Information-theoretically Secure Key Agreement over Partially Corrupted Channels

TL;DR

This paper explores the possibility of information-theoretically secure key agreement over channels partially controlled by adversaries, establishing bounds and constructions that ensure security when some communication remains private and unaltered.

Contribution

It formalizes security and reliability for key agreement over partially corrupted channels, deriving bounds and providing constructions that achieve optimal rates.

Findings

Secure key agreement is possible with partial channel control.

Bounds on key agreement rate are established.

Constructive protocols achieve the derived bounds.

Abstract

Key agreement is a fundamental cryptographic primitive. It has been proved that key agreement protocols with security against computationally unbounded adversaries cannot exist in a setting where Alice and Bob do not have dependent variables and communication between them is fully public, or fully controlled by the adversary. In this paper we consider this problem when the adversary can "partially" control the channel. We motivate these adversaries by considering adversarial corruptions at the physical layer of communication, give a definition of adversaries that can "partially" eavesdrop and "partially" corrupt the communication. We formalize security and reliability of key agreement protocols, derive bounds on the rate of key agreement, and give constructions that achieve the bound. Our results show that it is possible to have secret key agreement as long as some of the communicated symbols remain private and unchanged by the adversary. We relate our results to the previous known results, and discuss future work.