Detecting Algebraic Manipulation in Leaky Storage Systems
Abstract
Algebraic Manipulation Detection (AMD) Codes detect adversarial noise that is added to a coded message and stored in a storage that is opaque to the adversary. We study AMD codes when the storage can leak up to |G| bits of information about the stored codeword, where G is the group in which the stored codeword lives and is a constant. We propose -AMD codes that provide protection in this new setting, and define weak and strong -AMD codes that provide security for a random and an arbitrary message, respectively. We derive concrete and asymptotic bounds for the efficiency of these codes featuring a rate upper bound of 1- for the strong codes. We also define the class of LV-AMD codes that provide protection when leakage is in the form of a number of codeword components, and give constructions featuring a strong LV-AMD codes that asymptotically achieve the rate 1-. We describe applications of -AMD codes to, (i) robust ramp secret sharing scheme and, (ii) wiretap II channel when the adversary can eavesdrop a fraction of codeword components and tamper with all components of the codeword.
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