The collection of fine-grained consumption of users in the smart grid enables energy providers to propose new services (e.g. consumption forecasts or demand response protocols), but at the price of users' privacy: consumption data collected by smart meters reflects the use of all appliances by inhabitants in the household over time. Based on the observation that Secure Multi-party Computation (SMC) enables computing an aggregate without learning individual information, this paper proposes a privacy-preserving adaptation of an existing demand response protocol which is fed with users' personal data. An extension providing fraud resistance is also presented. Experimental results demonstrate that our protocol is able to reconcile privacy and utility.