New Properties of Intrinsic Information and Their Relation to Bound Secrecy
Abstract
The secret-key rate measures the rate at which Alice and Bob can extract secret bits from sampling a joint probability distribution, unknown to an eavesdropper Eve. The secret-key rate has been bounded above by the intrinsic information and reduced intrinsic information. However, we prove that the reduced intrinsic information is 0 if and only if the intrinsic information is 0. This result implies that at least one of the following two conjectures is false: bound secrecy exists, or the reduced intrinsic information equals the secret-key rate. We give an explicit construction of an information-erasing binarization for a candidate for bound secrecy. We then introduce some approaches for proving the existence of bound secrecy, such as reducing the channel space, linearly transforming Bob's map, and perturbing a channel for Eve.
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Cite
@article{arxiv.2308.09031,
title = {New Properties of Intrinsic Information and Their Relation to Bound Secrecy},
author = {Andrey Boris Khesin and Andrew Tung and Karthik Vedula},
journal= {arXiv preprint arXiv:2308.09031},
year = {2023}
}
Comments
23 pages, 1 figure