3-Party Distributed ORAM from Oblivious Set Membership

Distributed Oblivious RAM (DORAM) protocols allow a group of participants to obliviously access a secret-shared array at a secret-shared index, and DORAM is the key tool for secure multiparty computation (MPC) in the RAM model. In this work, we present a novel 3-party semi-honest DORAM protocol with O((κ + D) logN) communication per access, where N is the size of the memory, κ is a security parameter and D is the block size. Our protocol performs polylogarithmic computation and does not require homomorphic encryption. Under natural parameter choices, this is the most communication-efficient DORAM with these properties. To build this DORAM protocol, we first present an extremely efficient oblivious data structure for answering set membership queries. From this we build an oblivious hash table with asymptotically optimal memory usage and access cost and with negligible failure probability. We believe these are of independent interest.

[1]  Rafail Ostrovsky,et al.  Software protection and simulation on oblivious RAMs , 1996, JACM.

[2]  Srdjan Capkun,et al.  Software Grand Exposure: SGX Cache Attacks Are Practical , 2017, WOOT.

[3]  Michiel H. M. Smid,et al.  On the false-positive rate of Bloom filters , 2008, Inf. Process. Lett..

[4]  Michael Mitzenmacher,et al.  More Robust Hashing: Cuckoo Hashing with a Stash , 2008, ESA.

[5]  Michael T. Goodrich,et al.  Privacy-preserving group data access via stateless oblivious RAM simulation , 2011, SODA.

[6]  Stephen A. Cook,et al.  Time-bounded random access machines , 1972, J. Comput. Syst. Sci..

[7]  GoldreichOded,et al.  Software protection and simulation on oblivious RAMs , 1996 .

[8]  Yuval Ishai,et al.  Distributed Point Functions and Their Applications , 2014, EUROCRYPT.

[9]  Florian Mendel,et al.  Rasta: A cipher with low ANDdepth and few ANDs per bit , 2018, IACR Cryptol. ePrint Arch..

[10]  Benny Pinkas,et al.  Keyword Search and Oblivious Pseudorandom Functions , 2005, TCC.

[11]  Rafail Ostrovsky,et al.  Distributed Oblivious RAM for Secure Two-Party Computation , 2013, TCC.

[12]  Jonathan Katz,et al.  Revisiting Square-Root ORAM: Efficient Random Access in Multi-party Computation , 2016, 2016 IEEE Symposium on Security and Privacy (SP).

[13]  Kasper Green Larsen,et al.  Yes, There is an Oblivious RAM Lower Bound! , 2018, IACR Cryptol. ePrint Arch..

[14]  Elaine Shi,et al.  Circuit ORAM: On Tightness of the Goldreich-Ostrovsky Lower Bound , 2015, IACR Cryptol. ePrint Arch..

[15]  Elaine Shi,et al.  Path ORAM: an extremely simple oblivious RAM protocol , 2012, CCS.

[16]  Michael Mitzenmacher,et al.  Some Open Questions Related to Cuckoo Hashing , 2009, ESA.

[17]  Elaine Shi,et al.  Oblivious Hashing Revisited, and Applications to Asymptotically Efficient ORAM and OPRAM , 2017, ASIACRYPT.

[18]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[19]  Elaine Shi,et al.  Oblivious RAM with O((logN)3) Worst-Case Cost , 2011, ASIACRYPT.

[20]  Sarvar Patel,et al.  PanORAMa: Oblivious RAM with Logarithmic Overhead , 2018, 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS).

[21]  Benny Pinkas,et al.  Oblivious RAM Revisited , 2010, CRYPTO.

[22]  Stephan Krenn,et al.  Cache Games -- Bringing Access-Based Cache Attacks on AES to Practice , 2011, 2011 IEEE Symposium on Security and Privacy.

[23]  Juan del Cuvillo,et al.  Using innovative instructions to create trustworthy software solutions , 2013, HASP '13.

[24]  Rafail Ostrovsky,et al.  On the (in)security of hash-based oblivious RAM and a new balancing scheme , 2012, SODA.

[25]  Kartik Nayak,et al.  More is Less: Perfectly Secure Oblivious Algorithms in the Multi-Server Setting , 2018, IACR Cryptol. ePrint Arch..

[26]  Elaine Shi,et al.  Ring ORAM: Closing the Gap Between Small and Large Client Storage Oblivious RAM , 2014, IACR Cryptol. ePrint Arch..

[27]  Daniel Noble.  An Intimate Analysis of Cuckoo Hashing with a Stash , 2021, IACR Cryptol. ePrint Arch..

[28]  Yehuda Lindell,et al.  High-Throughput Semi-Honest Secure Three-Party Computation with an Honest Majority , 2016, IACR Cryptol. ePrint Arch..

[29]  David Chaum,et al.  Multiparty unconditionally secure protocols , 1988, STOC '88.

[30]  Kenneth J. Christensen,et al.  A new analysis of the false positive rate of a Bloom filter , 2010, Inf. Process. Lett..

[31]  Jonathan Katz,et al.  Secure two-party computation in sublinear (amortized) time , 2012, CCS.

[32]  Ittai Anati,et al.  Innovative Technology for CPU Based Attestation and Sealing , 2013 .

[33]  Abhi Shelat,et al.  SCORAM: Oblivious RAM for Secure Computation , 2014, IACR Cryptol. ePrint Arch..

[34]  Eyal Kushilevitz,et al.  Sub-logarithmic Distributed Oblivious RAM with Small Block Size , 2019, IACR Cryptol. ePrint Arch..

[35]  Martin R. Albrecht,et al.  Ciphers for MPC and FHE , 2015, IACR Cryptol. ePrint Arch..

[36]  Jan Willemson,et al.  Round-Efficient Oblivious Database Manipulation , 2011, ISC.

[37]  Bin Fan,et al.  Cuckoo Filter: Practically Better Than Bloom , 2014, CoNEXT.

[38]  David Evans,et al.  Obliv-C: A Language for Extensible Data-Oblivious Computation , 2015, IACR Cryptol. ePrint Arch..

[39]  A. Yao.  How to generate and exchange secrets , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[40]  Carlos V. Rozas,et al.  Innovative instructions and software model for isolated execution , 2013, HASP '13.

[41]  Yuval Ishai,et al.  Function Secret Sharing , 2015, EUROCRYPT.

[42]  Stanislaw Jarecki,et al.  Three-Party ORAM for Secure Computation , 2015, ASIACRYPT.

[43]  Rafail Ostrovsky,et al.  Alibi: A Flaw in Cuckoo-Hashing based Hierarchical ORAM Schemes and a Solution , 2020, IACR Cryptol. ePrint Arch..

[44]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[45]  Rasmus Pagh,et al.  Cuckoo Hashing , 2001, Encyclopedia of Algorithms.

[46]  Elaine Shi,et al.  Verifiable Oblivious Storage , 2014, Public Key Cryptography.

[47]  Michael T. Goodrich,et al.  Privacy-Preserving Access of Outsourced Data via Oblivious RAM Simulation , 2010, ICALP.

[48]  Rafail Ostrovsky,et al.  Efficient 3-Party Distributed ORAM , 2018, IACR Cryptol. ePrint Arch..

[49]  Elaine Shi,et al.  Onion ORAM: A Constant Bandwidth Blowup Oblivious RAM , 2016, TCC.

[50]  Abhi Shelat,et al.  Scaling ORAM for Secure Computation , 2017, IACR Cryptol. ePrint Arch..

[51]  Dragos Rotaru,et al.  MPC-Friendly Symmetric Key Primitives , 2016, CCS.

[52]  Kartik Nayak,et al.  ObliVM: A Programming Framework for Secure Computation , 2015, 2015 IEEE Symposium on Security and Privacy.

[53]  Kartik Nayak,et al.  OptORAMa: Optimal Oblivious RAM , 2020, IACR Cryptol. ePrint Arch..

[54]  Elaine Shi,et al.  Bucket ORAM: Single Online Roundtrip, Constant Bandwidth Oblivious RAM , 2015, IACR Cryptol. ePrint Arch..