International Association
for Cryptologic Research

In past years, entire research communities have arisen to address concerns of privacy and fairness in data analysis. At present, however, the public must trust that institutions will re-implement algorithms voluntarily to account for these social concerns. Due to additional cost, widespread adoption is unlikely without effective legal enforcement. A technical challenge for enforcement is that the methods proposed are often \emph{probabilistic mechanisms}, whose output must be drawn according to precise, and sometimes secret, distributions. The Differential Privacy (DP) case is illustrative: if a cheating curator answers queries according to an overly-accurate mechanism, privacy violations could go undetected. This raises our central question: \textit{Can we efficiently certify the output of a probabilistic mechanism enacted by an untrusted party?} To this end: \begin{enumerate} \item We introduce two new notions: {\it Certified Probabilistic Mechanisms} (CPM) and \emph{Random Variable Commitment Schemes} (RVCS). A CPM is an interactive protocol that forces a prover to enact a given probabilistic mechanism or be caught; importantly, the interaction does not reveal the mechanism's secret parameters. An RVCS---a key primitive for constructing CPMs---is a commitment scheme where the verifier is convinced that the commitment is to an RV sampled according to an agreed-upon distribution, but learns nothing else. \item We instantiate the general notion of CPM for the special case of Certifying DP. We build a lightweight, doubly-efficent interactive proof system to certify arbitrary-predicate counting queries released via the DP Binomial mechanism. The construction relies on a commitment scheme with perfect hiding and additive homomorphic properties that can be used to release a broad class of queries about a committed database, constructed on top of Pedersen commitments. \item Finally, we demonstrate the immediate feasibility of Certified DP via a highly-efficient and scalable prototype implementation to answer counting queries of arbitrary predicates. The mechanism is composed of an offline and online stage, where the online phase allows for non-interactive certification of queries. For example, we show that CDP queries over a US Census Public Use Microdata Sample (PUMS)~\cite{census-pums} ($n=7000$) can be completed in only 1.6~ms and verified in just \emph{38~$\mu$s}. Our implementation is available in open source at \url{https://github.com/jlwatson/certified-dp}.

We define and construct {\it Deniable Fully Homomorphic Encryption} based on the Learning With Errors (LWE) polynomial hardness assumption. Deniable FHE enables storing encrypted data in the cloud to be processed securely without decryption, maintaining deniability of the encrypted data, as well the prevention of vote-buying in electronic voting schemes where encrypted votes can be tallied without decryption. Our constructions achieve {\it compactness} independently of the level of deniability- both the size of the public key and the size of the ciphertexts are bounded by a fixed polynomial, independent of the faking probability achieved by the scheme. This is in contrast to all previous constructions of deniable encryption schemes (even without requiring homomorphisms) which are based on polynomial hardness assumptions, originating with the seminal work of Canetti, Dwork, Naor and Ostrovsky (CRYPTO 1997) in which the ciphertext size grows with the inverse of the faking probability. Canetti {\it et al.} argued that this dependence ``seems inherent'', but our constructions illustrate this is not the case. We note that the Sahai-Waters (STOC13) construction of deniable encryption from indistinguishability-obfuscation achieves compactness and can be easily modified to achieve deniable FHE as well, but it requires multiple, stronger sub-exponential hardness assumptions, which are furthermore not post-quantum secure. In contrast, our constructions rely only on the LWE polynomial hardness assumption, as currently required for FHE even without deniability. The running time of our encryption algorithm depends on the inverse of the faking probability, thus the scheme falls short of achieving simultaneously compactness, negligible deniability probability {\it and} polynomial encryption time. Yet, we believe that achieving compactness is a fundamental step on the way to achieving all properties simultaneously as has been the historical journey for other primitives such as functional encryption. Interestingly, we note that our constructions support large message spaces, whereas previous constructions were bit by bit, and can be run in online-offline model of encryption, where the bulk of computation is independent of the message and may be performed in an offline pre-processing phase. The running time of the online phase, is independent of the faking probability, whereas the offline encryption run-time grows with the inverse of the faking probability. At the heart of our constructions is a new way to use bootstrapping to obliviously generate FHE ciphertexts so that it supports faking under coercion.

The right of an individual to request the deletion of their personal data by an entity that might be storing it -- referred to as \emph{the right to be forgotten} -- has been explicitly recognized, legislated, and exercised in several jurisdictions across the world, including the European Union, Argentina, and California. However, much of the discussion surrounding this right offers only an intuitive notion of what it means for it to be fulfilled -- of what it means for such personal data to be deleted. In this work, we provide a formal definitional framework for the right to be forgotten using tools and paradigms from cryptography. In particular, we provide a precise definition of what could be (or should be) expected from an entity that collects individuals' data when a request is made of it to delete some of this data. Our framework captures most, though not all, relevant aspects of typical systems involved in data processing. While it cannot be viewed as expressing the statements of current laws (especially since these are rather vague in this respect), our work offers technically precise definitions that represent possibilities for what the law could reasonably expect, and alternatives for what future versions of the law could explicitly require. Finally, with the goal of demonstrating the applicability of our framework and definitions, we consider various natural and simple scenarios where the right to be forgotten comes up. For each of these scenarios, we highlight the pitfalls that arise even in genuine attempts at implementing systems offering deletion guarantees, and also describe technological solutions that provably satisfy our definitions. These solutions bring together techniques built by various communities.