A Practical Analysis of Oblivious Sorting Algorithms for Secure Multi-party Computation

Cryptographic secure computing methods like secure multi-party computation, circuit garbling and homomorphic encryption are becoming practical enough to be usable in applications. Such applications need special data-independent sorting algorithms to preserve privacy. In this paper, we describe the design and implementation of four different oblivious sorting algorithms. We improve two earlier designs based on sorting networks and quicksort with the capability of sorting matrices. We also propose two new designs—a naive comparison-based sort with a low round count and an oblivious radix sort algorithm that does not require any private comparisons. For all these algorithms, we present thorough complexity and performance analysis including detailed breakdown of running-time, network and memory usage.

[1]  Cynthia Dwork,et al.  Differential Privacy , 2006, ICALP.

[2]  Dan Bogdanov,et al.  Domain-Polymorphic Programming of Privacy-Preserving Applications , 2014, PLAS@ECOOP.

[3]  Bart Goethals,et al.  On Private Scalar Product Computation for Privacy-Preserving Data Mining , 2004, ICISC.

[4]  Vitaly Shmatikov,et al.  Robust De-anonymization of Large Sparse Datasets , 2008, 2008 IEEE Symposium on Security and Privacy (sp 2008).

[5]  Ivan Damgård,et al.  Multiparty Computation from Somewhat Homomorphic Encryption , 2012, IACR Cryptol. ePrint Arch..

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

[7]  Daesung Kwon,et al.  Information Security and Cryptology – ICISC 2012 , 2012, Lecture Notes in Computer Science.

[8]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[9]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[10]  Ran Canetti,et al.  Advances in Cryptology – CRYPTO 2012 , 2012, Lecture Notes in Computer Science.

[11]  Katsumi Takahashi,et al.  Oblivious Radix Sort: An Efficient Sorting Algorithm for Practical Secure Multi-party Computation , 2014, IACR Cryptol. ePrint Arch..

[12]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[13]  Xenofontas A. Dimitropoulos,et al.  SEPIA: Privacy-Preserving Aggregation of Multi-Domain Network Events and Statistics , 2010, USENIX Security Symposium.

[14]  Thomas C. Melvin,et al.  European Patent Office , 2002 .

[15]  Bingsheng Zhang,et al.  Generic Constant-Round Oblivious Sorting Algorithm for MPC , 2011, ProvSec.

[16]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[17]  Alexandre V. Evfimievski,et al.  Privacy preserving mining of association rules , 2002, Inf. Syst..

[18]  Wenliang Du,et al.  Bureaucratic protocols for secure two-party sorting, selection, and permuting , 2010, ASIACCS '10.

[19]  Jacques Stern,et al.  Advances in Cryptology — EUROCRYPT ’99 , 1999, Lecture Notes in Computer Science.

[20]  Katsumi Takahashi,et al.  Practically Efficient Multi-party Sorting Protocols from Comparison Sort Algorithms , 2012, ICISC.

[21]  Craig Gentry,et al.  Fully homomorphic encryption using ideal lattices , 2009, STOC '09.

[22]  Dan Bogdanov,et al.  Domain-polymorphic language for privacy-preserving applications , 2013, PETShop '13.

[23]  Latanya Sweeney,et al.  k-Anonymity: A Model for Protecting Privacy , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[24]  Ran Canetti,et al.  Universally composable security: a new paradigm for cryptographic protocols , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[25]  Donald E. Knuth,et al.  The Art of Computer Programming: Volume 3: Sorting and Searching , 1998 .

[26]  ASHWIN MACHANAVAJJHALA,et al.  L-diversity: privacy beyond k-anonymity , 2006, 22nd International Conference on Data Engineering (ICDE'06).

[27]  Dan Bogdanov,et al.  High-performance secure multi-party computation for data mining applications , 2012, International Journal of Information Security.

[28]  Dan Bogdanov,et al.  Oblivious Sorting of Secret-Shared Data , 2013 .

[29]  Choonsik Park,et al.  Information Security and Cryptology - ICISC 2004, 7th International Conference, Seoul, Korea, December 2-3, 2004, Revised Selected Papers , 2005, ICISC.

[30]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[31]  Dan Bogdanov.  Sharemind: programmable secure computations with practical applications , 2013 .

[32]  Kristján Valur Jónsson,et al.  Secure Multi-Party Sorting and Applications , 2011, IACR Cryptol. ePrint Arch..