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Balancing Privacy and Robustness in Coded Computing Under Profiled Workers

Rimpi Borah, J. Harshan, Aaditya Sharma

TL;DR

This work extends Numerically Stable Lagrange Coded Computing (NS-LCC) to environments with profiled, untrusted workers, explicitly modeling both curious and Byzantine attackers under finite-precision arithmetic.The core methods include a Chebyshev-node based encoding, a DCT-based robustness reconstruction, and a mutual-information security (MIS) framework to quantify privacy leakage from colluding workers.Key contributions are (i) finite-precision MIS and localization-error bounds that depend on evaluation-index placement, (ii) strategies to assign evaluation indices to unreliable workers to separately optimize privacy and robustness, and (iii) a low-complexity greedy algorithm that jointly balances the two objectives.The results illuminate a fundamental trade-off: index placements that maximize privacy tend to worsen error localization, while robust localization demands reduce privacy, and the proposed joint approach provides practical near-optimal balancing for distributed coded computing with profiled workers.

Abstract

In distributed computing with untrusted workers, the assignment of evaluation indices plays a critical role in determining both privacy and robustness. In this work, we study how the placement of unreliable workers within the Numerically Stable Lagrange Coded Computing (NS-LCC) framework influences privacy and the ability to localize Byzantine errors. We derive analytical bounds that quantify how different evaluation-index assignments affect privacy against colluding curious workers and robustness against Byzantine corruption under finite-precision arithmetic. Using these bounds, we formulate optimization problems that identify privacy-optimal and robustness-optimal index placements and show that the resulting assignments are fundamentally different. This exposes that index choices that maximizes privacy degrade error-localization, and vice versa. To jointly navigate this trade-off, we propose a low-complexity greedy assignment strategy that closely approximates the optimal balance between privacy and robustness.

Balancing Privacy and Robustness in Coded Computing Under Profiled Workers

TL;DR

This work extends Numerically Stable Lagrange Coded Computing (NS-LCC) to environments with profiled, untrusted workers, explicitly modeling both curious and Byzantine attackers under finite-precision arithmetic.The core methods include a Chebyshev-node based encoding, a DCT-based robustness reconstruction, and a mutual-information security (MIS) framework to quantify privacy leakage from colluding workers.Key contributions are (i) finite-precision MIS and localization-error bounds that depend on evaluation-index placement, (ii) strategies to assign evaluation indices to unreliable workers to separately optimize privacy and robustness, and (iii) a low-complexity greedy algorithm that jointly balances the two objectives.The results illuminate a fundamental trade-off: index placements that maximize privacy tend to worsen error localization, while robust localization demands reduce privacy, and the proposed joint approach provides practical near-optimal balancing for distributed coded computing with profiled workers.

Abstract

In distributed computing with untrusted workers, the assignment of evaluation indices plays a critical role in determining both privacy and robustness. In this work, we study how the placement of unreliable workers within the Numerically Stable Lagrange Coded Computing (NS-LCC) framework influences privacy and the ability to localize Byzantine errors. We derive analytical bounds that quantify how different evaluation-index assignments affect privacy against colluding curious workers and robustness against Byzantine corruption under finite-precision arithmetic. Using these bounds, we formulate optimization problems that identify privacy-optimal and robustness-optimal index placements and show that the resulting assignments are fundamentally different. This exposes that index choices that maximizes privacy degrade error-localization, and vice versa. To jointly navigate this trade-off, we propose a low-complexity greedy assignment strategy that closely approximates the optimal balance between privacy and robustness.
Paper Structure (14 sections, 3 theorems, 13 equations, 1 figure, 4 tables, 1 algorithm)

This paper contains 14 sections, 3 theorems, 13 equations, 1 figure, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Robust Numerically Stable Lagrange Coded Computing
  3. Encoding
  4. Distribution of Shares among the Worker Nodes
  5. Computation at the Worker Nodes
  6. Function Reconstruction
  7. Privacy and Security Analyses of Robust NS-LCC
  8. Privacy against Curious Workers
  9. Robustness against Byzantine Workers
  10. Privacy and Localization Error based Assignment
  11. Assignment based on MIS
  12. Assignment based on Localization Error
  13. Assignment based on Joint MIS and Localization Error
  14. Summary

Key Result

Proposition 1

For a given $N$, $k$, $t$, $y$, $\sigma_{n}$, and when $y=O(\sigma_n)$ the MIS metric defined in eq:MIS bound can be upper bounded as where $\mathbf{\Sigma}_T=\mathbf{H}_T \mathbf{H}_T^T$ and $\mathbf{\tilde{\Sigma}}_T = \mathbf{W}_T \mathbf{W}_T^T$ and $\mathbf{H}_T$ and $\mathbf{W}_T$ is defined in eq:HT_WT_scaled.

Figures (1)

  • Figure 1: Results at $\mathcal{S}^*_g$ for different values of $w$ and $\sigma_p^2$ with parameters $N=21$, $\nu=12$, $k=3$, $t=A=3$, $y=10^{10}$, $\sigma_n=10^{23}$, $\zeta=100$.

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • proof
  • Proposition 3