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Static-graph simulator quantifying how a node's peering degree trades off propagation speed, adversary exposure, deanonymization, and reliability in the Blend network. Scales to 1e6 nodes (sparse CSR + sampled Dijkstra); the adversary and deanonymization metrics are exact at every N. Model (ms): seeded d-regular peer graph (matching-union), Blend cascade (sender -> blend_hops timed-release mix relays -> final flood), geographic link base + exponential transport jitter, per-node processing lag, free-running release-clock mixing. Metrics: - propagation: full-delay mean/p50/p90/p99, path/broadcast split, coverage times - reliability: message success-delivery-rate ~ (1-unresponsive_frac)^blend_hops and flood coverage, with unresponsive nodes modelled as routing holes - adversary (exact): observed/eclipsed fractions, random + worst-case placement - deanonymization (exact): P(whole blend path adversarial) ~ f_adv^blend_hops, and full deanonymization (path adversarial AND honest sender peered with an adversary) = deanon_rate * observed_frac Deterministic blake2b seed streams, three parquet tables, joblib parallelism, memguard, an analytic verify harness, 50 unit tests, and an auto-installing Makefile. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
69 lines
4.9 KiB
Markdown
69 lines
4.9 KiB
Markdown
# pd — peering-degree Monte-Carlo graph simulator
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Quantifies how a node's **peering degree** trades off, in the Blend network:
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- **propagation speed** — the full delay (ms) of a message: a random sender routes it along a
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`blend_hops`-relay Blend path (each relay a free-running timed-release mix node) and the last
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relay floods the whole network;
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- **adversary exposure** — with a fraction `f_adv` of adversarial nodes, how many honest nodes are
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peered with ≥1 adversary (**observed**) and how many are fully surrounded (**eclipsed**);
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- **deanonymization** — tying propagation to the adversary: how often a message's *whole* blend path
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is adversarial (**deanonymization** — the adversary owns the cascade end-to-end) and how often the
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honest sender is *additionally* peered with an adversary (**full deanonymization** — the message is
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tied back to its originator); and
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- **reliability under churn** — with a fraction `unresponsive_frac` of nodes that relay nothing, the
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**message success-delivery-rate** (fraction of messages that survive the whole blend cascade to a
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responsive final relay) and the flood **coverage** of those that do.
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The peer graph is a seeded random **d-regular** graph (exactly `degree` symmetric peers, identical
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for everyone from one global seed). This is static-graph analysis — no consensus — so it is far
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lighter than the TSI simulators and scales to **10⁶ nodes** (sparse CSR + sampled Dijkstra; the
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adversary metrics are exact at every N).
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## Model (all delays in ms)
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- **Link delay:** geographic base (metro 15 → antipodal 200 ms) + exponential transport jitter.
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- **Processing lag:** each node draws a fixed lag from a categorical distribution (default
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{10, 50, 100} ms at {0.5, 0.4, 0.1}), incurred every time it relays.
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- **Blend mixing:** each relay releases on a free-running clock whose successive intervals are
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Uniform{0…`max_blend_delay`} whole seconds; a held message waits for the relay's next release
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(the renewal residual). Mixing happens only at the `blend_hops` relays; the final flood is plain.
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- **Unresponsive nodes:** a random `unresponsive_frac` of the population relays nothing (its outgoing
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edges are removed). Relays are drawn from the whole node list *blind to responsiveness*, so a
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message dies if any relay on its path is unresponsive — the delivery-rate then tracks
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`(1−unresponsive_frac)^blend_hops`. Unresponsive nodes still *receive*, but they are routing holes,
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so a delivered flood can strand pockets; a higher peering degree supplies redundant paths that keep
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coverage high. This axis affects propagation only, not the adversary metrics.
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- **Deanonymization:** relays are picked *blind to who is adversarial*, so P(the whole blend path is
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adversarial) is the exact hypergeometric `C(n_adv, blend_hops) / C(N−1, blend_hops)` ≈
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`f_adv^blend_hops` (**deanon_rate**) — placement-independent, driven by path length, not degree.
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Multiplying by the fraction of honest nodes with ≥1 adversary peer (`observed_frac`, which the
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worst-case-coverage placement maximizes) gives **full_deanon_rate** — the honest sender is *also*
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directly exposed, so the message is tied to its originator. Lengthening the blend path is the
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dominant defence; a higher degree speeds propagation but *raises* the chance a sender directly
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touches the adversary. Both are exact at every N (no Monte-Carlo), like the other adversary metrics.
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## Quick start
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```
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make install # or reuse a sibling venv: PYTHONPATH=src <python> -m pd.sweep ...
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make smoke # fast end-to-end -> runs/<ts>_smoke/{propagation,adversary}.parquet + figures/
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make verify # analytic checks (closed forms + graph invariants)
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make test # unit tests
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make sweep # configs/default.yaml (N up to 1e5, both adversary modes)
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make sweep-fullscale # configs/fullscale.yaml (N up to 1e6, random-mode exact)
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make figures RUN=runs/<dir>
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```
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## Outputs
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Three parquets per run: `propagation.parquet` (`full_delay_ms_*`, `delivery_rate`, `frac_reached`,
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`coverN_ms` vs degree / blend_hops / N / unresponsive_frac), `adversary.parquet` (`observed_frac` /
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`eclipsed_frac` vs degree / f_adv / mode, random + worst-case envelope), and `deanon.parquet`
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(`deanon_rate` / `full_deanon_rate` vs degree / blend_hops / f_adv / mode — propagation paths crossed
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with the adversary set). Figures render all three, including delivery-rate and flood-coverage vs the
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unresponsive fraction and the deanonymization rates vs blend-path length, f_adv, and degree.
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## Layout
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`src/pd/`: `graph` (matching-union CSR d-regular), `propagation` (Blend cascade), `mixclock`
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(release-clock residual), `adversary` (exact observation/eclipse + deanonymization + placement),
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`config`/`engine`/`sweep`/`metrics`, `plotting`. `configs/` sweeps, `tests/`, `scripts/` shims.
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Reports of record live outside the sim at `reports/blend/pd/`.
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