New Properties of Intrinsic Information and Their Relation to Bound Secrecy

TL;DR

This paper investigates the properties of intrinsic information related to secret-key rates, proving a key equivalence and exploring the existence of bound secrecy through explicit constructions and new approaches.

Contribution

It establishes that reduced intrinsic information is zero if and only if intrinsic information is zero, challenging existing conjectures about bound secrecy.

Findings

Reduced intrinsic information equals zero iff intrinsic information is zero.

Constructed an explicit information-erasing binarization example.

Proposed new methods for proving the existence of 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.