Group Discounts Compatible with Buyer Privacy
  We show how group discounts can be offered without forcing buyers to surrender their anonymity, as long as buyers can use their own computing devices (e.g. smartphone, tablet or computer) to perform a purchase. Specifically, we present a protocol for privacy-preserving group discounts. The protocol allows a group of buyers to prove how many they are without disclosing their identities. Coupled with an anonymous payment system, this makes group discounts compatible with buyer privacy (that is, buyer anonymity). 
Josep Domingo-Ferrer and Alberto Blanco-Justicia
cs.CR