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• W2182170992 abstract "We present information-theoretic definitions and results for analyzing symmetric-key encryptionschemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained.We adopt two lines of analysis, one based on lossless source coding, and another akin to ratedistortiontheory. We start by presenting a new information-theoretic metric for security, calledǫ-symbol secrecy, and derive associated fundamental bounds. This metric provides a parameterizationof secrecy that spans other information-theoretic metrics for security, such as weaksecrecy and perfect secrecy. We then introduce list-source codes (LSCs), which are a generalframework for mapping a key length (entropy) to a list size that an eavesdropper has to resolvein order to recover a secret message. We provide explicit constructions of LSCs, and show thatLSCs that achieve high symbol secrecy also achieve a favorable tradeoff between key length anduncertainty list size. We also demonstrate that, when the source is uniformly distributed, thehighest level of symbol secrecy for a fixed key length can be achieved through a constructionbased on minimum-distance separable (MDS) codes. Using an analysis related to rate-distortiontheory, we then show how symbol secrecy can be used to determine the probability that an eavesdroppercorrectly reconstructs functions of the original plaintext. More specifically, we presentlower bounds for the minimum-mean-squared-error of estimating a target function of the plaintextgiven that a certain set of functions of the plaintext is known to be hard (or easy) to infer,either by design of the security system or by restrictions imposed on the adversary. We illustratehow these bounds can be applied to characterize security properties of symmetric-key encryptionschemes, and, in particular, extend security claims based on symbol secrecy to a functionalsetting. Finally, we discuss the application of our methods in key distribution, storage andprivacy." @default.
• W2182170992 created "2016-06-24" @default.
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• W2182170992 date "2015-03-30" @default.
• W2182170992 modified "2023-09-26" @default.
• W2182170992 title "Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security" @default.
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• W2182170992 hasPublicationYear "2015" @default.
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