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secp256k1 Point-Addition Challenge with Lumbda Attack
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secp256k1 Point-Addition Challenge with Lumbda Attack
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| **Author:** foxhop · agent blackops
| **Started:** 2026-06-04
| **Status:** Phase B reversible arithmetic landed; no upstream
submission yet
| **Upstream challenge:** `ecdsa.fail `__ (Eigen
Labs · Google Quantum AI lineage)
| **Substrate:** `lumbda.com `__
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What This Page Tracks
---------------------
A quantum-reversible attack on a secp256k1 point addition, written
entirely in lumbda — a Lisp/Scheme derivative across four implementation
tiers: Python bytecode VM, C tree-walker + JIT, C + x86_64 JIT, & pure
x86_64 assembly. Lumbda's docs & live runtimes sit at
`lumbda.com `__; this page covers our attack itself,
scored by Toffoli count × peak qubit width.
Lower score wins. Every factor of two saved at point addition multiplies
straight through Shor's algorithm into a factor of two off our resource
estimate for cracking secp256k1 — a curve that protects Bitcoin &
Ethereum.
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Where This Work Lives in Our Stack
----------------------------------
ecdsa.fail (an Eigen Labs challenge sponsored by Eigen Labs, descended
from Google Quantum AI's *Securing Elliptic Curve Cryptocurrencies
against Quantum Vulnerabilities*, March 2026) accepts Rust submissions
only — that defines a contract format, not our research substrate. Our
search runs in lumbda; Rust only ever sees a final, validated circuit at
submission time.
Why lumbda — four reasons:
- **Cross-tier portal validation.** Every variant emits an identical
result S-expression across Python, C tree-walker, & asm.
Byte-mismatch on any tier halts promotion to a next phase. Rust gives
us one tier with no cross-tier check.
- **Fleet sharding via TCP + S-expression portals.** Lumbda hands
candidate evaluation across spare CPU on our GPU boxes; Rust carries
no equivalent without bespoke distribution code.
- **A CUDA path already exists.** Our ``bend`` primitive on
`lumbda.com `__ dispatches GPU work over a binary
wire (magic ``BSHK``). Bend hands lumbda's upstream-format
``ops.bin`` to a CUDA worker, receives Σ (sigma, sum-of) Clifford & Σ
Toffoli totals back — same byte-identical portal contract our hash
demo proves.
- **Future CUDA growth feeds back.** Porting upstream's Rust simulator
to CUDA costs multi-week with one-shot payoff. Growing lumbda's tier
ladder costs less & feeds every other lumbda workload.
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Phase B — Reversible Arithmetic Landed
--------------------------------------
Twelve steps after Roetteler et al. (2017), modular arithmetic over
secp256k1's prime field, lumbda-native:
- **Steps 1–8** — modular add, subtract, multiply, square, inverse
(Bernstein-Yang safegcd flavor), exponentiation
- **Steps 9–10** — refined Bernstein-Yang modular inverse wired into a
real point-addition circuit
- **emit-ops.bin walker** — lumbda → (to) upstream QECCOPS1 binary
format
Status: cross-tier validated on Python tier. C-tier & asm-tier
escalation routes through a QEMU guest (``ecdsa/vm-runner.sh``) — host
policy locked after a 2026-06-03 C-tier OOM crash. Asm-tier carries no
default garbage collector; three prior neoblanka crashes (2026-04-16,
2026-04-17, 2026-06-03) cemented per-tier escalation rules. See lumbda's
CLAUDE shard on asm memory discipline.
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Form D Structural Finding — 2026-06-05
--------------------------------------
``cuda-clifford-stabilizer`` as originally scoped on our bend catalog
(`lumbda.com/bend `__) does not apply to a
point-addition circuit. Build agent measured Toffoli fraction at 13.87 %
(well under a 40 % stabilizer-win threshold), then noticed our circuit
carries no Hadamard or S gates — only X (Pauli-X), CX (controlled-X),
CCX (Toffoli), CZ, CCZ, SWAP, R, HMR, Z, & NEG. State never leaves a
computational basis. Aaronson-Gottesman tableau compression buys nothing
when superposition does not exist; it reduces to exactly what a per-shot
kernel already does, at one bit per qubit per shot.
Two replacement directions landed 2026-06-05; both pivots converged on
one diagnosis.
**Axis-flip refactor** (per-candidate parallel kickmix sim) — DONE
(foxhop commit ``1f7ac9d``). 217 Mops/s (mega-ops per second) at K=32
M=4 on a RTX 3090; 23.7× (times) over per-shot N=4 at same M. Both
kernels saturate at ~220–250 Mops/s. Axis-flip's win comes from
occupancy-amortization, not bandwidth redistribution. Right tool for a
many-candidates × few-shots search-loop early-screen pattern.
**QECCOPS2 packed ops.bin** — DONE (foxhop commit ``90484ca``). 1.07×
kernel speedup, 2.33× on-disk shrink (716 MB → 307 MB). Our original
3.5× projection assumed 56 B/op stayed VRAM-resident; ``ops_loader.c``
already narrowed to 28 B on load, so realistic ceiling sat at 1.17×.
Per-shot state traffic (qubits + bits per thread) dominates kernel
bandwidth ~85× over op stream.
**Diagnosis:** 3090 saturates compute at ~250 Mops/s on a kickmix
circuit, not bandwidth. Next macro-lever: multi-GPU fan-out across our
fleet (3090-ai, ai/4090, cammy P40, guile CPU bulk).
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Measured Numbers — RTX 3090
---------------------------
Against HEAD's 12.8 M-op kickmix ``ops.bin`` (716 MB) via bend:
========= ===== ====== ====== ====== ========
n_batches shots wire-s cpu-ms gpu-ms gpu/cpu
========= ===== ====== ====== ====== ========
1 64 5.5 42 5 107 0.008
16 1 024 7.3 850 5 800 0.146
64 4 096 11.4 3 444 6 216 0.553
128 8 192 17.1 7 060 6 604 **1.07**
========= ===== ====== ====== ====== ========
Crossover at ~115 batches. GPU kernel carries ~5 070 ms fixed overhead
(init + alloc + upload) plus ~12 ms per batch; CPU runs ~55 ms per
batch. Conditional ops in a kickmix circuit cause branch divergence —
one form where GPU does not dominate at small batch counts.
Honest signal, not hype.
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What Lives Where
----------------
- **Lab repo (private)** — lumbda source for our attack, circuit build
/ sim / score / candidate sweep, QEMU envelope around C-tier &
asm-tier runs, run artifacts under ``runs/lumbda-*/``
- **Bend catalog & wire protocol** —
`lumbda.com/bend `__
- **Upstream challenge** —
`ecdsafail/ecdsafail-challenge `__
- **Lineage** — `Google Quantum AI · ECC quantum
vulnerabilities `__ (Zenodo dataset
19597130, March 2026)
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Pareto Frontier We Aim To Beat
------------------------------
Upstream README reports two Google private Pareto points sitting below a
textbook 1.07 × 10¹⁰ score; upstream claims both points sit strictly
beatable.
+-------------------+-------------------+-------------+-------------+
| Variant | Toffoli | Peak qubits | Score |
| | (avg/shot) | | |
+===================+===================+=============+=============+
| Challenge initial | 3 942 753 | 2 715 | 1.07 × 10¹⁰ |
| circuit | | | |
| (textbook) | | | |
+-------------------+-------------------+-------------+-------------+
| Google private, | 2 700 000 | 1 175 | 3.2 × 10⁹ |
| low-qubit Pareto | | | |
| point | | | |
+-------------------+-------------------+-------------+-------------+
| Google private, | 2 100 000 | 1 425 | 3.0 × 10⁹ |
| low-gate Pareto | | | |
| point | | | |
+-------------------+-------------------+-------------+-------------+
Our lumbda-tier validation gates each variant against byte-identical
cross-tier portals before we ever spend Rust submission budget against
9024 Fiat-Shamir-derived test points.
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Why Track This Publicly
-----------------------
A challenge of this shape rewards aggressive, asymmetric search. Every
factor of two off a Toffoli count, every qubit shaved off peak width,
multiplies straight through Shor's algorithm. Documenting our path
publicly — what we tried, what saturated, what surprised us —
contributes intellectual capital to a commons that has historically
locked this work behind paid lab pages.
This page tracks public-facing progress only. Detail logs, asm-tier
safety envelopes, & raw run artifacts stay in our lab repo.
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| **Source:**
https://foxhop.net/5243e3fe-6146-11f1-8ce9-040140774501/secp256k1-point-addition-challenge-with-lumbda-attack
| **Snapshot:** 2026-06-06T06:25:21Z
| **Generator:** Remarkbox ``50b9d1e``