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Publication# Triangle Network Secrecy

Abstract

We characterize the secret message capacity of the triangle network, that consists of a source, a relay and a destination connected through orthogonal erasure channels. A passive eavesdropper, Eve, wiretaps any one of the three channels. The source and the relay can each generate unlimited private randomness; the relay and the destination can publicly provide strictly causal channel state information. Our achievable scheme is expressed through a linear program (LP) with 11 inequalities that captures a minimal set of secret key generation methods and the use of them for message encryption. Our outer bound is expressed also through a linear program, in this case with 41 constraints, constructed from general information inequalities. We prove that the optimal value of the outer bound LP is no larger than that of the scheme LP, which implies that the solution of the achievable scheme LP is the capacity. We find that equipping the relay with private randomness increases the secrecy rate by more than 40% in some cases and that cut-set bounds, directly applied in the network, are not always tight. Because the derivation of the inner and outer bound are both lengthy, we describe in this paper the achievability scheme, outline the outer bound, and provide the full derivations online [1]. We also make available Matlab functions that take as input the erasure probabilities and evaluate the inner and outer bounds.

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Ontological neighbourhood

Symmetric-key algorithm

Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both the encryption of plaintext and the decryption of ciphertext. The keys may be identical, or there may be a simple transformation to go between the two keys. The keys, in practice, represent a shared secret between two or more parties that can be used to maintain a private information link. The requirement that both parties have access to the secret key is one of the main drawbacks of symmetric-key encryption, in comparison to public-key encryption (also known as asymmetric-key encryption).

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Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. Network topology can be used to define or describe the arrangement of various types of telecommunication networks, including command and control radio networks, industrial fieldbusses and computer networks. Network topology is the topological structure of a network and may be depicted physically or logically. It is an application of graph theory wherein communicating devices are modeled as nodes and the connections between the devices are modeled as links or lines between the nodes.

Encryption

In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decipher a ciphertext back to plaintext and access the original information. Encryption does not itself prevent interference but denies the intelligible content to a would-be interceptor. For technical reasons, an encryption scheme usually uses a pseudo-random encryption key generated by an algorithm.

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