research-article

Data-oblivious graph algorithms for secure computation and outsourcing

Authors:

Marina Blanton,

Mehrdad AlisagariAuthors Info & Claims

ASIA CCS '13: Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security

Pages 207 - 218

https://doi.org/10.1145/2484313.2484341

Published: 08 May 2013 Publication History

Abstract

This work treats the problem of designing data-oblivious algorithms for classical and widely used graph problems. A data-oblivious algorithm is defined as having the same sequence of operations regardless of the input data and data-independent memory accesses. Such algorithms are suitable for secure processing in outsourced and similar environments, which serves as the main motivation for this work. We provide data-oblivious algorithms for breadth-first search, single-source single-destination shortest path, minimum spanning tree, and maximum flow, the asymptotic complexities of which are optimal, or close to optimal, for dense graphs.

References

[1]

M. Ajtai. Oblivious RAMs without cryptographic assumptions. In STOC, pages 181--190, 2010.

Digital Library

[2]

L. Arge, M. Bender, E. Demaine, B. Holland-Minkley, and J. Munro. Cache-oblivious priority queue and graph algorithm applications. In STOC, pages 268--276, 2002.

Digital Library

[3]

L. Arge, M. Bender, E. Demaine, B. Holland-Minkley, and J. Munro. An optimal cache-oblivious priority queue and its application to graph algorithms. SIAM Journal on Computing, pages 1672--1695, 2007.

Digital Library

[4]

M. Atallah, K. Frikken, and S. Wang. Private outsourcing of matrix multiplication over closed semi-rings. In SECRYPT, pages 136--144, 2012.

[5]

M. Blanton and E. Aguiar. Private and oblivious set and multiset operations. In ASIACCS, 2012.

Digital Library

[6]

M. Blanton, M. Atallah, K. Frikken, and Q. Malluhi. Secure and efficient outsourcing of sequence comparisons. In ESORICS, pages 505--522, 2012.

Digital Library

[7]

D. Boneh, D. Mazieres, and R. Popa. Remote oblivious storage: Making oblivious RAM practical. Technical Report MIT-CSAIL-TR-2011-018, MIT, 2011.

[8]

J. Brickell and V. Shmatikov. Privacy-preserving graph algorithms in the semi-honest model. In ASIACRYPT, pages 236--252, 2005.

Digital Library

[9]

G. Brodal. Cache-oblivious algorithms and data structures. In SWAT, pages 3--13, 2004.

[10]

G. Brodal, R. Fagerberg, U. Meyer, and N. Zeh. Cache-oblivious data structures and algorithms for undirected breadth-first search and shortest paths. In SWAT, pages 480--492, 2004.

[11]

C. Cachin, S. Micali, and M. Stadler. Computationally private information retrieval with polylog communication. In EUROCRYPT, pages 402--414, 1999.

Digital Library

[12]

R. Canetti. Security and composition of multiparty cryptographic protocols. Journal of Cryptology, 13(1):143--202, 2000.

Digital Library

[13]

O. Catrina and S. de Hoogh. Improved primitives for secure multiparty integer computation. In SCN, pages 182--199, 2010.

Digital Library

[14]

B. Chor, O. Goldreich, E. Kushilevitz, and M. Sudan. Private information retrieval. In FOCS, pages 41--50, 1995.

Digital Library

[15]

B. Chor, E. Kushilevitz, O. Goldreich, and M. Sudan. Private information retrieval. Journal of the ACM, pages 965--981, 1998.

Digital Library

[16]

T. Cormen, C. Leiserson, R. Rivest, and C. Stein. Introduction to algorithms. The MIT Press, 2009.

Digital Library

[17]

I. Damgård, S. Meldgaard, and J. Nielsen. Perfectly secure oblivious RAM without random oracles. In TCC, pages 144--163, 2011.

Digital Library

[18]

D. Eppstein, M. Goodrich, and R. Tamassia. Privacy-preserving data-oblivious geometric algorithms for geographic data. In GIS, pages 13--22, 2010.

Digital Library

[19]

C. Erway, A. Kupcu, C. Papamanthou, and R. Tamassia. Dynamic provable data possession. In CCS, pages 213--222, 2009.

Digital Library

[20]

P. Failla. Heuristic search in encrypted graphs. In SECURWARE, pages 82--87, 2010.

Digital Library

[21]

K.B. Frikken and P. Golle. Private social network analysis: how to assemble pieces of a graph privately. In ACM Workshop on Privacy in the Electronic Society (WPES), pages 89--98, 2006.

Digital Library

[22]

C. Gentry and Z. Ramzan. Single-database private information retrieval with constant communication rate. In ICALP, pages 803--815, 2005.

Digital Library

[23]

O. Goldreich. Towards a theory of software protection and simulation by oblivious RAMs. In STOC, pages 182--194, 1987.

Digital Library

[24]

O. Goldreich and R. Ostrovsky. Software protection and simulation on oblivious RAMs. Journal of the ACM, 43(3):431--473, 1996.

Digital Library

[25]

M. Goodrich. Randomized Shellsort: A simple oblivious sorting algorithm. In SODA, pages 1262--1277, 2010.

Digital Library

[26]

M. Goodrich. Data-oblivious external-memory algorithms for the compaction, selection, and sorting of outsourced data. In SPAA, pages 379--388, 2011.

Digital Library

[27]

M. Goodrich and M. Mitzenmacher. Privacy-preserving access of outsourced data via oblivious RAM simulation. In ICALP, pages 576--587, 2011.

Digital Library

[28]

M. Goodrich, O. Ohrimenko, and R. Tamassia. Data-oblivious graph drawing model and algorithms. Arxiv preprint arXiv:1209:0756, 2012.

[29]

E. Kushilevitz, S. Lu, and R. Ostrovsky. On the (in) security of hash-based oblivious RAM and a new balancing scheme. In SODA, pages 143--156, 2012.

Digital Library

[30]

E. Kushilevitz and R. Ostrovsky. Replication is not needed: Single database, computationally-private information retrieval. In FOCS, pages 364--373, 1997.

Digital Library

[31]

H. Lipmaa. An oblivious transfer protocol with log-squared total communication. In Information Security Conference (ISC), pages 314--328, 2005.

Digital Library

[32]

K. Mouratidis and M. Yiu. Shortest path computation with no information leakage. VLDB Endowment, 5(8):692--703, 2012.

Digital Library

[33]

R. Ostrovsky. Efficient computation on oblivious RAMs. In STOC, pages 514--523, 1990.

Digital Library

[34]

B. Pinkas and T. Reinman. Oblivious RAM revisited. In CRYPTO, pages 502--519, 2010.

Digital Library

[35]

A. Shamir. How to share a secret. Communications of the ACM, 22(11):612--613, 1979.

Digital Library

[36]

E. Shi, E. Stefanov, and M. Li. Oblivious RAM with O((logN)3) worst-case cost. In ASIACRYPT, pages 197--214, 2011.

Digital Library

[37]

E. Stefanov, E. Shi, and D. Song. Towards practical oblivious RAM. In Network and Distributed System Security Symposium (NDSS), 2012.

[38]

S. Wang, X. Ding, R. Deng, and F. Bao. Private information retrieval using trusted hardware. In ESORICS, pages 49--64, 2006.

Digital Library

[39]

P. Williams and R. Sion. Usable PIR. In Network and Distributed System Security Symposium (NDSS), 2008.

[40]

P. Williams, R. Sion, and B. Carbunar. Building castles out of mud: Practical access pattern privacy and correctness on untrusted storage. In CCS, pages 139--148, 2008.

Digital Library

[41]

A. Yao. How to generate and exchange secrets. In FOCS, pages 162--167, 1986.

Digital Library

Cited By

Ehrmanntraut VMeyer UAyday EVaidya J(2024)Privacy-Preserving Breadth-First-Search and Maximal FlowProceedings of the 23rd Workshop on Privacy in the Electronic Society10.1145/3689943.3695041(73-97)Online publication date: 20-Nov-2024
https://dl.acm.org/doi/10.1145/3689943.3695041
Tiruye BBiernacki LAdem TMola PAustin T(2024)Octal: Efficient Automatic Data-Oblivious Program Transformations to Eliminate Side-Channel Leakage2024 IEEE Secure Development Conference (SecDev)10.1109/SecDev61143.2024.00018(129-139)Online publication date: 7-Oct-2024
https://doi.org/10.1109/SecDev61143.2024.00018
Ngai NDemertzis IChamani JPapadopoulos D(2024)Distributed & Scalable Oblivious Sorting and Shuffling2024 IEEE Symposium on Security and Privacy (SP)10.1109/SP54263.2024.00153(4277-4295)Online publication date: 19-May-2024
https://doi.org/10.1109/SP54263.2024.00153
Show More Cited By

Index Terms

Data-oblivious graph algorithms for secure computation and outsourcing
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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Published In

cover image ACM Conferences

ASIA CCS '13: Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security

May 2013

574 pages

ISBN:9781450317672

DOI:10.1145/2484313

General Chairs:
Kefei Chen
Shanghai Jiao Tong University, China
,
Qi Xie
Hangzhou Normal University, China
,
Weidong Qiu
Shanghai Jiao Tong University, China
,
Program Chairs:
Ninghui Li
Purdue University, USA
,
Wen-Guey Tzeng
National Chiao Tung University, Taiwan

Copyright © 2013 ACM.

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SIGSAC: ACM Special Interest Group on Security, Audit, and Control

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New York, NY, United States

Publication History

Published: 08 May 2013

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ASIA CCS '13

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SIGSAC

ASIA CCS '13: 8th ACM Symposium on Information, Computer and Communications Security

May 8 - 10, 2013

Hangzhou, China

Acceptance Rates

ASIA CCS '13 Paper Acceptance Rate 35 of 216 submissions, 16%;

Overall Acceptance Rate 418 of 2,322 submissions, 18%

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Cited By

Ehrmanntraut VMeyer UAyday EVaidya J(2024)Privacy-Preserving Breadth-First-Search and Maximal FlowProceedings of the 23rd Workshop on Privacy in the Electronic Society10.1145/3689943.3695041(73-97)Online publication date: 20-Nov-2024
https://dl.acm.org/doi/10.1145/3689943.3695041
Tiruye BBiernacki LAdem TMola PAustin T(2024)Octal: Efficient Automatic Data-Oblivious Program Transformations to Eliminate Side-Channel Leakage2024 IEEE Secure Development Conference (SecDev)10.1109/SecDev61143.2024.00018(129-139)Online publication date: 7-Oct-2024
https://doi.org/10.1109/SecDev61143.2024.00018
Ngai NDemertzis IChamani JPapadopoulos D(2024)Distributed & Scalable Oblivious Sorting and Shuffling2024 IEEE Symposium on Security and Privacy (SP)10.1109/SP54263.2024.00153(4277-4295)Online publication date: 19-May-2024
https://doi.org/10.1109/SP54263.2024.00153
Li XLuo YGao M(2024)Bulkor: Enabling Bulk Loading for Path ORAM2024 IEEE Symposium on Security and Privacy (SP)10.1109/SP54263.2024.00103(4258-4276)Online publication date: 19-May-2024
https://doi.org/10.1109/SP54263.2024.00103
He SDing HTian TLiu HJiang H(2024)VPCS: Verifiable Query Scheme for Privacy-preserving Constrained Shortest Path over Encrypted Graph Data2024 IEEE International Conference on Web Services (ICWS)10.1109/ICWS62655.2024.00145(1217-1226)Online publication date: 7-Jul-2024
https://doi.org/10.1109/ICWS62655.2024.00145
Chen CZheng FCui JCao YLiu GWu JZhou J(2024)Survey and open problems in privacy-preserving knowledge graph: merging, query, representation, completion, and applicationsInternational Journal of Machine Learning and Cybernetics10.1007/s13042-024-02106-6Online publication date: 2-Mar-2024
https://doi.org/10.1007/s13042-024-02106-6
Guo JSun J(2024)Secure shortest distance queries over encrypted graph in cloud computingWireless Networks10.1007/s11276-024-03692-730:4(2633-2646)Online publication date: 29-Feb-2024
https://doi.org/10.1007/s11276-024-03692-7
Luo NWeng CSingh JTan GRaykova MPiskac R(2024)Privacy-Preserving Regular Expression Matching Using TNFAComputer Security – ESORICS 202410.1007/978-3-031-70890-9_12(225-246)Online publication date: 6-Sep-2024
https://doi.org/10.1007/978-3-031-70890-9_12
Ostrovsky B(2024)Privacy-Preserving DijkstraAdvances in Cryptology – CRYPTO 202410.1007/978-3-031-68400-5_3(74-110)Online publication date: 16-Aug-2024
https://doi.org/10.1007/978-3-031-68400-5_3
Li XSun NLuo YGao M(2023)SODA: A Set of Fast Oblivious Algorithms in Distributed Secure Data AnalyticsProceedings of the VLDB Endowment10.14778/3587136.358714216:7(1671-1684)Online publication date: 8-May-2023
https://dl.acm.org/doi/10.14778/3587136.3587142
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