Recency Queries with Succinct Representation

In the context of the sliding-window set membership problem, and caching policies that require knowledge of item recency, we formalize the problem of Recency on a stream. Informally, the query asks, "when was the last time I saw item x?" Existing structures, such as hash tables, can support a recency query by augmenting item occurrences with timestamps. To support recency queries on a window of W items, this might require ?(W log W) bits. We propose a succinct data structure for Recency. By combining sliding-window dictionaries in a hierarchical structure, and careful design of the underlying hash tables, we achieve a data structure that returns a 1+? approximation to the recency of every item in O(log(? W)) time, in only (1+o(1))(1+?)(?+Wlog(?^(-1))) bits. Here, ? is the information-theoretic lower bound on the number of bits for a set of size W, in a universe of cardinality N

Bloom Filters in Adversarial Environments

Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are independent of the internal randomness of the data structure. In this work, we consider data structures in a more robust model, which we call the adversarial model. Roughly speaking, this model allows an adversary to choose inputs and queries adaptively according to previous responses. Specifically, we consider a data structure known as "Bloom filter" and prove a tight connection between Bloom filters in this model and cryptography. A Bloom filter represents a set $S$ of elements approximately, by using fewer bits than a precise representation. The price for succinctness is allowing some errors: for any $x \in S$ it should always answer `Yes', and for any $x \notin S$ it should answer `Yes' only with small probability. In the adversarial model, we consider both efficient adversaries (that run in polynomial time) and computationally unbounded adversaries that are only bounded in the number of queries they can make. For computationally bounded adversaries, we show that non-trivial (memory-wise) Bloom filters exist if and only if one-way functions exist. For unbounded adversaries we show that there exists a Bloom filter for sets of size $n$ and error $\varepsilon$, that is secure against $t$ queries and uses only $O(n \log{\frac{1}{\varepsilon}}+t)$ bits of memory. In comparison, $n\log{\frac{1}{\varepsilon}}$ is the best possible under a non-adaptive adversary

Probabilistic data types

Dissertação de mestrado integrado em Engenharia InformáticaConflict-Free Replicated Data Types (CRDTs) provide deterministic outcomes from concurrent executions. The conflict resolution mechanism uses information on the ordering of the last operations performed, which indicates if a given operation is known by a replica, typically using some variant of version vectors. This thesis will explore the construction of CRDTs that use a novel stochastic mechanism that can track with high accuracy knowledge of the occurrence of recently performed operations and with less accuracy for older operations. The aim is to obtain better scaling properties and avoid the use of metadata that is linear on the number of replicas.Conflict-Free Replicated Data Types (CRDTs) oferecem resultados determinísticos de execuções concorrentes. O mecanismo de resolução de conflitos usa informação sobre a ordenação das últimas operações realizadas, que indica se uma dada operação é conhecida por uma réplica, geralmente usando alguma variante de version vectors. Esta tese explorara a construção de CRDTs que utilizam um novo mecanismo estocástico que pode identificar com alta precisão o conhecimento sobre a ocorrência de operações realizadas recentemente e com menor precisão para operações mais antigas. O objetivo é a obtenção de melhores propriedades de escalabilidade e evitar o uso de metadados em quantidade linear em relação ao número de réplicas

Encapsulated Search Index: Public-Key, Sub-linear, Distributed, and Delegatable

We build the first sub-linear (in fact, potentially constant-time) public-key searchable encryption system: − server can publish a public key $PK$. − anybody can build an encrypted index for document $D$ under $PK$. − client holding the index can obtain a token $z_w$ from the server to check if a keyword $w$ belongs to $D$. − search using $z_w$ is almost as fast (e.g., sub-linear) as the non-private search. − server granting the token does not learn anything about the document $D$, beyond the keyword $w$. − yet, the token $z_w$ is specific to the pair $(D, w)$: the client does not learn if other keywords $w\u27\neq w$ belong to $D$, or if w belongs to other, freshly indexed documents $D\u27$. − server cannot fool the client by giving a wrong token $z_w$. We call such a primitive Encapsulated Search Index (ESI). Our ESI scheme can be made $(t, n)$- distributed among $n$ servers in the best possible way: non-interactive, verifiable, and resilient to any coalition of up to $(t − 1)$ malicious servers. We also introduce the notion of delegatable ESI and show how to extend our construction to this setting. Our solution — including public indexing, sub-linear search, delegation, and distributed token generation — is deployed as a commercial application by Atakama