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Anupam Datta

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Published work

30 published item(s)

preprint2026arXiv

Evergreen: Efficient Claim Verification for Semantic Aggregates

With recent semantic query processing engines, semantic aggregation has become a primitive operator, enabling the reduction of a relation into a natural language aggregate using an LLM. However, the resulting semantic aggregate may contain claims that are not grounded in the underlying relation. Verifying such claims is challenging: they often involve quantifiers, groupings, and comparisons over relations that far exceed LLM context windows and require a costly combination of semantic and symbolic processing. We present Evergreen, a system that recasts claim verification as a semantic query processing task with tailored optimizations and provenance capture. Evergreen compiles each claim into a declarative semantic verification query and executes it on the same engine that produced the aggregate. To reduce cost and latency, Evergreen avoids unnecessary LLM calls through verification-aware optimizations (early stopping, relevance sorting, and estimation with confidence sequences) and general-purpose optimizations for semantic queries (operator fusion, similarity filtering, and prompt caching). Each verdict is accompanied by citations that identify a minimal set of tuples justifying the result, with semantics based on semiring provenance for first-order logic. On a benchmark of real-world restaurant review datasets reflecting production-inspired workloads, Evergreen achieves excellent verification quality (F1 = 1.00) with a strong LLM while reducing cost by 3.2x and latency by 4.0x compared to unoptimized verification. Even with a significantly weaker LLM, Evergreen outperforms a strong LLM-as-a-judge baseline in F1 at 48x lower cost and 2.3x lower latency. Relative to a retrieval-augmented agent, Evergreen compares favorably in F1 and latency with similar cost when both use a strong LLM; yet, with a much weaker LLM, it achieves the same F1 at 63x lower cost and 4.2x lower latency.

preprint2023arXiv

Identifying and Mitigating the Security Risks of Generative AI

Every major technical invention resurfaces the dual-use dilemma -- the new technology has the potential to be used for good as well as for harm. Generative AI (GenAI) techniques, such as large language models (LLMs) and diffusion models, have shown remarkable capabilities (e.g., in-context learning, code-completion, and text-to-image generation and editing). However, GenAI can be used just as well by attackers to generate new attacks and increase the velocity and efficacy of existing attacks. This paper reports the findings of a workshop held at Google (co-organized by Stanford University and the University of Wisconsin-Madison) on the dual-use dilemma posed by GenAI. This paper is not meant to be comprehensive, but is rather an attempt to synthesize some of the interesting findings from the workshop. We discuss short-term and long-term goals for the community on this topic. We hope this paper provides both a launching point for a discussion on this important topic as well as interesting problems that the research community can work to address.

preprint2022arXiv

Faithful Explanations for Deep Graph Models

This paper studies faithful explanations for Graph Neural Networks (GNNs). First, we provide a new and general method for formally characterizing the faithfulness of explanations for GNNs. It applies to existing explanation methods, including feature attributions and subgraph explanations. Second, our analytical and empirical results demonstrate that feature attribution methods cannot capture the nonlinear effect of edge features, while existing subgraph explanation methods are not faithful. Third, we introduce \emph{k-hop Explanation with a Convolutional Core} (KEC), a new explanation method that provably maximizes faithfulness to the original GNN by leveraging information about the graph structure in its adjacency matrix and its \emph{k-th} power. Lastly, our empirical results over both synthetic and real-world datasets for classification and anomaly detection tasks with GNNs demonstrate the effectiveness of our approach.

preprint2022arXiv

Order-sensitive Shapley Values for Evaluating Conceptual Soundness of NLP Models

Previous works show that deep NLP models are not always conceptually sound: they do not always learn the correct linguistic concepts. Specifically, they can be insensitive to word order. In order to systematically evaluate models for their conceptual soundness with respect to word order, we introduce a new explanation method for sequential data: Order-sensitive Shapley Values (OSV). We conduct an extensive empirical evaluation to validate the method and surface how well various deep NLP models learn word order. Using synthetic data, we first show that OSV is more faithful in explaining model behavior than gradient-based methods. Second, applying to the HANS dataset, we discover that the BERT-based NLI model uses only the word occurrences without word orders. Although simple data augmentation improves accuracy on HANS, OSV shows that the augmented model does not fundamentally improve the model's learning of order. Third, we discover that not all sentiment analysis models learn negation properly: some fail to capture the correct syntax of the negation construct. Finally, we show that pretrained language models such as BERT may rely on the absolute positions of subject words to learn long-range Subject-Verb Agreement. With each NLP task, we also demonstrate how OSV can be leveraged to generate adversarial examples.

preprint2021arXiv

Reconstructing Actions To Explain Deep Reinforcement Learning

Feature attribution has been a foundational building block for explaining the input feature importance in supervised learning with Deep Neural Network (DNNs), but face new challenges when applied to deep Reinforcement Learning (RL).We propose a new approach to explaining deep RL actions by defining a class of \emph{action reconstruction} functions that mimic the behavior of a network in deep RL. This approach allows us to answer more complex explainability questions than direct application of DNN attribution methods, which we adapt to \emph{behavior-level attributions} in building our action reconstructions. It also allows us to define \emph{agreement}, a metric for quantitatively evaluating the explainability of our methods. Our experiments on a variety of Atari games suggest that perturbation-based attribution methods are significantly more suitable in reconstructing actions to explain the deep RL agent than alternative attribution methods, and show greater \emph{agreement} than existing explainability work utilizing attention. We further show that action reconstruction allows us to demonstrate how a deep agent learns to play Pac-Man game.

preprint2020arXiv

Influence Paths for Characterizing Subject-Verb Number Agreement in LSTM Language Models

LSTM-based recurrent neural networks are the state-of-the-art for many natural language processing (NLP) tasks. Despite their performance, it is unclear whether, or how, LSTMs learn structural features of natural languages such as subject-verb number agreement in English. Lacking this understanding, the generality of LSTM performance on this task and their suitability for related tasks remains uncertain. Further, errors cannot be properly attributed to a lack of structural capability, training data omissions, or other exceptional faults. We introduce *influence paths*, a causal account of structural properties as carried by paths across gates and neurons of a recurrent neural network. The approach refines the notion of influence (the subject's grammatical number has influence on the grammatical number of the subsequent verb) into a set of gate or neuron-level paths. The set localizes and segments the concept (e.g., subject-verb agreement), its constituent elements (e.g., the subject), and related or interfering elements (e.g., attractors). We exemplify the methodology on a widely-studied multi-layer LSTM language model, demonstrating its accounting for subject-verb number agreement. The results offer both a finer and a more complete view of an LSTM's handling of this structural aspect of the English language than prior results based on diagnostic classifiers and ablation.

preprint2020arXiv

Interpreting Interpretations: Organizing Attribution Methods by Criteria

Motivated by distinct, though related, criteria, a growing number of attribution methods have been developed tointerprete deep learning. While each relies on the interpretability of the concept of "importance" and our ability to visualize patterns, explanations produced by the methods often differ. As a result, input attribution for vision models fail to provide any level of human understanding of model behaviour. In this work we expand the foundationsof human-understandable concepts with which attributionscan be interpreted beyond "importance" and its visualization; we incorporate the logical concepts of necessity andsufficiency, and the concept of proportionality. We definemetrics to represent these concepts as quantitative aspectsof an attribution. This allows us to compare attributionsproduced by different methods and interpret them in novelways: to what extent does this attribution (or this method)represent the necessity or sufficiency of the highlighted inputs, and to what extent is it proportional? We evaluate our measures on a collection of methods explaining convolutional neural networks (CNN) for image classification. We conclude that some attribution methods are more appropriate for interpretation in terms of necessity while others are in terms of sufficiency, while no method is always the most appropriate in terms of both.

preprint2020arXiv

Spaced Repetition and Mnemonics Enable Recall of Multiple Strong Passwords

We report on a user study that provides evidence that spaced repetition and a specific mnemonic technique enable users to successfully recall multiple strong passwords over time. Remote research participants were asked to memorize 4 Person-Action-Object (PAO) stories where they chose a famous person from a drop-down list and were given machine-generated random action-object pairs. Users were also shown a photo of a scene and asked to imagine the PAO story taking place in the scene (e.g., Bill Gates---swallowing---bike on a beach). Subsequently, they were asked to recall the action-object pairs when prompted with the associated scene-person pairs following a spaced repetition schedule over a period of 127+ days. While we evaluated several spaced repetition schedules, the best results were obtained when users initially returned after 12 hours and then in $1.5\times$ increasing intervals: 77% of the participants successfully recalled all 4 stories in 10 tests over a period of 158 days. Much of the forgetting happened in the first test period (12 hours): 89% of participants who remembered their stories during the first test period successfully remembered them in every subsequent round. These findings, coupled with recent results on naturally rehearsing password schemes, suggest that 4 PAO stories could be used to create usable and strong passwords for 14 sensitive accounts following this spaced repetition schedule, possibly with a few extra upfront rehearsals. In addition, we find that there is an interference effect across multiple PAO stories: the recall rate of 100% (resp. 90%) for participants who were asked to memorize 1 PAO story (resp. 2 PAO stories) is significantly better than the recall rate for participants who were asked to memorize 4 PAO stories. These findings yield concrete advice for improving constructions of password management schemes and future user studies.

preprint2016arXiv

CASH: A Cost Asymmetric Secure Hash Algorithm for Optimal Password Protection

An adversary who has obtained the cryptographic hash of a user's password can mount an offline attack to crack the password by comparing this hash value with the cryptographic hashes of likely password guesses. This offline attacker is limited only by the resources he is willing to invest to crack the password. Key-stretching tools can help mitigate the threat of offline attacks by making each password guess more expensive for the adversary to verify. However, key-stretching increases authentication costs for a legitimate authentication server. We introduce a novel Stackelberg game model which captures the essential elements of this interaction between a defender and an offline attacker. We then introduce Cost Asymmetric Secure Hash (CASH), a randomized key-stretching mechanism that minimizes the fraction of passwords that would be cracked by a rational offline attacker without increasing amortized authentication costs for the legitimate authentication server. CASH is motivated by the observation that the legitimate authentication server will typically run the authentication procedure to verify a correct password, while an offline adversary will typically use incorrect password guesses. By using randomization we can ensure that the amortized cost of running CASH to verify a correct password guess is significantly smaller than the cost of rejecting an incorrect password. Using our Stackelberg game framework we can quantify the quality of the underlying CASH running time distribution in terms of the fraction of passwords that a rational offline adversary would crack. We provide an efficient algorithm to compute high quality CASH distributions for the defender. Finally, we analyze CASH using empirical data from two large scale password frequency datasets. Our analysis shows that CASH can significantly reduce (up to $50\%$) the fraction of password cracked by a rational offline adversary.

preprint2016arXiv

Information Flow for Security in Control Systems

This paper considers the development of information flow analyses to support resilient design and active detection of adversaries in cyber physical systems (CPS). The area of CPS security, though well studied, suffers from fragmentation. In this paper, we consider control systems as an abstraction of CPS. Here, we extend the notion of information flow analysis, a well established set of methods developed in software security, to obtain a unified framework that captures and extends system theoretic results in control system security. In particular, we propose the Kullback Liebler (KL) divergence as a causal measure of information flow, which quantifies the effect of adversarial inputs on sensor outputs. We show that the proposed measure characterizes the resilience of control systems to specific attack strategies by relating the KL divergence to optimal detection techniques. We then relate information flows to stealthy attack scenarios where an adversary can bypass detection. Finally, this article examines active detection mechanisms where a defender intelligently manipulates control inputs or the system itself in order to elicit information flows from an attacker's malicious behavior. In all previous cases, we demonstrate an ability to investigate and extend existing results by utilizing the proposed information flow analyses.

preprint2016arXiv

Towards Human Computable Passwords

An interesting challenge for the cryptography community is to design authentication protocols that are so simple that a human can execute them without relying on a fully trusted computer. We propose several candidate authentication protocols for a setting in which the human user can only receive assistance from a semi-trusted computer --- a computer that stores information and performs computations correctly but does not provide confidentiality. Our schemes use a semi-trusted computer to store and display public challenges $C_i\in[n]^k$. The human user memorizes a random secret mapping $σ:[n]\rightarrow\mathbb{Z}_d$ and authenticates by computing responses $f(σ(C_i))$ to a sequence of public challenges where $f:\mathbb{Z}_d^k\rightarrow\mathbb{Z}_d$ is a function that is easy for the human to evaluate. We prove that any statistical adversary needs to sample $m=\tildeΩ(n^{s(f)})$ challenge-response pairs to recover $σ$, for a security parameter $s(f)$ that depends on two key properties of $f$. To obtain our results, we apply the general hypercontractivity theorem to lower bound the statistical dimension of the distribution over challenge-response pairs induced by $f$ and $σ$. Our lower bounds apply to arbitrary functions $f $ (not just to functions that are easy for a human to evaluate), and generalize recent results of Feldman et al. As an application, we propose a family of human computable password functions $f_{k_1,k_2}$ in which the user needs to perform $2k_1+2k_2+1$ primitive operations (e.g., adding two digits or remembering $σ(i)$), and we show that $s(f) = \min\{k_1+1, (k_2+1)/2\}$. For these schemes, we prove that forging passwords is equivalent to recovering the secret mapping. Thus, our human computable password schemes can maintain strong security guarantees even after an adversary has observed the user login to many different accounts.

preprint2015arXiv

A Symbolic Logic with Concrete Bounds for Cryptographic Protocols

We present a formal logic for quantitative reasoning about security properties of network protocols. The system allows us to derive concrete security bounds that can be used to choose key lengths and other security parameters. We provide axioms for reasoning about digital signatures and random nonces, with security properties based on the concrete security of signature schemes and pseudorandom number generators (PRG). The formal logic supports first-order reasoning and reasoning about protocol invariants, taking concrete security bounds into account. Proofs constructed in our logic also provide conventional asymptotic security guarantees because of the way that concrete bounds accumulate in proofs. As an illustrative example, we use the formal logic to prove an authentication property with concrete bounds of a signature-based challenge-response protocol.

preprint2015arXiv

Audit Games with Multiple Defender Resources

Modern organizations (e.g., hospitals, social networks, government agencies) rely heavily on audit to detect and punish insiders who inappropriately access and disclose confidential information. Recent work on audit games models the strategic interaction between an auditor with a single audit resource and auditees as a Stackelberg game, augmenting associated well-studied security games with a configurable punishment parameter. We significantly generalize this audit game model to account for multiple audit resources where each resource is restricted to audit a subset of all potential violations, thus enabling application to practical auditing scenarios. We provide an FPTAS that computes an approximately optimal solution to the resulting non-convex optimization problem. The main technical novelty is in the design and correctness proof of an optimization transformation that enables the construction of this FPTAS. In addition, we experimentally demonstrate that this transformation significantly speeds up computation of solutions for a class of audit games and security games.

preprint2015arXiv

Automated Experiments on Ad Privacy Settings: A Tale of Opacity, Choice, and Discrimination

To partly address people's concerns over web tracking, Google has created the Ad Settings webpage to provide information about and some choice over the profiles Google creates on users. We present AdFisher, an automated tool that explores how user behaviors, Google's ads, and Ad Settings interact. AdFisher can run browser-based experiments and analyze data using machine learning and significance tests. Our tool uses a rigorous experimental design and statistical analysis to ensure the statistical soundness of our results. We use AdFisher to find that the Ad Settings was opaque about some features of a user's profile, that it does provide some choice on ads, and that these choices can lead to seemingly discriminatory ads. In particular, we found that visiting webpages associated with substance abuse changed the ads shown but not the settings page. We also found that setting the gender to female resulted in getting fewer instances of an ad related to high paying jobs than setting it to male. We cannot determine who caused these findings due to our limited visibility into the ad ecosystem, which includes Google, advertisers, websites, and users. Nevertheless, these results can form the starting point for deeper investigations by either the companies themselves or by regulatory bodies.

preprint2015arXiv

Equivalence-based Security for Querying Encrypted Databases: Theory and Application to Privacy Policy Audits

Motivated by the problem of simultaneously preserving confidentiality and usability of data outsourced to third-party clouds, we present two different database encryption schemes that largely hide data but reveal enough information to support a wide-range of relational queries. We provide a security definition for database encryption that captures confidentiality based on a notion of equivalence of databases from the adversary's perspective. As a specific application, we adapt an existing algorithm for finding violations of privacy policies to run on logs encrypted under our schemes and observe low to moderate overheads.

preprint2015arXiv

Influence in Classification via Cooperative Game Theory

A dataset has been classified by some unknown classifier into two types of points. What were the most important factors in determining the classification outcome? In this work, we employ an axiomatic approach in order to uniquely characterize an influence measure: a function that, given a set of classified points, outputs a value for each feature corresponding to its influence in determining the classification outcome. We show that our influence measure takes on an intuitive form when the unknown classifier is linear. Finally, we employ our influence measure in order to analyze the effects of user profiling on Google's online display advertising.

preprint2015arXiv

Program Actions as Actual Causes: A Building Block for Accountability

Protocols for tasks such as authentication, electronic voting, and secure multiparty computation ensure desirable security properties if agents follow their prescribed programs. However, if some agents deviate from their prescribed programs and a security property is violated, it is important to hold agents accountable by determining which deviations actually caused the violation. Motivated by these applications, we initiate a formal study of program actions as actual causes. Specifically, we define in an interacting program model what it means for a set of program actions to be an actual cause of a violation. We present a sound technique for establishing program actions as actual causes. We demonstrate the value of this formalism in two ways. First, we prove that violations of a specific class of safety properties always have an actual cause. Thus, our definition applies to relevant security properties. Second, we provide a cause analysis of a representative protocol designed to address weaknesses in the current public key certification infrastructure.

preprint2015arXiv

System M: A Program Logic for Code Sandboxing and Identification

Security-sensitive applications that execute untrusted code often check the code's integrity by comparing its syntax to a known good value or sandbox the code to contain its effects. System M is a new program logic for reasoning about such security-sensitive applications. System M extends Hoare Type Theory (HTT) to trace safety properties and, additionally, contains two new reasoning principles. First, its type system internalizes logical equality, facilitating reasoning about applications that check code integrity. Second, a confinement rule assigns an effect type to a computation based solely on knowledge of the computation's sandbox. We prove the soundness of system M relative to a step-indexed trace-based semantic model. We illustrate both new reasoning principles of system M by verifying the main integrity property of the design of Memoir, a previously proposed trusted computing system for ensuring state continuity of isolated security-sensitive applications.

preprint2014arXiv

A Methodology for Information Flow Experiments

Information flow analysis has largely ignored the setting where the analyst has neither control over nor a complete model of the analyzed system. We formalize such limited information flow analyses and study an instance of it: detecting the usage of data by websites. We prove that these problems are ones of causal inference. Leveraging this connection, we push beyond traditional information flow analysis to provide a systematic methodology based on experimental science and statistical analysis. Our methodology allows us to systematize prior works in the area viewing them as instances of a general approach. Our systematic study leads to practical advice for improving work on detecting data usage, a previously unformalized area. We illustrate these concepts with a series of experiments collecting data on the use of information by websites, which we statistically analyze.

preprint2013arXiv

Adaptive Regret Minimization in Bounded-Memory Games

Online learning algorithms that minimize regret provide strong guarantees in situations that involve repeatedly making decisions in an uncertain environment, e.g. a driver deciding what route to drive to work every day. While regret minimization has been extensively studied in repeated games, we study regret minimization for a richer class of games called bounded memory games. In each round of a two-player bounded memory-m game, both players simultaneously play an action, observe an outcome and receive a reward. The reward may depend on the last m outcomes as well as the actions of the players in the current round. The standard notion of regret for repeated games is no longer suitable because actions and rewards can depend on the history of play. To account for this generality, we introduce the notion of k-adaptive regret, which compares the reward obtained by playing actions prescribed by the algorithm against a hypothetical k-adaptive adversary with the reward obtained by the best expert in hindsight against the same adversary. Roughly, a hypothetical k-adaptive adversary adapts her strategy to the defender's actions exactly as the real adversary would within each window of k rounds. Our definition is parametrized by a set of experts, which can include both fixed and adaptive defender strategies. We investigate the inherent complexity of and design algorithms for adaptive regret minimization in bounded memory games of perfect and imperfect information. We prove a hardness result showing that, with imperfect information, any k-adaptive regret minimizing algorithm (with fixed strategies as experts) must be inefficient unless NP=RP even when playing against an oblivious adversary. In contrast, for bounded memory games of perfect and imperfect information we present approximate 0-adaptive regret minimization algorithms against an oblivious adversary running in time n^{O(1)}.

preprint2013arXiv

Audit Games

Effective enforcement of laws and policies requires expending resources to prevent and detect offenders, as well as appropriate punishment schemes to deter violators. In particular, enforcement of privacy laws and policies in modern organizations that hold large volumes of personal information (e.g., hospitals, banks, and Web services providers) relies heavily on internal audit mechanisms. We study economic considerations in the design of these mechanisms, focusing in particular on effective resource allocation and appropriate punishment schemes. We present an audit game model that is a natural generalization of a standard security game model for resource allocation with an additional punishment parameter. Computing the Stackelberg equilibrium for this game is challenging because it involves solving an optimization problem with non-convex quadratic constraints. We present an additive FPTAS that efficiently computes a solution that is arbitrarily close to the optimal solution.

preprint2013arXiv

Differentially Private Data Analysis of Social Networks via Restricted Sensitivity

We introduce the notion of restricted sensitivity as an alternative to global and smooth sensitivity to improve accuracy in differentially private data analysis. The definition of restricted sensitivity is similar to that of global sensitivity except that instead of quantifying over all possible datasets, we take advantage of any beliefs about the dataset that a querier may have, to quantify over a restricted class of datasets. Specifically, given a query f and a hypothesis H about the structure of a dataset D, we show generically how to transform f into a new query f_H whose global sensitivity (over all datasets including those that do not satisfy H) matches the restricted sensitivity of the query f. Moreover, if the belief of the querier is correct (i.e., D is in H) then f_H(D) = f(D). If the belief is incorrect, then f_H(D) may be inaccurate. We demonstrate the usefulness of this notion by considering the task of answering queries regarding social-networks, which we model as a combination of a graph and a labeling of its vertices. In particular, while our generic procedure is computationally inefficient, for the specific definition of H as graphs of bounded degree, we exhibit efficient ways of constructing f_H using different projection-based techniques. We then analyze two important query classes: subgraph counting queries (e.g., number of triangles) and local profile queries (e.g., number of people who know a spy and a computer-scientist who know each other). We demonstrate that the restricted sensitivity of such queries can be significantly lower than their smooth sensitivity. Thus, using restricted sensitivity we can maintain privacy whether or not D is in H, while providing more accurate results in the event that H holds true.

preprint2013arXiv

GOTCHA Password Hackers!

We introduce GOTCHAs (Generating panOptic Turing Tests to Tell Computers and Humans Apart) as a way of preventing automated offline dictionary attacks against user selected passwords. A GOTCHA is a randomized puzzle generation protocol, which involves interaction between a computer and a human. Informally, a GOTCHA should satisfy two key properties: (1) The puzzles are easy for the human to solve. (2) The puzzles are hard for a computer to solve even if it has the random bits used by the computer to generate the final puzzle --- unlike a CAPTCHA. Our main theorem demonstrates that GOTCHAs can be used to mitigate the threat of offline dictionary attacks against passwords by ensuring that a password cracker must receive constant feedback from a human being while mounting an attack. Finally, we provide a candidate construction of GOTCHAs based on Inkblot images. Our construction relies on the usability assumption that users can recognize the phrases that they originally used to describe each Inkblot image --- a much weaker usability assumption than previous password systems based on Inkblots which required users to recall their phrase exactly. We conduct a user study to evaluate the usability of our GOTCHA construction. We also generate a GOTCHA challenge where we encourage artificial intelligence and security researchers to try to crack several passwords protected with our scheme.

preprint2013arXiv

Naturally Rehearsing Passwords

We introduce quantitative usability and security models to guide the design of password management schemes --- systematic strategies to help users create and remember multiple passwords. In the same way that security proofs in cryptography are based on complexity-theoretic assumptions (e.g., hardness of factoring and discrete logarithm), we quantify usability by introducing usability assumptions. In particular, password management relies on assumptions about human memory, e.g., that a user who follows a particular rehearsal schedule will successfully maintain the corresponding memory. These assumptions are informed by research in cognitive science and validated through empirical studies. Given rehearsal requirements and a user's visitation schedule for each account, we use the total number of extra rehearsals that the user would have to do to remember all of his passwords as a measure of the usability of the password scheme. Our usability model leads us to a key observation: password reuse benefits users not only by reducing the number of passwords that the user has to memorize, but more importantly by increasing the natural rehearsal rate for each password. We also present a security model which accounts for the complexity of password management with multiple accounts and associated threats, including online, offline, and plaintext password leak attacks. Observing that current password management schemes are either insecure or unusable, we present Shared Cues--- a new scheme in which the underlying secret is strategically shared across accounts to ensure that most rehearsal requirements are satisfied naturally while simultaneously providing strong security. The construction uses the Chinese Remainder Theorem to achieve these competing goals.

preprint2012arXiv

The Johnson-Lindenstrauss Transform Itself Preserves Differential Privacy

This paper proves that an "old dog", namely -- the classical Johnson-Lindenstrauss transform, "performs new tricks" -- it gives a novel way of preserving differential privacy. We show that if we take two databases, $D$ and $D'$, such that (i) $D'-D$ is a rank-1 matrix of bounded norm and (ii) all singular values of $D$ and $D'$ are sufficiently large, then multiplying either $D$ or $D'$ with a vector of iid normal Gaussians yields two statistically close distributions in the sense of differential privacy. Furthermore, a small, deterministic and \emph{public} alteration of the input is enough to assert that all singular values of $D$ are large. We apply the Johnson-Lindenstrauss transform to the task of approximating cut-queries: the number of edges crossing a $(S,\bar S)$-cut in a graph. We show that the JL transform allows us to \emph{publish a sanitized graph} that preserves edge differential privacy (where two graphs are neighbors if they differ on a single edge) while adding only $O(|S|/ε)$ random noise to any given query (w.h.p). Comparing the additive noise of our algorithm to existing algorithms for answering cut-queries in a differentially private manner, we outperform all others on small cuts ($|S| = o(n)$). We also apply our technique to the task of estimating the variance of a given matrix in any given direction. The JL transform allows us to \emph{publish a sanitized covariance matrix} that preserves differential privacy w.r.t bounded changes (each row in the matrix can change by at most a norm-1 vector) while adding random noise of magnitude independent of the size of the matrix (w.h.p). In contrast, existing algorithms introduce an error which depends on the matrix dimensions.

preprint2011arXiv

A Logical Method for Policy Enforcement over Evolving Audit Logs

We present an iterative algorithm for enforcing policies represented in a first-order logic, which can, in particular, express all transmission-related clauses in the HIPAA Privacy Rule. The logic has three features that raise challenges for enforcement --- uninterpreted predicates (used to model subjective concepts in privacy policies), real-time temporal properties, and quantification over infinite domains (such as the set of messages containing personal information). The algorithm operates over audit logs that are inherently incomplete and evolve over time. In each iteration, the algorithm provably checks as much of the policy as possible over the current log and outputs a residual policy that can only be checked when the log is extended with additional information. We prove correctness and termination properties of the algorithm. While these results are developed in a general form, accounting for many different sources of incompleteness in audit logs, we also prove that for the special case of logs that maintain a complete record of all relevant actions, the algorithm effectively enforces all safety and co-safety properties. The algorithm can significantly help automate enforcement of policies derived from the HIPAA Privacy Rule.

preprint2011arXiv

Formal Verification of Differential Privacy for Interactive Systems

Differential privacy is a promising approach to privacy preserving data analysis with a well-developed theory for functions. Despite recent work on implementing systems that aim to provide differential privacy, the problem of formally verifying that these systems have differential privacy has not been adequately addressed. This paper presents the first results towards automated verification of source code for differentially private interactive systems. We develop a formal probabilistic automaton model of differential privacy for systems by adapting prior work on differential privacy for functions. The main technical result of the paper is a sound proof technique based on a form of probabilistic bisimulation relation for proving that a system modeled as a probabilistic automaton satisfies differential privacy. The novelty lies in the way we track quantitative privacy leakage bounds using a relation family instead of a single relation. We illustrate the proof technique on a representative automaton motivated by PINQ, an implemented system that is intended to provide differential privacy. To make our proof technique easier to apply to realistic systems, we prove a form of refinement theorem and apply it to show that a refinement of the abstract PINQ automaton also satisfies our differential privacy definition. Finally, we begin the process of automating our proof technique by providing an algorithm for mechanically checking a restricted class of relations from the proof technique.

preprint2011arXiv

On the Semantics of Purpose Requirements in Privacy Policies

Privacy policies often place requirements on the purposes for which a governed entity may use personal information. For example, regulations, such as HIPAA, require that hospital employees use medical information for only certain purposes, such as treatment. Thus, using formal or automated methods for enforcing privacy policies requires a semantics of purpose requirements to determine whether an action is for a purpose or not. We provide such a semantics using a formalism based on planning. We model planning using a modified version of Markov Decision Processes, which exclude redundant actions for a formal definition of redundant. We use the model to formalize when a sequence of actions is only for or not for a purpose. This semantics enables us to provide an algorithm for automating auditing, and to describe formally and compare rigorously previous enforcement methods.