The Fragile Lock

Almost everything you do online—from bank transfers to "private" chats—is protected by a mathematical lock called RSA (or ECC).

This lock isn't "unbreakable." It's just slow to break.

To break a modern 2048-bit RSA key, a classical supercomputer would need to perform quintillions of calculations. It would take longer than the age of the universe.

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1. The Factoring Secret

RSA works because of prime numbers.

1. It is very easy to multiply two giant prime numbers together: $P \times Q = N$.
2. It is nearly impossible to find $P$ and $Q$ if you only know $N$.

Imagine a giant jigsaw puzzle. Multiplying is like looking at the completed picture. Factoring is like being given a pile of generic blue pieces and being told to build the ocean perfectly.

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2. The Shor Attack

As we learned in Module 8, Shor's Algorithm doesn't "guess" the pieces. It uses Quantum Periodicity to find the underlying structure of the number $N$.

• A Classical computer must check every possibility (Exponential time).
• A Quantum computer uses interference to find the "answer wave" (Polynomial time).

If you have a large enough quantum computer (about 20 million physical qubits), the "Age of the Universe" problem becomes a "10 minute" problem.

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3. The Reach of the Threat

It’s not just passwords. If RSA breaks:

• Digital Signatures fail (you can fake someone's identity).
• SSL/TLS Certificates fail (you can't trust that google.com is really Google).
• Blockchain/Crypto fail (someone could mathematically "discover" your private key and spend your Bitcoin).

graph TD
    A[Public Key: N] --> B{Classical Computer}
    B -->|Tries every combination| C[Billions of Years]
    
    A --> D{Quantum Computer}
    D -->|Shor's Algorithm| E[10 Minutes]
    
    E --> F[Privacy Collapses]

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4. Summary: The Asymmetry Problem

Encryption is built on Asymmetry—the idea that it's easy to lock but hard to unlock. Quantum computing destroys that asymmetry for certain types of math. We need new math where the asymmetry still holds even against a quantum monster.

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Exercise: The "Safe" Analogy

1. Imagine a safe with 1,000 dials.
2. A Classical Burglar has to try every combination. ($10^{100}$ possibilities).
3. A Quantum Burglar has a magic stethoscope that can "hear" the tumblers of all 1,000 dials at once.
4. The Quantum Burglar doesn't need to be lucky; they just need to listen.

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What's Next?

If the "Padlock" is broken, what is the new lock? In the next lesson, we look at Post-Quantum Cryptography.