Approximately how many symmetric keys would be needed if every IoT device communicated with every other device, given ~30 billion smart devices existed by end of 2020?

Roughly $10^{20}$ (a hundred quintillion) symmetric keys — an astronomically impractical number.

The calculation:

• ~30 billion ($3 \times 10^{10}$) smart devices connected by end of 2020
• If "everyone communicates with everyone" (fully connected), the number of symmetric keys needed is:

$$\frac{n(n-1)}{2} \approx \frac{(3 \times 10^{10})^2}{2} \approx 10^{20}$$

This is about 100,000,000,000,000,000,000 keys.

This illustrates why:

• Pure symmetric key distribution does not scale for the IoT era
• Public-key cryptography and key exchange protocols (like Diffie-Hellman or TLS) are essential
• Even then, managing keys on billions of low-power devices (sensors, smart home gadgets) remains one of the biggest open challenges in applied cryptography

Tip: This is a great example to remember when asked "why do we need asymmetric cryptography?" — the key management problem at scale makes symmetric-only systems impossible.