Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Individual Confidential Computing of Polynomials over Non-Uniform Information

Saar Tarnopolsky, Zirui, Deng, Vinayak Ramkumar, Netanel Raviv, Alejandro Cohen

TL;DR

This work tackles secure distributed polynomial computation when user data are non-uniform, a setting where conventional perfect subset privacy assumptions break down. It introduces Individual Confidential Computing (ICC), combining a smoothing technique via random linear codes with information-set based polynomial computation to render encoded data nearly uniform and bound information leakage to a single untrusted provider (admin and workers). The main results provide explicit conditions on the key size $m$ and probabilistic guarantees that $I(\tilde{X}; X_{\mathcal{R}})$ remains negligible while enabling reliable decoding of $f(X)$, even in the presence of stragglers. The approach advances practical privacy guarantees for confidential computing in non-uniform data regimes, with concrete leakage bounds under both variational distance and mutual information. This yields a robust framework for privacy-preserving coded computation applicable to real-world cloud settings with non-uniform data distributions.

Abstract

In this paper, we address the problem of secure distributed computation in scenarios where user data is not uniformly distributed, extending existing frameworks that assume uniformity, an assumption that is challenging to enforce in data for computation. Motivated by the pervasive reliance on single service providers for data storage and computation, we propose a privacy-preserving scheme that achieves information-theoretic security guarantees for computing polynomials over non-uniform data distributions. Our framework builds upon the concept of perfect subset privacy and employs linear hashing techniques to transform non-uniform data into approximately uniform distributions, enabling robust and secure computation. We derive leakage bounds and demonstrate that information leakage of any subset of user data to untrusted service providers, i.e., not only to colluding workers but also (and more importantly) to the admin, remains negligible under the proposed scheme.

Individual Confidential Computing of Polynomials over Non-Uniform Information

TL;DR

This work tackles secure distributed polynomial computation when user data are non-uniform, a setting where conventional perfect subset privacy assumptions break down. It introduces Individual Confidential Computing (ICC), combining a smoothing technique via random linear codes with information-set based polynomial computation to render encoded data nearly uniform and bound information leakage to a single untrusted provider (admin and workers). The main results provide explicit conditions on the key size and probabilistic guarantees that remains negligible while enabling reliable decoding of , even in the presence of stragglers. The approach advances practical privacy guarantees for confidential computing in non-uniform data regimes, with concrete leakage bounds under both variational distance and mutual information. This yields a robust framework for privacy-preserving coded computation applicable to real-world cloud settings with non-uniform data distributions.

Abstract

In this paper, we address the problem of secure distributed computation in scenarios where user data is not uniformly distributed, extending existing frameworks that assume uniformity, an assumption that is challenging to enforce in data for computation. Motivated by the pervasive reliance on single service providers for data storage and computation, we propose a privacy-preserving scheme that achieves information-theoretic security guarantees for computing polynomials over non-uniform data distributions. Our framework builds upon the concept of perfect subset privacy and employs linear hashing techniques to transform non-uniform data into approximately uniform distributions, enabling robust and secure computation. We derive leakage bounds and demonstrate that information leakage of any subset of user data to untrusted service providers, i.e., not only to colluding workers but also (and more importantly) to the admin, remains negligible under the proposed scheme.
Paper Structure (11 sections, 1 theorem, 27 equations, 2 figures)

This paper contains 11 sections, 1 theorem, 27 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Computation System Model
  3. Privacy and Security Metrics
  4. Preliminaries
  5. Smoothing
  6. Code-Based Polynomial Computation Scheme
  7. Main Results
  8. Leakage Proof of Theorem \ref{['theorem:main_theorem']} Under Variational Distance
  9. Leakage Proof of Theorem \ref{['theorem:main_theorem']} Under Mutual Information
  10. Smoothing
  11. Inequality Proof

Key Result

Theorem 1

Let $X \in \mathbb{F}_{q}^{n}$ be a non-uniform random variable with distribution $p_X$, let $a > 1$, let $p\ge 2$ be an integer, and let $\epsilon>0$. Consider a scheme in which $X$ is encoded using an $(n,q,r,d,S)$ Code-Based Polynomial Computation scheme as in Sec. sec:coded_based_linear_comp, wi then with probability at least $1 - \frac{1}{a}$, the encoding $\tilde{X} = X + KG$ satisfies ICC,

Figures (2)

  • Figure 1: Individual confidential computing (ICC) scheme for non-uniform data, $X\in \mathbb{F}_q^n$, drawn from some unknown distribution. Red dashed line represents the "security barrier" in ICC scheme. Instead of protecting the admin's data against colluding workers lee2017speedingwang2022breakingyu2019lagranged2020gasp, ICC protects the user's data against the service provider as a whole.
  • Figure 2: Key size $m$ as a function of (a) information leakage and (b) entropy of the data, for $n = 262144 = 2^{18}$, $p=2$, $q=2$, $r=2$.

Theorems & Definitions (6)

  • Definition 1: Individual Confidential Computing
  • Remark 1
  • Remark 2
  • Definition 2
  • Theorem 1
  • Example 1