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1. Short Paper: Probabilistically Almost-Oblivious Computation

   https://doi.org/10.1145/3411506.3417598  

   Sweet, Ian; Darais, David; Hicks, Michael (November 2020, Programming Languages and Analysis for Security (PLAS))

   null (Ed.)

   Memory-trace Obliviousness (MTO) is a noninterference property: programs that enjoy it have neither explicit nor implicit information leaks, even when the adversary can observe the program counter and the address trace of memory accesses. Probabilistic MTO relaxes MTO to accept probabilistic programs. In prior work, we developed λobliv, whose type system aims to enforce PMTO [2]. We showed that lambda-obliv could typecheck (recursive) Tree ORAM [6], a sophisticated algorithm that implements a probabilistically oblivious key-value store. We conjectured that λobliv ought to be able to typecheck more optimized oblivious data structures (ODSs)[8], but that its type system was as yet too weak.In this short paper we show we were wrong: ODSs cannot be implemented in lambda-obliv because they are not actually PMTO, due to the possibility of overflow, which occurs when a oram_write silently fails due to a local lack of space. This was surprising to us because Tree ORAM can also overflow but is still PMTO. The paper explains what is going on and sketches the task of adapting the PMTO property, and lambda-obliv's type system, to characterize ODS security. 

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2. Sound Probabilistic Inference Via Guide Types

   https://doi.org/10.1145/3453483.3454077  

   Wang, Di; Hoffmann, Jan; Reps, Thomas (June 2021, PLDI '21: 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation)

   null (Ed.)

   Probabilistic programming languages aim to describe and automate Bayesian modeling and inference. Modern languages support programmable inference, which allows users to customize inference algorithms by incorporating guide programs to improve inference performance. For Bayesian inference to be sound, guide programs must be compatible with model programs. One pervasive but challenging condition for model-guide compatibility is absolute continuity, which requires that the model and guide programs define probability distributions with the same support. This paper presents a new probabilistic programming language that guarantees absolute continuity, and features general programming constructs, such as branching and recursion. Model and guide programs are implemented as coroutines that communicate with each other to synchronize the set of random variables they sample during their execution. Novel guide types describe and enforce communication protocols between coroutines. If the model and guide are well-typed using the same protocol, then they are guaranteed to enjoy absolute continuity. An efficient algorithm infers guide types from code so that users do not have to specify the types. The new programming language is evaluated with an implementation that includes the type-inference algorithm and a prototype compiler that targets Pyro. Experiments show that our language is capable of expressing a variety of probabilistic models with nontrivial control flow and recursion, and that the coroutine-based computation does not introduce significant overhead in actual Bayesian inference. 

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3. A Theory of Composition for Differential Obliviousness

   Zhou, Mingxun; Shi, Elaine; Chan, Hubert; Maimon, Shir (April 2023, Eurocrypt 2023)

   Differential obliviousness (DO) is a privacy notion which guarantees that the access patterns of a program satisfies differential privacy. Differential obliviousness was studied in a sequence of recent works as a relaxation of full obliviousness. Earlier works showed that DO not only allows us to circumvent the logarithmic-overhead barrier of fully oblivious algorithms, in many cases, it also allows us to achieve polynomial speedup over full obliviousness, since it avoids “padding to the worst-case” behavior of fully oblivious algorithms. Despite the promises of differential obliviousness (DO), a significant barrier that hinders its broad application is the lack of composability. In particular, when we apply one DO algorithm to the output of another DO algorithm, the composed algorithm may no longer be DO (with reasonable parameters). Specifically, the outputs of the first DO algorithm on two neighboring inputs may no longer be neighboring, and thus we cannot directly benefit from the DO guarantee of the second algorithm. In this work, we are the first to explore a theory of composition for differentially oblivious algorithms. We propose a refinement of the DO notion called (ε, δ)-neighbor-preserving-DO, or (ε,δ)-NPDO for short, and we prove that our new notion indeed provides nice compositional guarantees. In this way, the algorithm designer can easily track the privacy loss when composing multiple DO algorithms. We give several example applications to showcase the power and expressiveness of our new NPDO notion. One of these examples is a result of independent interest: we use the com- positional framework to prove an optimal privacy amplification theorem for the differentially oblivious shuffle model. In other words, we show that for a class of distributed differentially private mechanisms in the shuffle-model, one can replace the perfectly secure shuffler with a DO shuffler, and nonetheless enjoy almost the same privacy amplification enabled by a shuffler. 

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4. Doquet: Differentially Oblivious Range and Join Queries with Private Data Structures

   https://doi.org/10.14778/3625054.3625055  

   Qiu, Lina; Kellaris, Georgios; Mamoulis, Nikos; Nissim, Kobbi; Kollios, George (September 2023, Proceedings of the VLDB Endowment)

   Most cloud service providers offer limited data privacy guarantees, discouraging clients from using them for managing their sensitive data. Cloud providers may use servers with Trusted Execution Environments (TEEs) to protect outsourced data, while supporting remote querying. However, TEEs may leak access patterns and allow communication volume attacks, enabling an honest-but-curious cloud provider to learn sensitive information. Oblivious algorithms can be used to completely hide data access patterns, but their high overhead could render them impractical. To alleviate the latter, the notion of Differential Obliviousness (DO) has been recently proposed. DO applies differential privacy (DP) on access patterns while hiding the communication volume of intermediate and final results; it does so by trading some level of privacy for efficiency. We present Doquet:DifferentiallyOblivious Range and JoinQueries with Private Data Structures, a framework for DO outsourced database systems. Doquet is the first approach that supports private data structures, indices, selection, foreign key join, many-to-many join, and their composition select-join in arealisticTEE setting, even when the accesses to the private memory can be eavesdropped on by the adversary. We prove that the algorithms in Doquet satisfy differential obliviousness. Furthermore, we implemented Doquet and tested it on a machine having a second generation of Intel SGX (TEE); the results show that Doquet offers up to an order of magnitude speedup in comparison with other fully oblivious and differentially oblivious approaches. 

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5. Probabilistic Resource-Aware Session Types

   https://doi.org/10.1145/3571259  

   Das, Ankush; Wang, Di; Hoffmann, Jan (January 2023, Proceedings of the ACM on Programming Languages)

   Session types guarantee that message-passing processes adhere to predefined communication protocols. Prior work on session types has focused on deterministic languages but many message-passing systems, such as Markov chains and randomized distributed algorithms, are probabilistic. To implement and analyze such systems, this article develops the meta theory of probabilistic session types with an application focus on automatic expected resource analysis. Probabilistic session types describe probability distributions over messages and are a conservative extension of intuitionistic (binary) session types. To send on a probabilistic channel, processes have to utilize internal randomness from a probabilistic branching or external randomness from receiving on a probabilistic channel. The analysis for expected resource bounds is smoothly integrated with the type system and is a variant of automatic amortized resource analysis. Type inference relies on linear constraint solving to automatically derive symbolic bounds for various cost metrics. The technical contributions include the meta theory that is based on a novel nested multiverse semantics and a type-reconstruction algorithm that allows flexible mixing of different sources of randomness without burdening the programmer with complex type annotations. The type system has been implemented in the language NomosPro with linear-time type checking. Experiments demonstrate that NomosPro is applicable in different domains such as cost analysis of randomized distributed algorithms, analysis of Markov chains, probabilistic analysis of amortized data structures and digital contracts. NomosPro is also shown to be scalable by (i) implementing two broadcast and a bounded retransmission protocol where messages are dropped with a fixed probability, and (ii) verifying the limiting distribution of a Markov chain with 64 states and 420 transitions. 

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