Practical applications

You now have all the building blocks. Hashing, one key, two keys, agreeing on a secret, calculating on a curve. What follows is no new math any more — it's the same handful of ideas, stacked differently each time. And every stacking has a name you know from the news or from your own screen.

Feel free to read these parts in any order. They do build on the chapters before them, but not on each other.

1. Digital signatures
   Proving that you wrote something, without a pen, in a way no one can fake.
2. Certificates and certificate authorities
   A signature doesn't say who signed. A certificate does — and here we take one apart field by field.
3. Hybrid encryption: how it really works
   Why no real system chooses between one key and two — they use both.
4. HTTPS end to end
   What happens between enter and the padlock, and what that padlock precisely does not mean.
5. Messaging apps: Signal and WhatsApp
   Why Signal and WhatsApp can't read your message, and what they do know about you.
6. Your phone and your laptop
   Your phone is secured with four digits and still a thief can't get in. How?
7. Post-quantum: what if the quantum computer arrives
   The quantum computer doesn't break everything — but it does break exactly half of this book. Which half, and what is being done about it.

You don't have to read them in order. Each part stands on its own. If you come across a word you don't know, it's in the word box at the top of that part — or in a chapter that this part refers back to.