Replace IBM Quantum back end with /dev/urandom

Claim being tested: the Q‑Day Prize submission in this repo demonstrates a quantum attack on ECDLP — specifically, key recovery on curves up to 17 bits using IBM Quantum hardware.

This branch applies a single surgical patch (−29 / +30 lines) to projecteleven.py. The patch replaces the IBM Quantum backend inside solve_ecdlp() with os.urandom. Everything else — circuit construction, the ripple‑carry oracle, the extraction pipeline, the d·G == Q verifier — runs byte‑for‑byte unchanged. If the quantum computer were contributing measurable signal, this substitution should break the recoveries. It does not. The author's own CLI recovers every reported private key at statistically indistinguishable rates from the IBM hardware runs.

- if token:
- service = QiskitRuntimeService(...)
- ...
- backend = service.backend(backend_name)
- ...
- qc_t = transpile(qc, backend, optimization_level=optimization_level)
- ...
- sampler = SamplerV2(mode=backend)
- job = sampler.run([qc_t], shots=shots)
- ...
- result = job.result()
- pub_result = result[0]
- counts = pub_result.data.cr.get_counts()
+ # /dev/urandom patch: generate `shots` uniform-random bitstrings of the
+ # same length as the circuit's classical register. Everything downstream
+ # of `counts` is the author's code, unchanged.
+ import os as _os
+ from collections import Counter as _Counter
+
+ nbits = qc.num_clbits
+ bpb = (nbits + 7) // 8
+ mask = (1 << nbits) - 1
+
+ _bitstrings = []
+ for _ in range(shots):
+ v = int.from_bytes(_os.urandom(bpb), "big") & mask
+ _bitstrings.append(format(v, f"0{nbits}b"))
+ counts = dict(_Counter(_bitstrings))

Every d is byte‑identical to the author's reported hardware result. The author ran each once. So did /dev/urandom. Both "succeeded."

| challenge | author's reported d | urandom attempts | recovered d | |---|---|---|---| | 16‑bit | 20,248 | ✅ ✅ ✅ ✅ ❌ | 20,248 (4/5) | | 17‑bit 🏆 | 1,441 | ❌ ❌ ✅ ✅ ❌ | 1,441 (2/5) |

The 17‑bit result is the one awarded 1 BTC. /dev/urandom recovers it ~40% of runs on a laptop. The author ran it once on IBM ibm_fez and claimed a quantum result. No quantum computer was harmed in the recovery of this private key.

The author's extraction takes each shot's (j, k, r) and accepts d_cand = (r − j)·k⁻¹ mod n iff it passes the classical verifier d_cand · G == Q. Under uniform noise, d_cand is uniform on [0, n), so:

P(≥1 verified hit in S shots) = 1 − (1 − 1/n)^S

The engineering in this repo is genuine and non‑trivial. The critique here is narrowly about the cryptanalytic claim: that these hardware runs constitute ECDLP key recovery by a quantum computer. They do not. They are classical verification applied to uniform‑random candidates — reproducible without any quantum hardware at all.