Compared to the best prior work, we achieve a $14times$ reduction in the computation and a $11times$ reduction in the communication required to perform a “hole punch,” a $55times$ reduction in the communication required to redeem a punch card, and a $128times$ reduction in the computation time required to redeem a card. Much of our performance improvement can be attributed to removing the reliance on pairings or range proofs present in prior work, which has only addressed this problem in the context of more general loyalty systems. By tailoring our scheme to punch cards and related loyalty systems, we demonstrate that we can reduce communication and computation costs by orders of magnitude.
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