This paper presents a new privacy-preserving smart metering system. Our scheme is private under the differential privacy model and therefore provides strong and provable guarantees. With our scheme, an (electricity) supplier can periodically collect data from smart meters and derive aggregated statistics while learning only limited information about the activities of individual households. For example, a supplier cannot tell from a user's trace when he watched TV or turned on heating. Our scheme is simple, efficient and practical. Processing cost is very limited: smart meters only have to add noise to their data and encrypt the results with an efficient stream cipher.
A recent paper @cite_21 proposes another technique to privately aggregate time series data. This work differs from ours as follows: (1) they use a Diffie-Hellman-based encryption scheme, whereas our construction is based on a more efficient construction that only use modular additions. This approach is better adapted to resource constrained devices like smart meters. (2) Although @cite_21 does not require the establishment (and storage) of pairwise keys between nodes as opposed to our approach, it is unclear how @cite_21 can be extended to tolerate node and communication failures. By contrast, our scheme is more robust, as the encryption key of non-responding nodes is known to other nodes in the network that can help to recover the aggregate. (3) Finally, @cite_21 uses a different noise generation method from ours, but this technique only satisfies the relaxed @math -differential privacy definition. Indeed, in their scheme, each node adds noise probabilistically which means that none of the nodes add noise with some positive probability @math . Although @math can be arbitrarily small, this also decreases the utility. By contrast, in our scheme, @math while ensuring nearly optimal utility.
@cite_21
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We present a new tensoring technique for LWE-based fully homomorphic encryption. While in all previous works, the ciphertext noise grows quadratically @math with every multiplication before "refreshing", our noise only grows linearly @math . We use this technique to construct a scale-invariant fully homomorphic encryption scheme, whose properties only depend on the ratio between the modulus q and the initial noise level B, and not on their absolute values. Our scheme has a number of advantages over previous candidates: It uses the same modulus throughout the evaluation process no need for "modulus switching", and this modulus can take arbitrary form. In addition, security can be classically reduced from the worst-case hardness of the GapSVP problem with quasi-polynomial approximation factor, whereas previous constructions could only exhibit a quantum reduction from GapSVP. We present a novel approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), without Gentry's bootstrapping procedure. Specifically, we offer a choice of FHE schemes based on the learning with error (LWE) or ring-LWE (RLWE) problems that have 2λ security against known attacks. For RLWE, we have: • A leveled FHE scheme that can evaluate L-level arithmetic circuits with O(λ · L3) per-gate computation -- i.e., computation quasi-linear in the security parameter. Security is based on RLWE for an approximation factor exponential in L. This construction does not use the bootstrapping procedure. • A leveled FHE scheme that uses bootstrapping as an optimization, where the per-gate computation (which includes the bootstrapping procedure) is O(λ2), independent of L. Security is based on the hardness of RLWE for quasi-polynomial factors (as opposed to the sub-exponential factors needed in previous schemes). We obtain similar results to the above for LWE, but with worse performance. Based on the Ring LWE assumption, we introduce a number of further optimizations to our schemes. As an example, for circuits of large width -- e.g., where a constant fraction of levels have width at least λ -- we can reduce the per-gate computation of the bootstrapped version to O(λ), independent of L, by batching the bootstrapping operation. Previous FHE schemes all required Ω(λ3.5) computation per gate. At the core of our construction is a much more effective approach for managing the noise level of lattice-based ciphertexts as homomorphic operations are performed, using some new techniques recently introduced by Brakerski and Vaikuntanathan (FOCS 2011). We consider distributed plurality consensus in a complete graph of size @math with @math initial opinions. We design an efficient and simple protocol in the asynchronous communication model that ensures that all nodes eventually agree on the initially most frequent opinion. In this model, each node is equipped with a random Poisson clock with parameter @math . Whenever a node's clock ticks, it samples some neighbors, uniformly at random and with replacement, and adjusts its opinion according to the sample. A prominent example is the so-called two-choices algorithm in the synchronous model, where in each round, every node chooses two neighbors uniformly at random, and if the two sampled opinions coincide, then that opinion is adopted. This protocol is very efficient and well-studied when @math . If @math for some small @math , we show that it converges to the initial plurality opinion within @math rounds, w.h.p., as long as the initial difference between the largest and second largest opinion is @math . On the other side, we show that there are cases in which @math rounds are needed, w.h.p. One can beat this lower bound in the synchronous model by combining the two-choices protocol with randomized broadcasting. Our main contribution is a non-trivial adaptation of this approach to the asynchronous model. If the support of the most frequent opinion is at least @math times that of the second-most frequent one and @math , then our protocol achieves the best possible run time of @math , w.h.p. We relax full synchronicity by allowing @math nodes to be poorly synchronized, and the well synchronized nodes are only required to be within a certain time difference from one another. We enforce this synchronicity by introducing a novel gadget into the protocol. In 2009, Gentry proposed the first Fully Homomorphic Encryption (FHE) scheme, an extremely powerful cryptographic primitive that enables to perform computations, i.e., to evaluate circuits, on encrypted data without decrypting them first. This has many applications, in particular in cloud computing. In all currently known FHE schemes, encryptions are associated to some (non-negative integer) noise level, and at each evaluation of an AND gate, the noise level increases. This is problematic because decryption can only work if the noise level stays below some maximum level @math at every gate of the circuit. To ensure that property, it is possible to perform an operation called to reduce the noise level. However, bootstrapping is time-consuming and has been identified as a critical operation. This motivates a new problem in discrete optimization, that of choosing where in the circuit to perform bootstrapping operations so as to control the noise level; the goal is to minimize the number of bootstrappings in circuits. In this paper, we formally define the , we design a polynomial-time @math -approximation algorithm using a novel method of rounding of a linear program, and we show a matching hardness result: @math -inapproximability for any @math .