Private DNA Sequencing: Hiding Information in Discrete Noise

TL;DR

This paper explores a privacy-preserving method for DNA sequencing by mixing known DNA samples as noise, analyzing the optimal noise distribution to maximize privacy while allowing individuals to recover their own genetic information.

Contribution

It introduces a formal framework for hiding genetic information using additive discrete noise and derives bounds on the optimal noise distribution for privacy enhancement.

Findings

Bounds on the worst-case noise distribution are close.

A convex relaxation provides a closed-form lower bound.

A greedy algorithm approximates the upper bound effectively.

Abstract

When an individual's DNA is sequenced, sensitive medical information becomes available to the sequencing laboratory. A recently proposed way to hide an individual's genetic information is to mix in DNA samples of other individuals. We assume that the genetic content of these samples is known to the individual but unknown to the sequencing laboratory. Thus, these DNA samples act as "noise" to the sequencing laboratory, but still allow the individual to recover their own DNA samples afterward. Motivated by this idea, we study the problem of hiding a binary random variable $X$ (a genetic marker) with the additive noise provided by mixing DNA samples, using mutual information as a privacy metric. This is equivalent to the problem of finding a worst-case noise distribution for recovering $X$ from the noisy observation among a set of feasible discrete distributions. We characterize upper and lower bounds to the solution of this problem, which are empirically shown to be very close. The lower bound is obtained through a convex relaxation of the original discrete optimization problem, and yields a closed-form expression. The upper bound is computed via a greedy algorithm for selecting the mixing proportions.