# Private Polynomial Computation for Noncolluding Coded Databases

## TL;DR

This paper introduces two new private polynomial computation schemes for noncolluding coded databases, improving efficiency for small message counts and matching asymptotic rates with existing methods.

## Contribution

The paper presents novel PPC schemes based on Reed-Solomon and systematic Lagrange encoding, extending previous linear computation methods to multivariate polynomials.

## Key findings

- Improved rates for small number of messages.
- Asymptotic rates match existing schemes.
- Leveraged star-product PIR and Lagrange coded computation ideas.

## Abstract

We consider private polynomial computation (PPC) over noncolluding coded databases. In such a setting a user wishes to compute a multivariate polynomial of degree at most $g$ over $f$ variables (or messages) stored in multiple databases while revealing no information about the desired polynomial to the databases. We construct two novel PPC schemes, where the first is a generalization of our previous work in private linear computation for coded databases. In this scheme we consider Reed-Solomon coded databases with Lagrange encoding, which leverages ideas from recently proposed star-product private information retrieval and Lagrange coded computation. The second scheme considers the special case of coded databases with systematic Lagrange encoding. Both schemes yield improved rates compared to the best known schemes from the literature for a small number of messages, while in the asymptotic case the rates match.

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Source: https://tomesphere.com/paper/1901.10286