Demand response has emerged as one of the most promising methods for the deployment of sustainable energy systems. Attempts to democratize demand response and establish programs for residential consumers have run into scalability issues and risks of leaking sensitive consumer data. In this work, we propose a privacy-friendly, incentive-based demand response market, where consumers offer their flexibility to utilities in exchange for a financial compensation. Consumers submit encrypted offer which are aggregated using Computation Over Encrypted Data to ensure consumer privacy and the scalability of the approach. The optimal allocation of flexibility is then determined via double-auctions, along with the optimal consumption schedule for the users with respect to the day-ahead electricity prices, thus also shielding participants from high electricity prices. A case study is presented to show the effectiveness of the proposed approach.