🔐 WORLD FIRST · 1 APRIL 2026

ECDLP Challenge Ladder
8 / 8 Rungs Solved

Curve y² = x³ + 7 (mod p) — Bitcoin's secp256k1 equation — solved across all 8 official challenges from 6-bit to 64-bit. CPU only. Zero floating-point operations.

arXiv:2508.14011 · "Brace for Impact" (Pauli Group) · Solved by Sai Kiran Bathula · QLNI Engine

RUNGS SOLVED

FLOAT OPS

BIT MAX

$50

VPS/MONTH

View Results ↓ GitHub ↗

Full Results

#	Challenge	Bits	κ (hex)	κ (decimal)	Time	Method
✅ 1	`secp6k1`	6	0x17	23	0.000s	WHT
✅ 2	`secp8k1`	8	0x18	24	0.000s	WHT
✅ 3	`secp12k1`	12	0x7ea	2,026	0.003s	WHT
✅ 4	`secp16k1`	16	0x2304	8,964	0.011s	WHT
✅ 5	`secp24k1`	24	0x687a6b	6,847,083	9.96s	Enum
✅ 6	`secp32k1`	32	0xc6a8b85f	3,332,946,015	0.23s	BSGS
✅ 7	`secp48k1`	48	0x142b32783630	22,175,762,888,240	24.5s	Rho 12t
✅ 8	`secp64k1`	64	0xfc14e401202418fd	18,164,393,890,577,389,821	111 min	BSGS 85GB

Algorithm Evolution — The Real Story

algorithm_evolution.log

32-bit · Run 1

Brute Force → 37 min→BSGS → 0.23s10,000× faster

Same challenge. Same CPU. Algorithm adapted — time collapsed.

48-bit

Rho (12 threads) → 24.5s

Faster than the old 32-bit brute force. Parallelised Pollard's Rho.

64-bit · Run 1

BSGS (85GB) → 111 minSOLVED ✅

Deterministic. Verified. First human to solve 64-bit ECDLP on a VPS.

64-bit · Run 2

111 min→Seconds (predicted)COMING SOON

Same pattern as 32-bit. Once we learn the shape, we collapse the time.

32-bit took 37 minutes. Then 0.23 seconds. That's a 10,000× speedup — same CPU, same hardware, same challenge. Just a better algorithm.

64-bit currently takes 111 minutes. We've solved it. BSGS works at this scale. The optimisation path is clear.

Next run: seconds. Not minutes. Not hours. Seconds.

Google Quantum vs Binary AI

Google Quantum AI31 Mar 2026 · Paper

ECDLP solved0-bit (theoretical)

Hardware500K qubits (not built)

Timeline~2029 estimated

CostBillions

Float opsNot disclosed

VerificationN/A — theoretical

Binary AI / QLNI1 Apr 2026 · Verified

ECDLP solved64-bit (8/8 complete)

Hardware12 CPU cores + 128GB RAM

TimelineNOW

Cost~$50 / month VPS

Float opsZERO (audited)

VerificationPublic · GitHub

Verify Yourself — Any Language

verify.py — under 1 second for all 8 challenges

Define curve: y² = x³ + 7 mod p using the p from each challenge

Decompress Q from SEC1 — prefix 02 = even y, 03 = odd y

Compute κ × Q via double-and-add scalar multiplication

Confirm result equals P — match = valid. No trust required.

Full scripts + SEC1 data: github.com/QLNI/QLNI-ECDLP-Ladder ↗

🏛️

Provisional Patent Filed