Shannon Theory vs. Wyner Wiretap Model: 6G Security Roots

Introduction : Physical layer security is becoming pillar of 6G wireless networks. To understand the basics behind this, let us analyze two theories that define meaning of “secrecy”. This page will discover Claude Shannon’s Information Theory and Aaron Wyner’s Wiretap Channel Model.

Claude Shannon Theorem

Shannon proved that “Perfect Secrecy” is indeed possible. However, his mathematical proof came with following requirements to be met.

• To achieve perfect secrecy, the Entropy (i.e. randomness) of the encryption key must be equal to or greater than the Entropy of the message itself.
• For example, If you want to send a 1GB file with unbreakable security, you need a 1GB random key that has never been used before.

6G issue : 6G will handle massive data streams (terabytes per second) and connect billions of IoT devices. Distributing and managing encryption keys that are as long as the data itself is logistically impossible. This limitation paved the way for a new approach that didn’t rely on pre-shared keys.

Wyner’s Breakthrough: The Wiretap Channel Model

In the year 1975, Aaron Wyner introduced “Wiretap Channel Model” which serves as foundation for modern physical layer security. Unlike Shannon, who focused on the keys, Wyner focused on the channel (the physical medium the signal travels through).

Let us understand the concept, with scenario having Allen (as transmitter), Bilal (as legitimate receiver) and Eva (as eavesdropper).

Wyner proved that secure communication is possible without a pre-shared secret key, provided one physical condition is met: Bilal’s channel must be “better” than Eva’s channel.

If the connection between Allen and Bilal has a higher signal quality (i.e. SNR ) than the connection between Allen and Eva, Allen can encode the data in a specific way.

This encoding ensures that Bilal can decode the message perfectly, while Eva sees nothing but unrecoverable noise; even if she has infinite computing power.

Secrecy Capacity Metric

It is the difference between the capacity of the main channel (Cb) and capacity of the eavesdropper’ channel (Ce). It is expressed as follows. The Secrecy capacity is a vital metric for 6G Physical Layer Security (PLS) peformance.

• As long as Cs is positive, secure communication is mathematically guaranteed.

Example : Manipulating channel

In legacy networks such as Wi-Fi, signals are broadcasted to all directions and as a result, Eve also gets the channel as good as Bilal’s. Let us understand, how 6G technologies naturally create the conditions Wyner has described to fulfill secure and keyless transmission.

• 1. 6G Solution : It utilizes features such as Massive MIMO and Beamforming. These technologies focus energy into tight, laser like beams directed specifically at Bilal.
• Result : Due to above, Bilal receives high quality signal (i.e. Cb is high). Eve is outside the beam and receives mostly noise (i.e. Ce is low). This creates a positive “Secrecy Capacity” which fulfills Wyner’s condition.

2. There is another technique known as artificial noise injection. In this technique, artificially noise is injected into Eve’s channel to degrade it. This is done by sending “jamming signal” into the direction where Eve is located.

3. The third solution offered by 6G is secret key generation from channel. Allen and Bilal measure random fluctuations of wireless channel between them. As channel is reciprocal but unique to their locations, they can use measurements carried to derive shared secret key. There is no need to exchange the key as used in traditional approach.

Summary: By applying Wyner’s Wiretap Channel theory to modern Beamforming and MIMO technologies, 6G networks aim to make data physically unreadable to eavesdroppers, realizing a level of security that is built into the very waves that carry our data.