Swapping IBM Quantum hardware for /dev/urandom in the Project Eleven QDay prize submission still recovers every reported ECDLP private key at statistically indistinguishable rates.
Key Takeaways
The 29/30-line patch modifies only the backend setup inside solve_ecdlp(); ripple-carry oracle, CDKM circuit, and d·G == Q verifier run byte-for-byte unchanged.
For 4-10 bit challenges, shots/n ranges from 1.9x to 1,170x; uniform-random candidate selection hits the classical verifier at near-100% probability by arithmetic alone.
The 1 BTC 17-bit key (n=65,173, 20,000 shots) has a theoretical urandom success rate of 26.43%; empirical laptop runs recover the correct key ~40% of the time.
Extraction accepts d_cand = (r-j)·k^-1 mod n iff d_cand·G == Q – classical verification on uniform-random candidates, no quantum signal required.
The submission’s own README admits random noise recovers d when shots >> n; every small challenge (4-10 bit) satisfies that condition by the author’s own parameters.