Synergy Between Circuit Obfuscation and Circuit Minimization

We study close connections between Indistinguishability Obfuscation (IO) and the Minimum Circuit Size Problem (MCSP), and argue that efficient algorithms/construction for MCSP and IO create a synergy. Some of our main results are: - If there exists a perfect (imperfect) IO that is computationally secure against nonuniform polynomial-size circuits, then for all k ? ?: NP ? ZPP^{MCSP} ? SIZE[n^k] (MA ? ZPP^{MCSP} ? SIZE[n^k]). - In addition, if there exists a perfect IO that is computationally secure against nonuniform polynomial-size circuits, then NEXP ? ZPEXP^{MCSP} ? P/poly. - If MCSP ? BPP, then statistical security and computational security for IO are equivalent. - If computationally-secure perfect IO exists, then MCSP ? BPP iff NP = ZPP. - If computationally-secure perfect IO exists, then ZPEXP ? BPP. To the best of our knowledge, this is the first consequence of strong circuit lower bounds from the existence of an IO. The results are obtained via a construction of an optimal universal distinguisher, computable in randomized polynomial time with access to the MCSP oracle, that will distinguish any two circuit-samplable distributions with the advantage that is the statistical distance between these two distributions minus some negligible error term. This is our main technical contribution. As another immediate application, we get a simple proof of the result by Allender and Das (Inf. Comput., 2017) that SZK ? BPP^{MCSP}

Approximate Set Union Via Approximate Randomization

We develop an randomized approximation algorithm for the size of set union problem \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert, which given a list of sets $A_1,...,A_m$ with approximate set size $m_i$ for $A_i$ with $m_i\in \left((1-\beta_L)|A_i|, (1+\beta_R)|A_i|\right)$, and biased random generators with Prob(x=\randomElm(A_i))\in \left[{1-\alpha_L\over |A_i|},{1+\alpha_R\over |A_i|}\right] for each input set $A_i$ and element $x\in A_i,$ where $i=1, 2, ..., m$. The approximation ratio for \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert is in the range $[(1-\epsilon)(1-\alpha_L)(1-\beta_L), (1+\epsilon)(1+\alpha_R)(1+\beta_R)]$ for any $\epsilon\in (0,1)$, where $\alpha_L, \alpha_R, \beta_L,\beta_R\in (0,1)$. The complexity of the algorithm is measured by both time complexity, and round complexity. The algorithm is allowed to make multiple membership queries and get random elements from the input sets in one round. Our algorithm makes adaptive accesses to input sets with multiple rounds. Our algorithm gives an approximation scheme with O(\setCount\cdot(\log \setCount)^{O(1)}) running time and $O(\log m)$ rounds, where $m$ is the number of sets. Our algorithm can handle input sets that can generate random elements with bias, and its approximation ratio depends on the bias. Our algorithm gives a flexible tradeoff with time complexity O\left(\setCount^{1+\xi}\right) and round complexity $O\left({1\over \xi}\right)$ for any $\xi\in(0,1)$

Soundtrack recommendation for images

The drastic increase in production of multimedia content has emphasized the research concerning its organization and retrieval. In this thesis, we address the problem of music retrieval when a set of images is given as input query, i.e., the problem of soundtrack recommendation for images. The task at hand is to recommend appropriate music to be played during the presentation of a given set of query images. To tackle this problem, we formulate a hypothesis that the knowledge appropriate for the task is contained in publicly available contemporary movies. Our approach, Picasso, employs similarity search techniques inside the image and music domains, harvesting movies to form a link between the domains. To achieve a fair and unbiased comparison between different soundtrack recommendation approaches, we proposed an evaluation benchmark. The evaluation results are reported for Picasso and the baseline approach, using the proposed benchmark. We further address two efficiency aspects that arise from the Picasso approach. First, we investigate the problem of processing top-K queries with set-defined selections and propose an index structure that aims at minimizing the query answering latency. Second, we address the problem of similarity search in high-dimensional spaces and propose two enhancements to the Locality Sensitive Hashing (LSH) scheme. We also investigate the prospects of a distributed similarity search algorithm based on LSH using the MapReduce framework. Finally, we give an overview of the PicasSound|a smartphone application based on the Picasso approach.Der drastische Anstieg von verfügbaren Multimedia-Inhalten hat die Bedeutung der Forschung über deren Organisation sowie Suche innerhalb der Daten hervorgehoben. In dieser Doktorarbeit betrachten wir das Problem der Suche nach geeigneten Musikstücken als Hintergrundmusik für Diashows. Wir formulieren die Hypothese, dass die für das Problem erforderlichen Kenntnisse in öffentlich zugänglichen, zeitgenössischen Filmen enthalten sind. Unser Ansatz, Picasso, verwendet Techniken aus dem Bereich der Ähnlichkeitssuche innerhalb von Bild- und Musik-Domains, um basierend auf Filmszenen eine Verbindung zwischen beliebigen Bildern und Musikstücken zu lernen. Um einen fairen und unvoreingenommenen Vergleich zwischen verschiedenen Ansätzen zur Musikempfehlung zu erreichen, schlagen wir einen Bewertungs-Benchmark vor. Die Ergebnisse der Auswertung werden, anhand des vorgeschlagenen Benchmarks, für Picasso und einen weiteren, auf Emotionen basierenden Ansatz, vorgestellt. Zusätzlich behandeln wir zwei Effizienzaspekte, die sich aus dem Picasso Ansatz ergeben. (i) Wir untersuchen das Problem der Ausführung von top-K Anfragen, bei denen die Ergebnismenge ad-hoc auf eine kleine Teilmenge des gesamten Indexes eingeschränkt wird. (ii) Wir behandeln das Problem der Ähnlichkeitssuche in hochdimensionalen Räumen und schlagen zwei Erweiterungen des Lokalitätssensitiven Hashing (LSH) Schemas vor. Zusätzlich untersuchen wir die Erfolgsaussichten eines verteilten Algorithmus für die Ähnlichkeitssuche, der auf LSH unter Verwendung des MapReduce Frameworks basiert. Neben den vorgenannten wissenschaftlichen Ergebnissen beschreiben wir ferner das Design und die Implementierung von PicassSound, einer auf Picasso basierenden Smartphone-Anwendung