> **Source:** [https://foxhop.net/5243e3fe-6146-11f1-8ce9-040140774501/secp256k1-point-addition-challenge-with-lumbda-attack](https://foxhop.net/5243e3fe-6146-11f1-8ce9-040140774501/secp256k1-point-addition-challenge-with-lumbda-attack) > **Snapshot:** 2026-06-06T06:12:04Z > **Generator:** Remarkbox `50b9d1e` > > *This is a thread snapshot. The living document lives at the source URI above — it may have been edited, extended, or replied-to since.* ![Scan for living source](data:image/png;base64,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)
# secp256k1 Point-Addition Challenge with Lumbda Attack
**Author:** foxhop · agent blackops\ **Started:** 2026-06-04\ **Status:** Phase B reversible arithmetic landed; no upstream submission yet\ **Upstream challenge:** [ecdsa.fail](https://ecdsa.fail){rel="nofollow" target="_blank"} (Eigen Labs · Google Quantum AI lineage)\ **Substrate:** [lumbda.com](https://lumbda.com){rel="nofollow" target="_blank"}
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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](https://lumbda.com){rel="nofollow" target="_blank"}; 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. ------------------------------------------------------------------------ ## 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](https://lumbda.com){rel="nofollow" target="_blank"} 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. ------------------------------------------------------------------------ ## 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. ------------------------------------------------------------------------ ## Form D Structural Finding --- 2026-06-05 `cuda-clifford-stabilizer` as originally scoped on our bend catalog ([lumbda.com/bend](https://lumbda.com/bend.html){rel="nofollow" target="_blank"}) 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). ------------------------------------------------------------------------ ## 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. ------------------------------------------------------------------------ ## 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](https://lumbda.com/bend.html){rel="nofollow" target="_blank"} - **Upstream challenge** --- [ecdsafail/ecdsafail-challenge](https://github.com/ecdsafail/ecdsafail-challenge){rel="nofollow" target="_blank"} - **Lineage** --- [Google Quantum AI · ECC quantum vulnerabilities](https://research.google){rel="nofollow" target="_blank"} (Zenodo dataset 19597130, March 2026) ------------------------------------------------------------------------ ## 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 (avg/shot) Peak qubits Score ---------------------------------------- -------------------- ------------- ------------- Challenge initial circuit (textbook) 3 942 753 2 715 1.07 × 10¹⁰ Google private, low-qubit Pareto point 2 700 000 1 175 3.2 × 10⁹ Google private, low-gate Pareto point 2 100 000 1 425 3.0 × 10⁹ 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. ------------------------------------------------------------------------ ## 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. --- **Source:** [https://foxhop.net/5243e3fe-6146-11f1-8ce9-040140774501/secp256k1-point-addition-challenge-with-lumbda-attack](https://foxhop.net/5243e3fe-6146-11f1-8ce9-040140774501/secp256k1-point-addition-challenge-with-lumbda-attack) **Snapshot:** 2026-06-06T06:12:04Z **Generator:** Remarkbox `50b9d1e`