New Math: Post-Quantum Cryptography
How to hide secrets in a Lattice. Meet the math that Quantum computers can't solve.
Fighting Fire with... More Complex Math
If Quantum computers are good at Factoring (RSA), the solution is simple: Stop using Factoring.
There are several areas of mathematics that are "Hard" even for a Quantum computer. This field is called Post-Quantum Cryptography (PQC).
1. Lattice-Based Cryptography
The most promising "Replacement" for RSA is based on Lattices.
- Imagine a giant grid of dots in 500 dimensions.
- The "Key" is finding the closest two dots to a random point in that space.
- Even for a quantum computer, navigating a 500-dimensional grid is an "Exponential" problem.
This is the math behind some of the new NIST standards like CRYSTALS-Kyber.
2. Hash-Based Signatures
Another reliable method uses "Hashes" (like the math behind Bitcoin).
- To break a hash, a quantum computer only gets a Quadratic Speedup (Grover's Algorithm, Module 8).
- If you just double the size of your hash (e.g., move from 256-bit to 512-bit), you effectively cancel out the quantum advantage!
3. The Transition Strategy
The goal is to create Agile Cryptography.
- We don't want to just switch from one lock to another.
- We want to build software that can swap its encryption math as easily as swapping a battery.
| Current Math | Quantum Status | PQC Replacement |
|---|---|---|
| RSA / Factoring | BROKEN | Lattices (Kyber) |
| Elliptic Curves | BROKEN | Lattices (Dilithium) |
| AES (Symmetric) | WEAKENED | Larger AES Keys |
| SHA (Hashing) | WEAKENED | Larger Hash Sizes |
graph LR
A[Data] --> B{Encryption Choice}
B -->|Old Way| C[RSA: Fast but Vulnerable]
B -->|New Way| D[Kyber: Slightly Slower but Secure]
D --> E[Safe from Quantum Hackers]
4. Summary: The Software Defense
PQC doesn't require a quantum computer to work. You can run PQC on your phone today! Many companies (like Google Chrome and Cloudflare) have already started using "Hybrid" encryption—protecting your data with both the old math and the new math simultaneously.
Exercise: The "Camouflage" Analogy
- A Bright Red Box (RSA) is easy for a hawk (Quantum computer) to see from the sky.
- If you paint the box Camouflage (Lattices), the hawk can't find it, even if its eyes are 100x better.
- The hawk (Quantum) is still powerful, but it's looking for the wrong signal.
What's Next?
If the math exists, why haven't we switched yet? In the next lesson, we look at the Real-World Challenges of upgrading the internet.