Privacy Amplification with Asymptotically Optimal Entropy Loss

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The authors study the problem of "Privacy amplification": key agreement between two parties who both know a weak secret w, such as a password. (Such a setting is ubiquitous on the internet, where passwords are the most commonly used security device.). They 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 w, so they assume only that w has some entropy from Eve's point of view. Thus, the goal of the protocol is to convert this non-uniform secret w into a uniformly distributed string R that is fully secret from Eve. R may then be used as a key for running symmetric cryptographic protocols (such as encryption, authentication, etc.).