Learning Character Strings via Mastermind Queries, with a Case Study Involving mtDNA

Michael T. Goodrich

doi:10.1109/tit.2012.2208581

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arXiv · 0904.4458

Learning Character Strings via Mastermind Queries, with a Case Study Involving mtDNA

Michael T. Goodrich

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Abstract

We study the degree to which a character string, $Q$, leaks details about itself any time it engages in comparison protocols with a strings provided by a 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 reasonable 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. We also provide the results of a case study we performed on a database of mitochondrial DNA, showing the vulnerability of existing real-world DNA data to the Mastermind attack.

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Michael T. Goodrich. 2009-04-28. Learning Character Strings via Mastermind Queries, with a Case Study Involving mtDNA. https://doi.org/10.1109/tit.2012.2208581

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