  A privacy-preserving Context-Aware Publish-Subscribe System (CA-PSS) enables
an intermediary (broker) to match the content from a publisher and the
subscription by a subscriber based on the current context while preserving
confidentiality of the subscriptions and notifications. While a
privacy-preserving Ride-Hailing Service (RHS) enables an intermediary (service
provider) to match a ride request with a taxi driver in a privacy-friendly
manner. In this work, we attack a privacy-preserving CA-PSS proposed by Nabeel
et al. (2013), where we show that any entity in the system including the broker
can learn the confidential subscriptions of the subscribers. We also attack a
privacy-preserving RHS called lpRide proposed by Yu et al. (2019), where we
show that any rider/driver can efficiently recover the secret keys of all other
riders and drivers. Also, we show that any rider/driver will be able to learn
the location of any rider. The attacks are based on our cryptanalysis of the
modified Paillier cryptosystem proposed by Nabeel et al. that forms a building
block for both the above protocols.
