Chapter Summary

Chapter Summary

Key Points

• 1.

  The wiretap channel provides keyless secrecy. The secrecy capacity $C_s = \max_{P_X}[I(X;Y) - I(X;Z)]$ quantifies the maximum rate of reliable communication that is simultaneously secret from an eavesdropper. The achievability uses stochastic encoding (random binning) — the same technique as Slepian–Wolf coding, repurposed for secrecy rather than compression.

• 2.

  Noise is the ally. Unlike all previous chapters where noise was the enemy, in secrecy coding the eavesdropper's noise is exploited. The secrecy rate is determined by the advantage the main channel has over the wiretap channel. If the eavesdropper's channel is better, $C_s = 0$ and no information-theoretic secrecy is possible.

• 3.

  The Gaussian secrecy capacity saturates. For the Gaussian wiretap channel, $C_s = \frac{1}{2}\log\frac{1 + P/\sigma^2_{Y}}{1 + P/\sigma^2_{Z}}$, which saturates at high SNR to $\frac{1}{2}\log(\sigma^2_{Z}/\sigma^2_{Y})$. More power does not help beyond a point — the secrecy advantage comes from the noise ratio, not the absolute power level.

• 4.

  Secret key generation from common randomness. Alice and Bob can generate a shared secret key from correlated observations, even when Eve overhears all public communication. The secret key capacity $C_K = I(X;Y) - I(X;Z)$ equals the wiretap secrecy capacity — a deep duality between wiretap coding and key agreement.

• 5.

  Channel reciprocity enables wireless key generation. In TDD systems, Alice and Bob observe correlated versions of the same channel realization, while Eve's channel is decorrelated by spatial separation. This provides practical key rates of 10–100 kbps through a protocol of quantization, information reconciliation, and privacy amplification.

• 6.

  MIMO wiretap: spatial secrecy. Multiple antennas transform the secrecy problem from one of hoping for a channel advantage to one of creating it. The transmitter can beamform the signal to Bob while injecting artificial noise in Bob's null space to confuse Eve — without requiring knowledge of Eve's channel.

• 7.

  Massive MIMO makes secrecy free. When $n_t \gg n_r + n_e$, the secrecy DoF equals the non-secrecy DoF. The excess spatial dimensions provide enough room to simultaneously serve the legitimate user at full rate and completely null the eavesdropper. Physical-layer security becomes a bonus of the antenna array.