Private Aggregation from Fewer Anonymous Messages

Consider the setup where n parties are each given an element \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_i$$\end{document}xi in the finite field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_q$$\end{document}Fq and the goal is to compute the sum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _i x_i$$\end{document}∑ixi in a secure fashion and with as little communication as possible. We study this problem in the anonymized model of Ishai et al. (FOCS 2006) where each party may broadcast anonymous messages on an insecure channel. We present a new analysis of the one-round “split and mix” protocol of Ishai et al. In order to achieve the same security parameter, our analysis reduces the required number of messages by a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varTheta (\log n)$$\end{document}Θ(logn) multiplicative factor. We also prove lower bounds showing that the dependence of the number of messages on the domain size, the number of parties, and the security parameter is essentially tight. Using a reduction of Balle et al. (2019), our improved analysis of the protocol of Ishai et al. yields, in the same model, an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \varepsilon , \delta \right) $$\end{document}ε,δ-differentially private protocol for aggregation that, for any constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon > 0$$\end{document}ε>0 and any \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta = \frac{1}{\text {poly}(n)}$$\end{document}δ=1poly(n), incurs only a constant error and requires only a constant number of messages per party. Previously, such a protocol was known only for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega (\log n)$$\end{document}Ω(logn) messages per party.

[1]  J. Stuart.  PROCEEDINGS - PART II , 1993 .

[2]  M. Kearns.  Efficient noise-tolerant learning from statistical queries , 1998, JACM.

[3]  Rafail Ostrovsky,et al.  Cryptography from Anonymity , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[4]  Nina Mishra,et al.  Privacy via pseudorandom sketches , 2006, PODS.

[5]  Nina Mishra,et al.  Privacy via the Johnson-Lindenstrauss Transform , 2012, J. Priv. Confidentiality.

[6]  Vaidy S. Sunderam,et al.  Secure multiparty aggregation with differential privacy: a comparative study , 2013, EDBT '13.

[7]  David P. Woodruff.  Sketching as a Tool for Numerical Linear Algebra , 2014, Found. Trends Theor. Comput. Sci..

[8]  Emiliano De Cristofaro,et al.  Efficient Private Statistics with Succinct Sketches , 2015, NDSS.

[9]  Peter Richtárik,et al.  Federated Learning: Strategies for Improving Communication Efficiency , 2016, ArXiv.

[10]  Ian Goodfellow,et al.  Deep Learning with Differential Privacy , 2016, CCS.

[11]  Úlfar Erlingsson,et al.  Prochlo: Strong Privacy for Analytics in the Crowd , 2017, SOSP.

[12]  Blaise Agüera y Arcas,et al.  Communication-Efficient Learning of Deep Networks from Decentralized Data , 2016, AISTATS.

[13]  Dan Boneh,et al.  Prio: Private, Robust, and Scalable Computation of Aggregate Statistics , 2017, NSDI.

[14]  Sarvar Patel,et al.  Practical Secure Aggregation for Privacy-Preserving Machine Learning , 2017, IACR Cryptol. ePrint Arch..

[15]  Adam D. Smith,et al.  Turning HATE Into LOVE: Homomorphic Ad Hoc Threshold Encryption for Scalable MPC , 2018, IACR Cryptol. ePrint Arch..

[16]  H. Brendan McMahan,et al.  Learning Differentially Private Recurrent Language Models , 2017, ICLR.

[17]  Badih Ghazi,et al.  On the Power of Multiple Anonymous Messages , 2019, IACR Cryptol. ePrint Arch..

[18]  Borja Balle,et al.  The Privacy Blanket of the Shuffle Model , 2019, CRYPTO.

[19]  Borja Balle,et al.  Improved Summation from Shuffling , 2019, ArXiv.

[20]  Eakta Jain,et al.  Differential privacy for eye-tracking data , 2019, ETRA.

[21]  Ninghui Li,et al.  Practical and Robust Privacy Amplification with Multi-Party Differential Privacy , 2019, ArXiv.

[22]  Badih Ghazi,et al.  Private Heavy Hitters and Range Queries in the Shuffled Model , 2019, ArXiv.

[23]  Adam D. Smith,et al.  Distributed Differential Privacy via Shuffling , 2018, IACR Cryptol. ePrint Arch..

[24]  Andreas Bulling,et al.  Privacy-aware eye tracking using differential privacy , 2018, ETRA.

[25]  Úlfar Erlingsson,et al.  Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity , 2018, SODA.

[26]  Borja Balle,et al.  Differentially Private Summation with Multi-Message Shuffling , 2019, ArXiv.

[27]  Badih Ghazi,et al.  Scalable and Differentially Private Distributed Aggregation in the Shuffled Model , 2019, ArXiv.

[28]  Úlfar Erlingsson,et al.  Encode, Shuffle, Analyze Privacy Revisited: Formalizations and Empirical Evaluation , 2020, ArXiv.

[29]  Adrià Gascón,et al.  Private Summation in the Multi-Message Shuffle Model , 2020, CCS.

[30]  Badih Ghazi,et al.  Pure Differentially Private Summation from Anonymous Messages , 2020, ITC.

[31]  Ninghui Li,et al.  Improving utility and security of the shuffler-based differential privacy , 2019, Proc. VLDB Endow..

[32]  Richard Nock,et al.  Advances and Open Problems in Federated Learning , 2019, Found. Trends Mach. Learn..