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Vector Commitments with Efficient Protocols for Privacy-preserving Smart Billing Applications

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In privacy-preserving smart billing applications, users receive signed readings from smart meters, calculate the total fee that should be paid and prove to service providers the correctness of the fee calculation without disclosing any further information. To calculate the total fee and prove its correctness, users receive a signed tariff policy from service providers.

Existing protocols allow users to prove efficiently the correctness of the fee calculation when tariff policies are simple, meaning that the price to be paid does not depend on users’ past consumption and is specified by a single service provider. However, when the price due depends on several policies signed by different entities, the proof of correctness involves a computation cost linear in the amount of entities. History-dependent tariff policies involve recalculations on meter readings.

We propose a method to efficiently calculate the total fee and prove its correctness when complex tariff policies are applied. Basically, it consists in creating an intermediate table that stores partial calculations. The intermediate table allows to speed up the computation of the proof of correctness and, when the usage of the intermediate table surpasses a threshold, the cost of creating the intermediate table is amortized.

We show how to build intermediate tables based on a novel primitive we call vector commitments. Essentially, vector commitments are commitments to a vector of values that can be opened to one of the values with cost independent of the size of the vector. We define vector commitments and propose several constructions based on different security assumptions.

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