### Privacy amplification with asymptotically optimal entropy lossPrivacy amplification with asymptotically optimal entropy loss

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 Author Chandran, Nishanth ♦ Kanukurthi, Bhavana ♦ Ostrovsky, Rafail ♦ Reyzin, Leonid Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2014 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Cryptographic protocols ♦ Authentication protocols ♦ Error-correcting codes ♦ Information-theoretic key agreement ♦ Key agreement Abstract We study the problem of “privacy amplification”: key agreement between two parties who both know a weak secret $\textit{w},$ such as a password. (Such a setting is ubiquitous on the internet, where passwords are the most commonly used security device.) We assume that the key agreement protocol is taking place in the presence of an active computationally unbounded adversary Eve. The adversary may have partial knowledge about $\textit{w},$ so we assume only that $\textit{w}$ has some entropy from Eve’s point of view. Thus, the goal of the protocol is to convert this nonuniform secret $\textit{w}$ into a uniformly distributed string $\textit{R}$ that is fully secret from Eve. $\textit{R}$ may then be used as a key for running symmetric cryptographic protocols (such as encryption, authentication, etc.). Because we make no computational assumptions, the entropy in $\textit{R}$ can come only from $\textit{w}.$ Thus, such a protocol must minimize the entropy loss during its execution, so that $\textit{R}$ is as long as possible. The best previous results have entropy loss of $Θ(κ^{2}),$ where $\textit{κ}$ is the security parameter, thus requiring the password to be very long even for small values of $\textit{κ}.$ In this work, we present the first protocol for information-theoretic key agreement that has entropy loss linear in the security parameter. The result is optimal up to constant factors. We achieve our improvement through a somewhat surprising application of error-correcting codes for the edit distance. The protocol can be extended to provide also “information reconciliation,” that is, to work even when the two parties have slightly different versions of $\textit{w}$ (e.g., when biometrics are involved). ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2014-09-08 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 61 Issue Number 5 Page Count 28 Starting Page 1 Ending Page 28

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Source: ACM Digital Library