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Oblivious Parallel Tight Compaction

Gilad Asharov, Ilan Komargodski, Wei-Kai Lin, Enoch Peserico, Elaine Shi, Adam D. Smith, Daniel Wichs, Yael Tauman Kalai
2020 Conference on Information-Theoretic Cryptography  
Tight compaction is not only an important algorithmic task by itself, but its oblivious version has also played a key role in recent constructions of oblivious RAM compilers.  ...  We present an oblivious deterministic algorithm for tight compaction such that for input arrays of n balls requires O(n) total work and O(log n) depth.  ...  To perform loose compaction on the "zoomed out" array we apply the naive 11:6 Oblivious Parallel Tight Compaction oblivious algorithm to compute routes.  ... 
doi:10.4230/lipics.itc.2020.11 dblp:conf/icits/AsharovKLPS20 fatcat:zjvcdb5j4bbhpl22urdhhpcrgi

Deterministic oblivious distribution (and tight compaction) in linear time [article]

Enoch Peserico
2018 arXiv   pre-print
Our O(N) result improves the running-time upper bounds for deterministic tight compaction, for randomized tight compaction, and for the simpler problem of randomized loose compaction (move the M marked  ...  As a corollary, we answer affirmatively to an open question about the existence of a deterministic oblivious algorithm with O(N) running time for tight compaction (move the M marked elements to the first  ...  tight compaction, randomized tight compaction, and randomized O(1)−loose compaction of n−element arrays.  ... 
arXiv:1807.06719v1 fatcat:nriz2pjlfrbazhen6znefuijnm

Optimal Sorting Circuits for Short Keys [article]

Wei-Kai Lin, Elaine Shi
2021 arXiv   pre-print
Building Blocks for the Oblivious PRAM Model In this section, we present some building blocks that can be implemented as deterministic, oblivious parallel algorithms.  ...  Sorting Short Keys on an Oblivious PRAM Now, we can put everything together and obtain an oblivious parallel algorithm that sorts an input array with short keys. Proof.  ...  In fact, to achieve this, we can use the tight compaction circuit by Asharov et al. [ALS21] , but replace some its building blocks with parallel versions (see Theorem 13 .1 for more details).  ... 
arXiv:2102.11489v2 fatcat:ui3fp5tiibeodorpujo2djxari

Data-Oblivious Data Structures

John C. Mitchell, Joe Zimmerman, Marc Herbstritt
2014 Symposium on Theoretical Aspects of Computer Science  
We also establish a new upper bound for oblivious data compaction, and use this result to show that an "offline" variant of the Oblivious RAM problem can be solved with O(log n log log n) expected amortized  ...  Data-oblivious algorithms play a significant role in secure cloud computing, since programs that are run on secret data-as in fully homomorphic encryption or secure multiparty computation-must be data-oblivious  ...  However, for the next section, we will need fast tight compaction.  ... 
doi:10.4230/lipics.stacs.2014.554 dblp:conf/stacs/MitchellZ14 fatcat:fvpe7ouwl5bkvejpxcik753ys4

Oblivious Network RAM and Leveraging Parallelism to Achieve Obliviousness [chapter]

Dana Dachman-Soled, Chang Liu, Charalampos Papamanthou, Elaine Shi, Uzi Vishkin
2015 Lecture Notes in Computer Science  
We present new constructions for obliviously simulating general or parallel programs in the Network RAM model.  ...  In this paper, we consider new models of computation in which the cost of obliviousness can be fundamentally reduced in comparison with the standard ORAM model.  ...  Lemma 2 (Log * -time parallel algorithm for colored compaction [4] ).  ... 
doi:10.1007/978-3-662-48797-6_15 fatcat:zxmytox75rfzrkobd5errdzzne

Oblivious Network RAM and Leveraging Parallelism to Achieve Obliviousness

Dana Dachman-Soled, Chang Liu, Charalampos Papamanthou, Elaine Shi, Uzi Vishkin
2018 Journal of Cryptology  
We present new constructions for obliviously simulating general or parallel programs in the Network RAM model.  ...  In this paper, we consider new models of computation in which the cost of obliviousness can be fundamentally reduced in comparison with the standard ORAM model.  ...  Lemma 2 (Log * -time parallel algorithm for colored compaction [4] ).  ... 
doi:10.1007/s00145-018-9301-4 fatcat:4uu32x765jhafnvyvibflmbgbq

Data-Oblivious External-Memory Algorithms for the Compaction, Selection, and Sorting of Outsourced Data [article]

Michael T. Goodrich
2011 arXiv   pre-print
We present data-oblivious algorithms in the external-memory model for compaction, selection, and sorting.  ...  We show that compaction and selection can be done data-obliviously using $O(N/B)$ I/Os, and sorting can be done, with a high probability of success, using $O((N/B)\log_{M/B} (N/B))$ I/Os.  ...  Tight Order-Preserving Compaction. Let us now show how to perform a tight order-preserving compaction for a dense array in a data-oblivious fashion using O((N/B) log M/B (N/B)) I/Os.  ... 
arXiv:1103.5102v1 fatcat:jl4u4cn3wrez5abbacp7hwyuca

Sorting Short Keys in Circuits of Size o(n log n) [article]

Gilad Asharov, Wei-Kai Lin, Elaine Shi
2020 arXiv   pre-print
More specifically, • Tight compaction from loose compaction.  ...  Tight Compaction from Loose Compaction In this section, we show how to construct a circuit for tight compaction from Loose Compaction and from a Swapper circuit.  ...  Afterwards, we run 1 instance of (⌈n/f (n)⌉ , f (n) · w)-tight compactor and (1 − ǫ 4 ) · n f (n) instances of (f (n), w)-tight compactor.  ... 
arXiv:2010.09884v2 fatcat:ji2762hgevbpxijglqczbp5sxu

Resource Oblivious Sorting on Multicores

Richard Cole, Vijaya Ramachandran
2017 ACM Transactions on Parallel Computing  
The parallel complexity (or critical path length) of the algorithm is O( n · n), which improves on previous bounds for optimal cache oblivious sorting. The algorithm also has low false sharing costs.  ...  Sequentially, it sorts n elements in O(n n) time cache-obliviously with an optimal number of cache misses.  ...  The Cache-Oblivious Parallel Implementation of SPMS To achieve efficient oblivious performance, the merging algorithm MS needs to be implemented using tasks achieving the optimal ideal costing, as defined  ... 
doi:10.1145/3040221 fatcat:sqh4ozlzq5fq5eommeo6onrscy

Resource Oblivious Sorting on Multicores [chapter]

Richard Cole, Vijaya Ramachandran
2010 Lecture Notes in Computer Science  
We improve on the above cache-oblivious processor-aware parallel implementation by using the Priority Work Stealing Scheduler (PWS) that we presented recently in a companion paper [12] .  ...  The parallel complexity (or critical path length) of the algorithm is O(log n log log n), which improves on previous bounds for deterministic sample sort.  ...  The Cache-Oblivious Parallel Implementation of SPMS To achieve efficient oblivious performance, the merging algorithm MS needs to be implemented using tasks achieving the optimal ideal costing, as defined  ... 
doi:10.1007/978-3-642-14165-2_20 fatcat:bkb3otgap5hmlh2kgymmiffcve

Privacy-Preserving Computation with Trusted Computing via Scramble-then-Compute

Hung Dang, Tien Tuan Anh Dinh, Ee-Chien Chang, Beng Chin Ooi
2017 Proceedings on Privacy Enhancing Technologies  
This is over an order-of-magnitude better than single-node data-oblivious algorithms. However, pJoin achieves only 2× speedup, because we cannot parallelize the oblivious expansion algorithm.  ...  Furthermore, its ability to parallelize enables privacy-preserving computation at scale.  ... 
doi:10.1515/popets-2017-0026 dblp:journals/popets/DangDCO17 fatcat:25kvpphyyjgolcsv5refjcp5y4

ERCW PRAMs and optical communication [chapter]

Philip D. MacKenzie, Vijaya Ramachandran
1996 Lecture Notes in Computer Science  
Topics: Parallel Algorithms, Theory of Parallel and Distributed Computing.  ...  This paper presents algorithms and lower bounds for several fundamental problems on the Exclusive Read, Concurrent W rite Parallel Random Access Machine ERCW PRAM and some results for unbounded fan-in,  ...  Tight bounds are not known for the ERCW PRAM. Furthermore, tight bounds are not known for many other problems, including the problems of compaction and nding the maximum.  ... 
doi:10.1007/bfb0024715 fatcat:awcspjz47vg5tlpsr5ndoyrx4q

ERCW PRAMs and optical communication

Philip D. MacKenzie, Vijaya Ramachandran
1998 Theoretical Computer Science  
This paper presents algorithms and lower bounds for several fundamental problems on the Exclusive Read, Concurrent Write Parallel Random Access Machine (ERCW PRAM) and some results for unbounded fan-in  ...  Our results for these two models are of importance because of the close relationship of the ERCW model to the OCPC model, a model of parallel computing based on dynamically reconfigurable optical networks  ...  Tight bounds are not known for the ERCW PRAM. Furthermore, tight bounds are not known for many other problems, including the problems of compaction and finding the maximum.  ... 
doi:10.1016/s0304-3975(97)00199-0 fatcat:el4duxqkjrfglcr4ouegge7doq

Compact Oblivious Routing in Weighted Graphs

Philipp Czerner, Harald Räcke, Fabrizio Grandoni, Grzegorz Herman, Peter Sanders
2020 European Symposium on Algorithms  
This paper designs compact routing schemes for the cost-measure congestion, where the goal is to minimize the maximum relative load of a link in the network (the relative load of a link is its traffic  ...  We show that for arbitrary undirected graphs we can obtain oblivious routing strategies with competitive ratio 𝒪̃(1) that have header length 𝒪̃(1), label size 𝒪̃(1), and require routing-tables of size  ...  The main result of this paper is the existence of a compact oblivious routing scheme, with competitive ratioÕ(1). 36:6 Compact Oblivious Routing in Weighted Graphs Transformation Schemes Our routing  ... 
doi:10.4230/lipics.esa.2020.36 dblp:conf/esa/CzernerR20 fatcat:j3pzquewrbbkffyuapsmzpqcka

Compact Oblivious Routing in Weighted Graphs [article]

Philipp Czerner
2020 arXiv   pre-print
This paper designs compact routing schemes for the cost-measure congestion, where the goal is to minimize the maximum relative load of a link in the network (the relative load of a link is its traffic  ...  We show that for arbitrary undirected graphs we can obtain oblivious routing strategies with competitive ratio $\tilde{\mathcal{O}}(1)$ that have header length $\tilde{\mathcal{O}}(1)$, label size $\tilde  ...  The main result of this paper is the existence of a compact oblivious routing scheme, with competitive ratioÕ(1).  ... 
arXiv:2007.02427v1 fatcat:vnytgd6zqbdlfd4nchv5fbw4gm
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