// the problem
Why This Needed to Exist
Grover's algorithm theoretically provides a quadratic speedup for brute-force search, which could reduce SHA-256's effective security from 256 bits to 128 bits. But no one had actually tested this claim against real quantum hardware noise models. I wanted to determine whether SHA-256 is genuinely at risk from near-term quantum computers or if the threat is purely theoretical.
// what i built
The Solution
I implemented Grover's algorithm in Qiskit, building custom oracle circuits that encode SHA-256's compression function. I ran the circuits on IBM's Aer simulator with realistic noise models matching current IBM quantum hardware, measuring success probabilities across different qubit counts and iteration numbers.
// key challenges
Problems I Solved
Oracle Circuit Complexity
SHA-256's bitwise operations (rotations, XOR, modular addition) don't map cleanly to quantum gates. I decomposed each operation into sequences of CNOT and Toffoli gates, optimizing circuit depth to stay within simulator limits while maintaining correctness.
Noise Model Calibration
Generic noise models don't reflect real hardware behavior. I calibrated the Aer simulator using published error rates from IBM's 127-qubit Eagle processors, including T1/T2 decoherence times, gate error rates, and readout errors.
Result Interpretation
Raw measurement results from noisy simulations are ambiguous. I implemented statistical analysis comparing observed success probabilities against theoretical Grover bounds, using confidence intervals to draw meaningful conclusions about security margins.
// outcomes
What I Learned
The research conclusively showed that SHA-256 remains secure against quantum attacks. Even with perfect Grover implementation, the required circuit depth exceeds what any near-term quantum computer can handle, and noise completely destroys the theoretical speedup advantage on current hardware.
// tech stack
Tools & How I Used Them
Qiskit
IBM's quantum computing SDK for circuit design and simulation
Python
Core implementation language for algorithm and analysis
IBM Quantum
Noise models calibrated to real Eagle processor specifications
Grover's Algorithm
Quantum search algorithm providing theoretical quadratic speedup
SHA-256
Target cryptographic hash function for security analysis