的聚集 $ñ\cdot （ñ-2）$。此外，我们的解决方案不需要受信任的第三方，并且可以物理实现（参与者在同一个房间并使用信封进行兑换），也可以通过Internet使用加密货币实现。