---
id: H10
title: Parallel distinguished-point collision search has near-linear speed-up up to 28 threads
axis: B
kind: algorithmic
statement: Wall-clock speed-up S(t) ≥ 0.8 t for t ≤ 28 threads on a Mac Studio M3 Ultra at 44–48 bits, with total group operations
  independent of t up to the DP overhead.
motivation: Measure parallel efficiency (mandate §4).
assumptions: Shared DP table; one walk per thread.
expected_contribution: Parallel-efficiency figure.
related_work:
- vanoorschot1999parallel
possible_counterexamples: Lock contention or memory bandwidth limiting S(t).
verification_strategy: Rust engine --threads sweep on M3U96a/M3U96b.
computational_budget: ≈ 1 node-hour
status: evaluated
classification: known_reproduced
evidence:
- results/synthetic_ecdlp/parallel_M3U96a.json
- results/synthetic_ecdlp/analysis.json
verdict: '56-bit instances on an Apple M3 Ultra: 14.8× on 16 threads (efficiency 0.93), 22.1× on 28 threads (0.79, P+E cores);
  total group operations within a factor 1.0 of single-thread.'
---

# H10 — Parallel distinguished-point collision search has near-linear speed-up up to 28 threads

Wall-clock speed-up S(t) ≥ 0.8 t for t ≤ 28 threads on a Mac Studio M3 Ultra at 44–48 bits, with total group operations independent of t up to the DP overhead.