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 protocols with a genomic querier, Bob, even if those protocols are cryptographically guaranteed to produce no additional information other than the scores that assess the degree to which Q matches strings offered by Bob. We show that such scenarios allow Bob to play variants of the game of mastermind with Q so as to learn the complete identity of Q. We show that there are a number of efficient implementations for Bob to employ in these mastermind attacks, depending on knowledge he has about the structure of Q, which show how quickly he can determine Q. Indeed, we show that Bob can discover Q using a number of rounds of test comparisons that is much smaller than the length of Q, under various assumptions regarding the types of scores that are returned by the cryptographic protocols and whether he can use knowledge about the distribution that Q comes from, e.g., using public knowledge about the properties of human DNA. We also provide the results of an experimental study we performed on a database of mitochondrial DNA, showing the vulnerability of existing real-world DNA data to the mastermind attack.