The Mastermind Attack on Genomic Data

In this paper, we study the degree to which a genomic string, $Q$,leaks details about itself any time it engages in comparison protocolswith a genomic querier, Bob, even if those protocols arecryptographically guaranteed to produce no additional information otherthan the scores that assess the degree to which $Q$ matches stringsoffered by Bob. We show that such scenarios allow Bob to play variantsof the game of Mastermind with $Q$ so as to learn the complete identityof $Q$. We show that there are a number of efficient implementationsfor Bob to employ in these Mastermind attacks, depending on knowledgehe has about the structure of $Q$, which show how quickly he candetermine $Q$. Indeed, we show that Bob can discover $Q$ using anumber of rounds of test comparisons that is much smaller than thelength of $Q$, under various assumptions regarding the types of scoresthat are returned by the cryptographic protocols and whether he can useknowledge about the distribution that $Q$ comes from, e.g., usingpublic knowledge about the properties of human DNA. We also providethe results of an experimental study we performed on a database ofmitochondrial DNA, showing the vulnerability of existing real-world DNAdata to the Mastermind attack.