One challenge when using private keys is that if they get stolen the damage can be very big, especially when used in blockchains to protect funds. Sharing the private key between multiple entities can secure the usage a bit, but most algorithms don't give privacy. In the context of a privacy-preserving service like Monero, where the source and destination of a transaction are hidden, these algorithms would leak information about the user. Applying Tandem to transactions on the Monero blockchain allows to protect the private key in case of loss, while keeping the owner of the transaction private.