1---2id: H103title: Parallel distinguished-point collision search has near-linear speed-up up to 28 threads4axis: B5kind: algorithmic6statement: 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 operations7 independent of t up to the DP overhead.8motivation: Measure parallel efficiency (mandate §4).9assumptions: Shared DP table; one walk per thread.10expected_contribution: Parallel-efficiency figure.11related_work:12- vanoorschot1999parallel13possible_counterexamples: Lock contention or memory bandwidth limiting S(t).14verification_strategy: Rust engine --threads sweep on M3U96a/M3U96b.15computational_budget: ≈ 1 node-hour16status: evaluated17classification: known_reproduced18evidence:19- results/synthetic_ecdlp/parallel_M3U96a.json20- results/synthetic_ecdlp/analysis.json21verdict: '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);22 total group operations within a factor 1.0 of single-thread.'23---2425# H10 — Parallel distinguished-point collision search has near-linear speed-up up to 28 threads2627Wall-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.28