How Quantum Computers Break Cryptography
Qubits, superposition, and Shor's Algorithm
Bits vs. Qubits
Classical computers run on bits — light switches that are either 0 or 1. Quantum computers use qubits that exist in superposition — holding the probability of being both 0 and 1 simultaneously. When qubits are linked through entanglement, their power scales exponentially: 300 qubits hold more states than there are atoms in the observable universe.
Interference: The Real Mechanism
Quantum computers don't crack codes by 'trying every password at once.' Measuring qubits in superposition gives random garbage. Instead, quantum algorithms use interference — choreographing qubits so wrong answers cancel out (destructive interference) while the correct answer amplifies (constructive interference).
Shor's Algorithm
In 1994, Peter Shor proved a quantum computer could find the hidden mathematical structure behind and without brute force. exploits the fact that prime factoring is tied to finding hidden repeating patterns — exactly what quantum interference excels at. A classical computer takes trillions of years to factor RSA-2048; a quantum computer could do it in minutes.
Grover's Algorithm and Symmetric Crypto
speeds up brute-force searches but only halves the effective key length. The fix is simple: upgrade to and SHA-256 to SHA-384/512. Symmetric tools survive quantum with minor upgrades. The real crisis is entirely in asymmetric cryptography.
Shor's breaks asymmetric crypto completely. Grover's only weakens symmetric crypto, which is easily fixed by doubling key sizes. This distinction is fundamental to understanding PQC.
Key Takeaways
- Qubits use superposition and entanglement to hold exponentially many states simultaneously
- Quantum algorithms use interference to amplify correct answers and cancel wrong ones
- Shor's Algorithm breaks RSA and ECC by finding hidden mathematical patterns