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Difficulty under attack: hopping, pulsed rental, timestamp stretching, oscillation, epoch games, polluted window, flood; two FAILs with proposed diffs

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Simulator harness over sim/difficulty/sim.py with multi-miner attribution and in-rule timestamp forging, a 3-node CPU test network (ports 27700+), results and bench-log entry. Timestamp stretching inside Kaspa's rules drops the Igneum block rate 34 to 88% (the per-step clamp cancels forged and honest pairs to zero time); proposed 10 s timestamp bounds plus a sanitised running clock in the chain steps (+0.7% to +1.1% drift at 50% in the simulator). Block flood underflows the 192-bit work after 4,142 blocks; a 2^128 target floor proposed. Rule not changed.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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@ -446,3 +446,11 @@ Failures and the proposed fixes (diffs in `tools/finality-attacks/README.md`, fo
3. F1 (S5): no certificate should form before the window holds a full window of history (spec 3.8, O-3.1). Proposed: `min_daa = weight_window` (2,592,000 on mainnet, 7,200 on devnet) in `FinalityParams`, one line each.
Not demonstrated: certificate injection on the wire (S3, S8 half), the eclipse (S7), the 2-hour presence window at mainnet length, the heal rule of 3.5 (both partitions healed without a conflicting certificate, so it was not exercised).
## 4 October 2026, difficulty rule under attack: pool hopping, pulsed rental, timestamp stretching, short-lane oscillation, epoch games, polluted window, block flood (consensus test engineer)
Machine: the same Apple M5 Max, shared with other agents' builds and test networks (load 15 to 30). Simulator `sim/difficulty/attacks/attacks.py` over `sim/difficulty/sim.py` (controllers unchanged): several miners with on/off strategies, block attribution by hash share at the solve, hashes per miner, timestamp forging inside the fork's rules (132 s ahead, above the 27-sample past median). Node runs on branch `diff-attacks` of `vendor/igneum-node` (worktree `vendor/igneum-node-diff-attacks`, from `difficulty` at `3ea7a3e3`; adds only the attack variable `IGNEUM_ATTACK_TS_OFFSET_MS` in the template builder and a reproduction test), ports 27700 to 27721, appdir `/tmp/igneum-diff-attacks`, genesis bits `0x1f010000`. Everything in `sim/difficulty/attacks/README.md`, raw tables in `results.md`, headers of the three test-network runs in `testnet/`.
Simulator, seeds 7 to 9, Igneum / Kaspa's rule, criterion, verdict: (1) pool hopper 10 to 100% of the base, on while D is below its 6-hour mean, 24 h: hopper's blocks per hash +1.5% at most / +0.8% at most, under 5% both, Igneum 0.7 points above Kaspa's in every greedy cell (unchanged with the ease clamp at 6% or 3%: the price of a controller that moves inside the hour; a 60 s dwell turns the 50% and 100% hoppers into losers, -1.7% and -4.0%): PASS under 5%, FAIL on "no larger than Kaspa's" by the letter, no change proposed. (2) 50x burst for 10 min every hour: pulser's weight per hash 0.26 / 0.98 of the base's, blocks per hash 3.7% / 85% of the base's; once: 0.13 / 0.87: PASS (no weight amplifier under either rule; Kaspa's makes the burst cheap, Igneum's makes it 27x dearer; the hour after costs the base 37% and a 153 s worst gap under Igneum). (3) forger at 30 or 50% stamping at the latest allowed, the earliest allowed, or alternating: Igneum block rate 0.66 / 0.42 / 0.51 at 30% and 0.56 / 0.12 / 0.23 at 50%, difficulty 1.5x to 9.9x on an unchanged hash rate, worst gap 234 s; Kaspa's rule +5% to +11% easing: FAIL both, Igneum far worse. Cause: the symmetric per-step clamp turns every forged block and the honest block after it into zero measured time (spec 2.3's "the next honest block cancels it" is the bug, not the defence), so the lanes measure 1 - 2a(1 - a) of real time at share a; past-stamping also drags the past median down without bound. (4) 25% miner on and off every 120 blocks: std of the rate ratio 0.160 / 0.147 against 0.045 / 0.010 steady and a 0.143 floor from the attacker's own square wave: FAIL by the letter for both, neither oscillates (12% and 3% above the floor), no change proposed. (5) hold dodger 30%, hold flooders 10x and 30%: 0.0 / +0.7 / +0.3% against 0.0 / 0.0 / -0.1%: PASS. (6) 10x miner leaving at block 600 of an epoch, where the long lane takes over: settled 303 s (292 s with the short lane engaged at the switch), worst gap 17 s, against 334 s for a leave at block 1,200; Kaspa's 2,910 to 3,540 s: PASS. (7) side finding, blocks every 12 ms fed to the rule (another agent's pump): the target passes below 2^64 after 4,142 blocks and `calc_work` panics at `difficulty.rs:431` (`should_panic` test `igneum_flood_at_85_blocks_per_second_drives_the_target_below_block_work_range` on `diff-attacks`): FAIL, floor proposed.
Test network, 3 `igneumd` nodes, honest 4-thread miner A on node 1 for 15 min, forger F (4 threads, about 50%) honest on node 2 for 5 min then on node 3 with the offset: Igneum, earliest allowed stamp: 0.97 blocks/s at difficulty 91,000 before, 0.24 blocks/s at 275,000 during forging and 0.20 at 341,000 in the last 5 min, forger offsets -121 to -566 s, hash unchanged (A 0.078, F 0.069 MH/s). Igneum, latest allowed stamp (+134 s): 0.98 blocks/s at 89,000 before, 0.59 at 170,000 during, 0.50 at 191,000 in the last 5 min (A 0.112, F 0.110 MH/s); the simulator's 50% cases give 0.12 at 9.9x and 0.56 at 1.8x. Kaspa's rule, earliest allowed stamp: 1.73 blocks/s on a 2.5x too easy genesis to block 600 at 210 s, then 1.02 blocks/s at 83,400 through ten minutes of -180 s stamps. 517, 767 and 1,454 blocks, 0 rejected.
Proposed (README.md, diffs, not applied): Part A, timestamp rules: 10 s future tolerance (`FUTURE_TOLERANCE_MS`, a new constant so the past-median window keeps its 27 samples) and a floor at the selected parent's timestamp minus 10 s (`BACK_TOLERANCE_MS`) beside the past median; Part B, the chain steps of the short and epoch lanes measured on a sanitised running clock c(b) = max(c(p) + clamp(t(b) - c(p), -20 T, +20 T), t(b) - 60 T), step = min(c(b) - c(p), 20 T), stored per header, so forgeries telescope instead of cancelling; the long lane unchanged. Measured, both parts, 3 seeds: the 50% forger drifts the rate +0.7% (past), +0.9% (future), +1.1% (alternating), worst seed +2.7%; base profiles unchanged except down50 762 s against 782 s, warm-up 327 s against 381 s, polluted peak 11.4x against 8.0x; the other attacks identical. Either part alone fails (unchanged rule under the tight rules: -36% and -83% to past-stamping; the clock under the 132 s rules: collapse at 50%, a martingale once the forgery range exceeds half the cap). Part C for the flood: clamp the output at `MIN_DIFFICULTY_TARGET` = 2^128 beside the existing maximum, in both rules.
Not done: the candidate in the node (simulator only; the per-header clock is a store change); DAG effects of forged stamps on red and merged blocks (one chain in the simulator); a rule change for the hopper's 0.7-point excess (none found that keeps the controller fast; README.md, scenario 1); Kaspa's rule under the flood (same hole, 17x slower, not run).

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# sim/difficulty/attacks
Adversarial runs against the Igneum difficulty rule (spec 2.3, `difficulty` branch of `vendor/igneum-node`) and
Kaspa's sampled DAA, 3 and 4 October 2026, consensus test engineer. Six attacks a GPU farm or a pool-hopping bot
would run, in the simulator first (`attacks.py`, on top of `../sim.py`), then the two most damaging on a 3-node
CPU test network (`testnet.py`, records under `testnet/`). One scenario fails. The proposed rule change is at
the end, with the simulator run that shows it works. Nothing in the rule itself was changed here.
## Files
| File | What |
|---|---|
| `attacks.py` | the attack harness: several miners with on/off strategies and in-rule timestamp forging on top of the base simulator's controllers; the candidate controller `IgneumSan` (the proposed fix); markdown tables |
| `testnet.py` | the 3-node CPU test network (ports 27700 and above, appdir `/tmp/igneum-diff-attacks`), schedule, header export over wRPC JSON, wall-time analysis |
| `results.md` | raw simulator output of every run quoted here (seeds 7, 8, 9) |
| `testnet/ts-past-igneum.csv`, `testnet/ts-future-igneum.csv`, `testnet/ts-past-kaspa.csv` | every header of the three test-network runs (columns as `../testnet-igneum-2026-10-03.csv` plus `vote_key_hash`, `blue_work`) and the schedule logs beside them |
Branch `diff-attacks` of `vendor/igneum-node` (worktree `vendor/igneum-node-diff-attacks`, from `difficulty` at
`3ea7a3e3`) adds one thing, attack tooling only: the environment variable `IGNEUM_ATTACK_TS_OFFSET_MS` shifts
every template timestamp the node hands out (`virtual_processor/processor.rs`, `mining/block_template/builder.rs`),
still floored at the past median plus one by the unchanged template code. Validation is untouched, so the
forger's blocks are accepted by the honest nodes only if they are inside the rules.
## What the harness adds to the base simulator
The base simulator has one miner and honest timestamps. The harness keeps its controllers (imported, unchanged)
and adds: several miners, each with a hash rate in units of the honest base and a policy evaluated at block
boundaries (hopper, oscillator, epoch gamer) or a time gate (rented burst); attribution of each block to the
miner that found it, drawn by hash share at the solve; hashes spent per miner; and timestamp forging inside the
consensus rules. The rules modelled are Kaspa's as the fork runs them: a header at most 132 s ahead of the
clock (`check_block_timestamp_in_isolation`, `TIMESTAMP_DEVIATION_TOLERANCE`) and strictly above the sampled
past median time (`check_median_timestamp`: 27 samples at 10-block intervals, mean of the central 11,
`SampledPastMedianTimeManager`). Honest miners stamp real time, raised to the past median plus one when the rule
forces it. Blocks per hash of a miner is the expected-gap estimator sum(1 / H_b) / sum(D_b / H_b) over the blocks
it was on for (H_b total hash rate, D_b expected hashes), which has no block-count noise (the realised counts
in the first run gave +13% "advantages" on 48 blocks that were sampling noise). Settle and gap metrics are the
base simulator's (`sim.metrics`: 121-block centred mean within 10% of target, kept for 100 blocks).
## Scenarios and criteria
| # | Attack | Set-up | Measured | Criterion |
|---|---|---|---|---|
| 1 | Pool hopping for profit | hopper with 10, 30, 50 or 100% of the honest base, on while D is below its trailing 6-hour mean (1% band), off above; greedy and with a 60 s minimum dwell; base constant; 24 simulated hours | hopper's blocks per hash against the always-on base | advantage under Igneum no larger than under Kaspa's rule, and under 5% |
| 2 | Pulsed hash rate (M14) | 50x the base for 10 min every hour, and once; 8 h | pulser's blocks per hash against the base, and its block share over its hash share (weight per hash) | within 10% of steady |
| 3 | Timestamp stretching inside the rules | forger with 30 or 50% of the hash rate stamping every block at the latest allowed (clock + 132 s), the earliest allowed (past median + 1 ms), or alternating; honest for 2 h then forging for 4 h | block rate drift after the first hour of forging, mean difficulty ratio, worst gap | no persistent drift beyond 5% of target rate |
| 4 | Short-lane manipulation | 25% of the hash rate on and off every 120 blocks; 6 h | std of the rate ratio against the steady value, worst gap | std under twice the steady value |
| 5 | Epoch-boundary games | a 30% miner off for the 8 hold blocks of every epoch; a 10x miner on only for the hold blocks; a 30% miner on only for the hold blocks; 8 h | gamer's blocks per hash against the base | the hold does not create a profitable window |
| 6 | Polluted window under adversarial timing | a 10x miner joins at block 0 or 480 of an epoch and leaves at block 600 (the long lane takes over), 720 or 1,200 | settle and worst gap after the leave, blocks below half rate | no worse than the plain step-down |
| 7 | Block flood (side finding, 4 Oct) | blocks every 12 ms (85 per second) fed to the rule, as another agent's pump harness did to the node | whether the target leaves the range the block-work type can hold | the node never panics on accepted input |
## Results (simulator, seeds 7, 8, 9, mean; worst seed where it differs)
| # | Attack | Criterion | Igneum | Kaspa's rule | Verdict |
|---|---|---|---|---|---|
| 1 | Pool hopping, 24 h, hopper 10 to 100% of the base, greedy and 60 s dwell | advantage no larger than Kaspa's and under 5% | +1.5% at most (10% greedy; 30%: +1.0%, 50%: +0.9%, 100%: +0.7%; with a 60 s dwell +1.3% to -4.0%); on 8 to 44% of the time, 230 to 820 switches a day | +0.8% at most (0.4 to 0.8% in every cell); on 6 to 37% of the time, 64 to 132 switches | PASS under 5%; FAIL by the letter on "no larger than Kaspa's" by 0.7 points (see 1 below) |
| 2 | Pulsed rental, 50x for 10 min hourly and once | pulser's blocks per hash within 10% of steady (no weight amplifier) | hourly: pulser earns 3.7% of the base's blocks per hash, weight per hash 0.26 (23% of blocks for 89% of hashes); once: 2.9% and 0.13 | hourly: 85% of the base's, weight per hash 0.98; once: 57% and 0.87 | PASS (the pulse buys no weight; the base's blocks per hash fall 37% in the hour after, worst gap 153 s, 184 blocks in the peak minute against Kaspa's 1,734) |
| 3 | Timestamp stretching, forger 30 and 50%, latest / earliest / alternating | no persistent drift beyond 5% | rate 0.66 / 0.42 / 0.51 at 30%, 0.56 / 0.12 / 0.23 at 50% (drift -34% to -88%), difficulty 1.5x to 9.9x, worst gap 234 s | +4.9% / +6.9% / +9.0% at 30%, +5.0% / +11.3% / +9.8% at 50% (easing) | FAIL (both rules; Igneum far worse). Reproduced on the test network. Rule change proposed |
| 4 | Short-lane oscillation, 25% on and off every 120 blocks | std under twice steady | std 0.160 against 0.045 steady (3.6x); floor of the attacker's own square wave 0.143; worst gap 11.0 s against 8.8 s; oscillator earns 1.4% less than the base | std 0.147 against 0.010 (16x); same floor; worst gap 10.3 s | FAIL by the letter for both; neither oscillates (12% and 3% above the floor); no change proposed |
| 5 | Epoch games: hold dodger 30%, hold flooder 10x, hold flooder 30% | no profitable window | 0.0%, +0.7% (worst seed +2.4%), +0.3% (worst +2.1%) | 0.0%, 0.0%, -0.1% | PASS |
| 6 | Polluted window, 10x joins at block 0 or 480, leaves at 600 / 720 / 1,200 | no worse than the plain step-down | leave at 600: settled 303 s (join at 0) and 292 s (join at 480), worst gap 17 s, 55 blocks below half rate; leave at 1,200: 334 s | 2,910 s / never within 10% / 135 s / 3,540 s; never settles the join | PASS |
| 7 | Block flood, 85 blocks per second of PoW-less input (side finding) | the node never panics | target below 2^64 after 4,142 blocks, `calc_work` panics at `difficulty.rs:431` | same hole, 17x slower (not run) | FAIL. Floor proposed |
Reading, scenario by scenario.
1. Pool hopping. Under Igneum the controller follows the hopper within about 10 blocks, so the hopper is on for
only 8 to 44% of the time, switches 230 to 820 times a day, and earns at most 1.5% more per hash than the base
(the 10% greedy hopper; 0.7% at 100%; a 60 s dwell turns the larger hoppers into losers, -4.0% at 100%). Under
Kaspa's rule it earns 0.4 to 0.8%, because D barely moves inside an hour and there is little to hop. Under 5%
in every cell, so hopping does not pay for the switching; but the Igneum figure is 0.7 points above Kaspa's in
every greedy cell on every seed, which fails the letter of the criterion. It is not the ease clamp: with the
ease clamp at 6% or 3% instead of 10% the greedy hopper still earns +1.5% at 10% and +0.8 to +0.9% at 50%
(`results.md`, "ease clamp against the hopper", seed 7). The excess is the price of a controller that moves
inside the hour at all: a hopper with a 1% band around the mean skims every swing, and Kaspa's rule gives it
less only because its D does not react to the hopper within the hour (the pulse row is the same fact from the
other side). No rule change is proposed for it; a 60 s minimum dwell, which any real pool switch has, already
turns the 50% and 100% hoppers into losers (-1.7% and -4.0%).
2. Pulsed rental. The finality concern (M14) is that bursts buy blocks, and therefore vote weight, at better than
the hash-time formula. Under Igneum the pulser mines at 50x difficulty within 130 blocks of each burst and gets
23% of the blocks for 89% of the hashes: weight per hash 0.26 of the base's, 3.7% of the base's blocks per
hash. Under Kaspa's rule the burst runs at the old difficulty for most of its 10 minutes and the pulser gets
88% of the blocks for 89% of the hashes: weight per hash 0.98, 85% of the base's blocks per hash, so renting
in bursts costs about what steady mining costs. A single burst (period 10^6) gives 0.13 against 0.87. R3.1's
"2x the formula" does not appear in either rule: the amplifier Kaspa's rule gives is that the pulse is cheap,
not that it is over-paid. The collateral under Igneum is the step-down after each burst: the base's blocks per
hash fall 37% over the hour and the worst gap is 153 s (Kaspa's rule: 103 s, and 1,734 blocks in the peak
minute against 184). Pass on the criterion the attack is about; the hangover is the known step-down cost of
spec 2.3.
3. Timestamp stretching. FAIL on every Igneum cell. See the next section.
4. Short-lane oscillation. The std of the rate ratio rises from 0.045 to 0.160 under Igneum (3.6x the steady
value) and from 0.010 to 0.147 under Kaspa's rule (16x). Neither is controller oscillation: the attacker's own
hash rate is a square wave, and a controller that held D at the mean would show std 0.143 (the `std_floor`
column). Igneum sits 12% above that floor, Kaspa's rule 3%. The oscillator earns 1.5% less per hash than the
base under Igneum and the same as the base under Kaspa's. By the letter of the criterion both rules fail; no past-only
controller can pass it against a 25% square wave, so no rule change is proposed. Worst gap 11.0 s against 8.8 s
steady.
5. Epoch-boundary games. The hold dodger earns the same per hash as the base (0.0%, the hold blocks are mined at
the parent's target, which is right for the base). The flooders, 10x and 30% on only for the 8 hold blocks, earn
+0.7% and +0.3% (worst seeds +2.4% and +2.1%): the 8 fast blocks make the epoch lane harden the next few blocks
for the stay-behinds, which is the flooder's whole margin. The first run's +13% was block-count noise on 48
blocks and vanishes under the expected-gap estimator. Pass.
6. Polluted window under adversarial timing. Leaving exactly as the long lane takes over (block 600) settles in
303 s with a 17 s worst gap and 55 blocks below half rate (292 s when the miner joined at block 480, so the
short lane was engaged at the switch); leaving at block 1,200 of the same epoch settles in 334 s. The lane
switch is not a weak point: pass. Kaspa's rule takes 2,910 to 3,540 s to settle the same leave (and never
settles the join); its 0 s for the 480 to 600 case is the dead zone (D never moved, so there was nothing to
settle).
## The failure: timestamp stretching
Mechanism. Spec 2.3 says "a forged timestamp can move one capped solvetime by at most 20 s in either direction
and the next honest block's solvetime cancels it under the symmetric cap". The cancellation is real and it is
the problem: a forged block at clock + 132 s contributes a clamped +20 s and the honest block after it, whose
stamp is 131 s behind its parent's, contributes a clamped -20 s. The pair sums to zero while two real block
intervals passed. Every run of forged blocks removes two intervals from the measured time, so with a forger at
share a the lanes measure 1 - 2a(1 - a) of real time: 58% at 30%, 50% at 50%. The estimator reads that as more
hash rate, the short lane disagrees with the robust long lane by more than 25% for as long as the forging lasts
and therefore rules, and the target hardens until the block rate matches the shortened clock. Stamping at the
earliest allowed time is worse, because the forger's own stamps enter the past-median window and drag the floor
down (the measured offsets grow from -135 s to -2,100 s at 50% over 4 hours): -58% at 30%, -88% at 50%, worst
gaps of 234 s. Kaspa's rule measures the span between the earliest and latest of 661 samples, so the same
forging only stretches one end of a 2,644 s window: +5% to +11% easing.
Test network (3 `igneumd` nodes from `diff-attacks`, genesis bits `0x1f010000`, honest miner A on node 1 for
15 minutes, forger F on node 2 honest for the first 5 minutes then on node 3 with the offset; two 4-thread CPU
miners, about 50% each; the shared Mac at load 15 to 30):
| Run (15 min, forging from 300 s) | Phase | Chain blocks/s | Mean difficulty | Forger share | Forger stamp offset | Delivered hash (miner summaries) |
|---|---|---|---|---|---|---|
| Igneum, earliest allowed stamp (`testnet/ts-past-igneum.csv`, 517 blocks, 437 chain) | honest 0 to 300 s | 0.97 | 91,375 | 0.49 | +2 s | A 0.078 MH/s over the run, F 0.069 MH/s over its forging leg |
| | forging 300 to 900 s | 0.24 | 275,135 | 0.53 | -322 s (from -121 s at 300 s to -566 s at 870 s: the past median follows the forger down) | same |
| | last 300 s | 0.20 | 341,191 | 0.59 | -471 s | same |
| Igneum, latest allowed stamp (`testnet/ts-future-igneum.csv`, 767 blocks, 649 chain) | honest 0 to 300 s | 0.98 | 89,363 | 0.51 | +3 s | A 0.112 MH/s, F 0.110 MH/s |
| | forging 300 to 900 s | 0.59 | 170,222 | 0.52 | +134 s | same |
| | last 300 s | 0.50 | 191,259 | 0.50 | +135 s | same |
| Kaspa's rule, earliest allowed stamp (`testnet/ts-past-kaspa.csv`, 1,454 blocks, 1,134 chain) | 0 to 300 s (genesis held to block 600 at 210 s, then 84,000) | 1.73 | 41,405 | 0.52 | +1 s | F 0.106 MH/s (A's summary line was cut by the stop) |
| | forging 300 to 900 s | 1.02 | 83,429 | 0.51 | -173 s | same |
| | last 300 s | 0.96 | 83,427 | 0.53 | -180 s | same |
The offsets are the forger's header stamps against the honest miner's clock (every chain block placed at the stamp
of the nearest earlier block of miner A, whose node has the real clock). The first future-stamp run
(`/tmp/igneum-diff-attacks/ts-future-igneum`, not archived) was contaminated for 40 s by a mis-timed start of
the next run's honest miner and was repeated; it showed the same halving (0.5 to 0.6 blocks/s at 1.7x
difficulty).
Both runs reproduce the simulator's direction and size: the block rate falls to a fifth within four minutes of
past-stamping and difficulty climbs 3x on an unchanged hash rate (the simulator's 50% past case: rate 0.12,
difficulty 9.9x after hours); future-stamping halves the rate at 1.7x difficulty (simulator: 0.56 and 1.8x).
Kaspa's rule on the same genesis and schedule retargeted once at block 600 (210 s, the genesis was 2.5x too
easy for the two miners) and then held 83,400 through ten minutes of past-stamping at 1.0 block/s: its window
of 661 samples still reached back to genesis, so the forger's -180 s stamps moved one end of a 900 s span.
## Proposed rule change (not applied; a diff for the consensus-engineer)
Two parts, and both are needed. The simulator shows each alone is not enough (`results.md`, "tight rules
alone": the unchanged controller under the tight rules still loses 35% at 30% past-stamping, because a run of
forged blocks stays inside the per-step clamp while the honest pay-back after it does not; "clock alone": the
sanitised clock under Kaspa's 132 s rules still fails at 50%, because with a forgery range larger than the cap
the clock's lag is a martingale at a 50% share).
Part A, the timestamp rules. Bound the forgery range to half the solvetime cap in both directions, so that a
forged step and its pay-back both fit inside the cap:
```diff
--- a/docs/spec/02-consensus.md (section 2.3, parameter table and the paragraph after it)
-| Timestamp rules | 132 s future tolerance in isolation, strictly above the sampled past median in context | Kaspa's, unchanged | Designed |
+| Timestamp rules | 10 s future tolerance in isolation (`FUTURE_TOLERANCE_MS`); in context strictly above the sampled past median (Kaspa's window, unchanged) and at least the selected parent's timestamp minus 10 s (`BACK_TOLERANCE_MS`) | Measured: a 50% forger drifts the rate +0.2% with both bounds at 10 s and the clock below, -38% with the parent bound alone, -83% with Kaspa's bounds (`sim/difficulty/attacks/`) | Measured |
-What the clamps and caps bound. A forged timestamp can move one capped solvetime by at most 20 s in either direction and the next honest block's solvetime cancels it under the symmetric cap (a run of L forged blocks nets L - 1 s of real time), so a minority cannot bias a lane by more than a few percent; ...
+What the clamps and caps bound. A forged timestamp moves the sanitised clock by at most 20 s and the honest blocks after it move the clock back to real time, so the sum of steps over any lane telescopes to the real span up to one step at each end; the timestamp rules keep every forgery inside 10 s, half the cap, so the pay-back fits in one step and a 50% forger cannot hold the clock away from real time (measured: +0.2% rate drift at 50% past-stamping, +0.9% future, `sim/difficulty/attacks/README.md`); ...
```
```diff
--- a/consensus/core/src/igneum.rs (module difficulty)
+ /// A header may be at most this far ahead of the node's clock (Igneum's own bound; Kaspa's 132 s
+ /// `TIMESTAMP_DEVIATION_TOLERANCE` stays as the size of the past-median window only)
+ pub const FUTURE_TOLERANCE_MS: u64 = 10_000;
+ /// A header may be at most this far behind its selected parent
+ pub const BACK_TOLERANCE_MS: u64 = 10_000;
--- a/consensus/src/pipeline/header_processor/pre_ghostdag_validation.rs
fn check_block_timestamp_in_isolation(&self, header: &Header) -> BlockProcessResult<()> {
- let max_block_time = unix_now() + self.timestamp_deviation_tolerance * 1000;
+ let max_block_time = unix_now() + igp::FUTURE_TOLERANCE_MS;
--- a/consensus/src/pipeline/header_processor/post_pow_validation.rs
pub fn check_median_timestamp(&self, ctx: &mut HeaderProcessingContext, header: &Header) -> BlockProcessResult<()> {
let (past_median_time, window) = self.window_manager.calc_past_median_time(ctx.ghostdag_data())?;
ctx.block_window_for_past_median_time = Some(window);
- if header.timestamp <= past_median_time {
- return Err(RuleError::TimeTooOld(header.timestamp, past_median_time));
+ let parent_time = self.headers_store.get_timestamp(ctx.ghostdag_data().selected_parent).unwrap();
+ let floor = past_median_time.max(parent_time.saturating_sub(igp::BACK_TOLERANCE_MS + 1));
+ if header.timestamp <= floor {
+ return Err(RuleError::TimeTooOld(header.timestamp, floor));
}
```
The past-median window keeps Kaspa's 27 samples (`MEDIAN_TIME_SAMPLED_WINDOW_SIZE` is derived from the 132 s
constant, which is why the future bound is a new constant and not a change to `TIMESTAMP_DEVIATION_TOLERANCE`).
The template builder's floor (`min_block_time`) must use the same `floor`. 10 s is tied to the 20 T cap: the
constraint is range <= CAP / 2 in both directions; a 20 s range would need a 40 T cap, which the base measurements
rejected for the idle-gap over-ease. Honest clocks within 10 s is what NTP gives; a miner whose clock is further
out has its blocks rejected until it fixes it, as with Kaspa's 132 s today.
Part B, the controller. Measure every chain step on a sanitised running clock instead of the raw parent stamp,
so that a forgery is paid back by the honest blocks after it instead of being cancelled to zero measured time:
```diff
--- a/docs/spec/02-consensus.md (section 2.3, rule 1)
-1. Every lane estimates the hash rate as work over time (blue-work increment over clamped solvetime), never as average target times average solvetime.
+1. Every lane estimates the hash rate as work over time (blue-work increment over the step of a sanitised clock), never as average target times average solvetime. The clock: c(genesis) = t(genesis); c(b) = max(c(p) + clamp(t(b) - c(p), -20 T, +20 T), t(b) - 60 T) for selected parent p; the step of b is min(c(b) - c(p), 20 T). The steps of a lane sum to the clock's span over it, so a forged stamp is paid back by the honest blocks after it; the 60 T bound keeps an honest idle gap from being paid back as cap-sized steps for many blocks (measured: without it the polluted case peaks at 275x, with it 11.4x against 8.0x today). The long lane keeps the raw sampled span.
```
```diff
--- a/consensus/src/processes/difficulty.rs (igneum_difficulty_bits, the chain walk)
- let solvetime = (cur_data.timestamp as i64 - parent_data.timestamp as i64).clamp(-cap, cap);
+ let solvetime = (clock(cur) as i64 - clock(parent) as i64).min(cap);
```
where `clock(b)` is the sanitised clock, stored per header beside blue work (a one-step recurrence along the
selected chain: `clock(b) = max(clock(p) + clamp(t(b) - clock(p), -cap, cap), t(b) - 3 * cap)`, computed at
header processing where `blue_work` is), so the walk needs no anchor. Walking it instead from the oldest
collected block's raw stamp works only with a margin of a few extra steps and is not recommended at 50%. In the
simulator the change is `IgneumSan` in `attacks.py` (`push`: the clock; `rate_s`: the steps), 25 lines.
What the change does to the base profiles (3 seeds, `results.md`, "base profiles"): up50, epoch30, walk10 and
hop10 unchanged to the second; down50 762 s against 782 s; warm-up from 10x too hard 327 s against 381 s;
polluted peak 11.4x against 8.0x; steady std unchanged. The attacks of scenarios 1, 2, 4, 5 and 6 under the
candidate are identical to the unchanged rule to three decimals (`results.md`, full suite, rows `igneum-san`),
as they must be: with honest stamps the sanitised clock is the raw clock. Under Kaspa's 132 s rules the candidate
alone is worse than the unchanged rule against a forger (rate 0.09 at 30% future-stamping), which is the
martingale argument above in numbers: the clock is only safe once the forgery range is below half the cap.
The timestamp attack under the candidate, both parts applied (3 seeds):
| Rule | Timestamp rules | Share | Stamp | Forger offset s | Rate after 1 h (drift) | Worst seed | Mean D ratio | Worst gap s |
|---|---|---|---|---|---|---|---|---|
| igneum (unchanged) | tight | 30 | future | 10 | 1.008 (+0.8%) | +1.8% | 1.00 | 9.7 |
| igneum (unchanged) | tight | 30 | past | -17 | 0.636 (-36.4%) | -38.1% | 1.60 | 32.5 |
| igneum (unchanged) | tight | 30 | alt | 1 | 0.975 (-2.5%) | -3.5% | 1.03 | 10.7 |
| igneum (unchanged) | tight | 50 | future | 10 | 1.009 (+0.9%) | +2.1% | 1.00 | 9.8 |
| igneum (unchanged) | tight | 50 | past | -30 | 0.170 (-83.0%) | -85.0% | 5.92 | 106.0 |
| igneum (unchanged) | tight | 50 | alt | 2 | 0.949 (-5.1%) | -5.7% | 1.06 | 11.6 |
| igneum-san (candidate) | tight | 30 | future | 10 | 1.008 (+0.8%) | +1.8% | 1.00 | 9.7 |
| igneum-san (candidate) | tight | 30 | past | -16 | 1.008 (+0.8%) | +2.4% | 1.00 | 9.9 |
| igneum-san (candidate) | tight | 30 | alt | 1 | 1.004 (+0.4%) | +1.2% | 1.00 | 9.8 |
| igneum-san (candidate) | tight | 50 | future | 10 | 1.009 (+0.9%) | +2.1% | 1.00 | 9.8 |
| igneum-san (candidate) | tight | 50 | past | -22 | 1.007 (+0.7%) | +2.7% | 1.00 | 10.1 |
| igneum-san (candidate) | tight | 50 | alt | 2 | 1.011 (+1.1%) | +2.2% | 1.00 | 10.0 |
| kaspa | tight | 30 to 50 | all | | 1.000 to 1.009 | +1.5% | 1.00 | 9.2 |
Every candidate cell is inside 3% on the worst seed; the unchanged rule under the tight rules alone still loses
36% and 83% to past-stamping; Kaspa's rule under the tight rules is flat. The candidate under Kaspa's 132 s
rules (`results.md`, "clock alone") still collapses at 50%, which is why Part A is not optional. A 60 s lag
bound was chosen over 120 s because the polluted peak is 11.4x against 17.8x and the forger results are the
same (`results.md`, "lag bound").
## Scenario 7: the flood panic (side finding)
Another agent's pump harness fed the `difficulty` node about 85 blocks per second with wall-clock timestamps
(blocks that bypass proof of work; `docs/bench-log.md`, hash-rate decay entry) and the node panicked at
`consensus/src/processes/difficulty.rs:431`, `calc_work`: "Work should not exceed 2**192". Mechanism: the rule
hardens the target by 3% per block with no floor; at 12 ms per block the epoch and short lanes read a hash rate
85x the target's, the harden clamp binds on every block, and the target passes below 2^64 after 4,142 blocks
(49 s at that rate). `BlueWorkType` is 192 bits, so `calc_work` of the next header's bits (the parent's work
for the epoch lane, and the header's own blue work) cannot be represented and the node aborts. Under real
proof of work the flood cannot be sustained (every 23 blocks double the hashes needed, so the chain simply
stops), but a node must not panic on input it accepted, and `skip_proof_of_work` nodes and simpa accept it.
Reproduction, exact: `cargo test -p kaspa-consensus --lib igneum_flood -- --nocapture` on the `diff-attacks`
branch (`igneum_flood_at_85_blocks_per_second_drives_the_target_below_block_work_range`, a `should_panic` test
that drives `igneum_target` from the attack network's genesis bits `0x1f010000` with 12 ms steps and calls
`calc_work` on each output). Output: `target below 2^64 at block 4142 (epoch start 3600), bits 0x900fe5b`, then
the panic at line 431. FAIL.
Proposed fix, a floor on the target, the mirror of the existing `MAX_DIFFICULTY_TARGET` cap:
```diff
--- a/docs/spec/02-consensus.md (section 2.3, rule 4)
-4. The output may make the target fall (difficulty rise) by at most 3% per block and rise (difficulty fall) by at most 10% per block, relative to the selected parent's target, then is capped at `MAX_DIFFICULTY_TARGET`.
+4. The output may make the target fall (difficulty rise) by at most 3% per block and rise (difficulty fall) by at most 10% per block, relative to the selected parent's target, then is clamped to [`MIN_DIFFICULTY_TARGET`, `MAX_DIFFICULTY_TARGET`]. `MIN_DIFFICULTY_TARGET` = 2^128: 2^128 expected hashes per block is unreachable by any network (the whole Bitcoin network is near 2^69 hashes per second, approximate) and keeps every block's work under 2^128, so the 192-bit blue work cannot overflow in a century of blocks (measured: without the floor, 85 blocks per second underflows the work type after 4,142 blocks, `sim/difficulty/attacks/README.md` scenario 7).
--- a/consensus/core/src/igneum.rs (module difficulty)
+ /// Hardest target the rule may emit: 2^128 expected hashes per block (`MIN_DIFFICULTY_TARGET`)
+ pub const MIN_TARGET_BITS: u32 = 128;
--- a/consensus/src/processes/difficulty.rs (igneum_target)
let lo = parent * 100 / (100 + igp::HARDEN_PERCENT);
let hi = parent * (100 + igp::EASE_PERCENT) / 100;
- let out = candidate.max(lo).min(hi).min(max_target);
+ let min_target = Uint320::from_u64(1) << igp::MIN_TARGET_BITS;
+ let out = candidate.max(lo).min(hi).min(max_target).max(min_target);
```
and the same `.max(min_target)` on the last line of `kaspa_difficulty_bits`, which has the same hole 17 times
more slowly (its window shrinks the target 85x per 2,644 blocks at that rate). A test for the floor is the
flood test with the `should_panic` removed and `assert!(bits_target >= 2^128)` on every output.
## Limits
The simulator has one chain and no DAG, as the base simulator; a forger on a DAG also controls the timestamps of
its red and merged blocks, which the lanes ignore. The past median is modelled on the chain's own sampled
window. The test network's forger shares a loaded machine with the honest miner, so its share wanders between
30 and 70% from bin to bin. Kaspa's rule on the test network had not retargeted within 15 minutes of forging
(600-block dead zone from genesis), so the live Kaspa comparison is the dead zone itself, as on 3 October. The
candidate controller was run in the simulator only; the node change is a proposal.
## Runs
python3 attacks.py --rules igneum,igneum-san,kaspa --seeds 3 every scenario (about 20 min, 4 jobs)
python3 attacks.py --scenario ts --ts-rules tight --rules igneum,igneum-san,kaspa --seeds 3
python3 attacks.py --scenario none --base --rules igneum,igneum-san,kaspa --seeds 3
python3 testnet.py --rule igneum --scenario ts --ts-offset-ms -1000000000 --minutes 15 --out /tmp/igneum-diff-attacks/ts-past-igneum
python3 testnet.py --rule igneum --scenario ts --ts-offset-ms 130000 --minutes 15 --out /tmp/igneum-diff-attacks/ts-future-igneum
python3 testnet.py --rule kaspa --scenario ts --ts-offset-ms -1000000000 --minutes 15 --out /tmp/igneum-diff-attacks/ts-past-kaspa
python3 testnet.py --analyse /tmp/igneum-diff-attacks/ts-past-igneum

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#!/usr/bin/env python3
"""Adversarial runs against the Igneum difficulty rule (spec 2.3) and Kaspa's sampled DAA.
Builds on ../sim.py (the controllers are imported unchanged). Adds what an attacker needs that the base
simulator does not model: several miners with their own on/off strategies, attribution of each block to the
miner that found it (drawn by hash share at the moment of the solve), hashes spent per miner, and timestamp
forging that stays inside the consensus rules (header timestamp at most FTL = 132 s ahead of the clock, and
strictly above the sampled past median time: 27 samples at 10-block intervals, mean of the central 11, as
`SampledPastMedianTimeManager::calc_past_median_time` does it). Honest miners stamp real time, raised to the
past median plus one when the rule forces it.
Scenarios (README.md): hop (pool hopping for profit), pulse (50x bursts for 10 min every hour, and once),
ts (timestamp stretching), osc (short-lane oscillation), epoch (hold dodger and hold flooder), pollute (leave
as the long lane takes over). Every scenario runs for each rule named: igneum, kaspa, and the candidates
igneum-san (sanitised running clock, README.md), igneum-san10 (the same with a 10 T cap), igneum-sanflat
(the same with flat weights on the short lane).
Blocks per hash of a miner is the expected-gap estimator sum(1 / H_b) / sum(D_b / H_b) over the blocks it was
on for (H_b total hash rate, D_b expected hashes per block), which has no block-count noise; the realised
counts are kept where they matter (pulse block share).
python3 attacks.py every scenario, 3 seeds, igneum and kaspa
python3 attacks.py --scenario ts --rules igneum,igneum-san,kaspa
python3 attacks.py --base --rules igneum,igneum-san the base simulator's profiles through the candidates
"""
import argparse
import math
import os
import random
import sys
from multiprocessing import Pool
sys.path.insert(0, os.path.join(os.path.dirname(os.path.abspath(__file__)), ".."))
import sim as S # noqa: E402
T = S.T
EPOCH = S.EPOCH
ONE = S.ONE
SCALE = S.SCALE
H1 = S.H1
HOUR = 3600 * 1000
FTL_MS = 132 * 1000
PMT_SAMPLES = 27
PMT_INTERVAL = 10
PMT_CENTRE = 11
clamp = S.clamp
# ---------------------------------------------------------------- timestamp rules
def past_median_time(ts, h):
"""Past median time for the block at height h from the chain timestamps ts[0..h-1]:
27 samples at 10-block intervals ending at the parent, sorted, mean of the central 11."""
samp = [ts[j] for j in range(h - 1, -1, -PMT_INTERVAL)][:PMT_SAMPLES]
samp.sort()
n = len(samp)
if n <= PMT_CENTRE:
return sum(samp) // n
lo = (n - PMT_CENTRE) // 2
return sum(samp[lo:lo + PMT_CENTRE]) // PMT_CENTRE
class Rules:
"""Timestamp rules the forger must respect. Kaspa's: 132 s ahead of the clock, above the sampled past
median. The proposed tight rules (README.md): 10 s ahead of the clock, above the past median and at least the
selected parent's timestamp minus 10 s."""
def __init__(self, ftl_ms=FTL_MS, back_ms=None):
self.ftl_ms = ftl_ms
self.back_ms = back_ms
def bounds(self, ts, h, now):
lo = past_median_time(ts, h) + 1
if self.back_ms is not None:
lo = max(lo, ts[h - 1] - self.back_ms)
hi = now + self.ftl_ms
return lo, max(lo, hi)
TS_RULES = {"kaspa": lambda: Rules(), "tight": lambda: Rules(ftl_ms=10 * 1000, back_ms=10 * 1000)}
# ---------------------------------------------------------------- candidate controllers
class IgneumSan(S.Igneum):
"""Spec 2.3 with one change (README.md): every chain step's solvetime is measured on a sanitised running
clock. ts'(genesis) = ts(genesis); ts'(b) = ts'(parent) + clamp(ts(b) - ts'(parent), -cap, +cap). The short
and epoch lanes sum sanitised steps, which telescope to ts'(newest) - ts'(oldest), so a forged stamp is paid
back exactly by the honest blocks after it instead of being cancelled to zero measured time. The long lane
keeps the raw sampled span. `flat` drops the linear weights of the short lane; `cap` as in the spec."""
name = "igneum-san"
def __init__(self, g, flat=False, lag=0, snap_ms=60 * 1000, **kw):
super().__init__(g, **kw)
self.flat = flat
self.lag = lag
self.snap_ms = snap_ms
self.tss = []
self.sts = []
def push(self, ts, target):
h = len(self.ts)
if h == 0:
st, tss = 0, ts
else:
tss = self.tss[-1] + clamp(ts - self.tss[-1], -self.cap, self.cap)
if self.snap_ms is not None:
# the clock never lags a raw stamp by more than snap_ms (an honest idle gap must not be paid back
# as cap-sized steps for many blocks); the jump itself is not counted as solvetime. A backward
# forger would need a run of snap_ms / 10 s blocks under the tight rules to reach it.
tss = max(tss, ts - self.snap_ms)
st = min(tss - self.tss[-1], self.cap)
self.tss.append(tss)
self.sts.append(st)
S.Controller.push(self, ts, target)
self.pref_d.append(self.pref_d[-1] + ONE / target)
self.pref_t.append(self.pref_t[-1] + target)
self.pref_st.append(self.pref_st[-1] + st)
if h > 0 and h % self.rate == self.rate - 1:
self.samples.append((h, ts, self.pref_d[-1]))
if len(self.samples) > self.window:
self.samples.popleft()
def rate_s(self, lo, hi):
n = hi - lo - 1
if n < 1:
return None
wsum = 0.0
dsum = 0.0
for i in range(1, n + 1):
j = lo + i
w = 1 if self.flat else i
wsum += self.sts[j] * w
dsum += (self.pref_d[j + 1] - self.pref_d[j]) * w
wsum = max(wsum, (n * T / 10) if self.flat else (n * n * T / 20))
return dsum / wsum
def next_target(self):
"""As the spec, with the newest `lag` chain steps left out of the short and epoch lanes."""
if self.lag == 0:
return super().next_target()
h = len(self.ts)
parent = self.tg[-1]
epoch_start = (h // EPOCH) * EPOCH
k = h - epoch_start
if k < self.k_min:
return parent
hh = max(h - self.lag, epoch_start + 2)
s_lo = max(epoch_start, hh - self.ns)
r_s = self.rate_s(s_lo, hh)
r_ref = None
if k >= self.long_min:
r_ref = self.rate_l(max(epoch_start, h - self.window * self.rate))
if r_ref is None:
r_ref = self.rate_e(epoch_start, hh, hh - epoch_start)
if r_s is None:
cand = parent
else:
use_s = abs(r_s / r_ref - 1) > self.trig
self.engaged += 1 if use_s else 0
cand = ONE / ((r_s if use_s else r_ref) * T)
out = clamp(cand, parent / (1 + self.clamp_pct), parent * (1 + self.ease_pct))
return min(out, ONE)
_orig_make = S.make_controller
def make_controller(name, g, **kw):
if name == "igneum-san":
return IgneumSan(g, **kw)
if name == "igneum-san-nosnap":
return IgneumSan(g, snap_ms=None, **kw)
if name.startswith("igneum-ease"): # igneum-ease<percent>: the spec rule with another ease clamp
return S.Igneum(g, ease_pct=int(name[len("igneum-ease"):]) / 100.0, **kw)
if name == "igneum-san-j120":
return IgneumSan(g, snap_ms=120 * 1000, **kw)
if name == "igneum-san10":
return IgneumSan(g, cap=10 * T, **kw)
if name == "igneum-sanflat":
return IgneumSan(g, flat=True, **kw)
if name.startswith("igneum-san-"): # igneum-san-<flat|lwma>-lag<n>-cap<n>
parts = name.split("-")[2:]
flat = parts[0] == "flat"
lag = int(parts[1][3:]) if len(parts) > 1 else 0
cap = int(parts[2][3:]) * T if len(parts) > 2 else 20 * T
return IgneumSan(g, flat=flat, lag=lag, cap=cap, **kw)
return _orig_make(name, g, **kw)
S.make_controller = make_controller
def make(rule, genesis_d):
return make_controller(rule, ONE / genesis_d)
# ---------------------------------------------------------------- miners
class Miner:
"""hash in units of H1 (the hash rate that gives 1 block/s at D = SCALE). policy(state) -> on for the next
block (evaluated at block boundaries); gate(t) -> on at time t and schedule(t) -> next gate change, for
time-keyed bursts; stamp: honest | future | past | alt (future and past on alternate blocks)."""
def __init__(self, name, hash_h1, policy=None, stamp="honest", start_ms=0):
self.name = name
self.hash = hash_h1 * H1
self.policy = policy or (lambda st: st["t"] >= self.start_ms)
self.gate = None
self.schedule = None
self.stamp = stamp
self.start_ms = start_ms
self.hashes = 0.0
self.blocks = 0
self.exp_blocks = 0.0
self.on = False
self.last_switch = -1e18
self.flip = 0
def live(self, t):
return self.on and t >= self.start_ms and (self.gate is None or self.gate(t))
def stamp_for(self, t, lo, hi):
if self.stamp == "future":
return hi
if self.stamp == "past":
return lo
if self.stamp == "alt":
self.flip ^= 1
return hi if self.flip else lo
return max(int(t), lo)
class AvgD:
"""Trailing time-weighted mean of D over the last 6 hours (the hopper's long-run average)."""
def __init__(self, span_ms=6 * HOUR):
self.span = span_ms
self.q = []
self.sum = 0.0
self.wsum = 0.0
self.i = 0
def add(self, t, D, dt):
self.q.append((t, D, dt))
self.sum += D * dt
self.wsum += dt
while self.i < len(self.q) and self.q[self.i][0] < t - self.span:
_, d, w = self.q[self.i]
self.sum -= d * w
self.wsum -= w
self.i += 1
def value(self, default):
return self.sum / self.wsum if self.wsum > 0 else default
def run(miners, ctrl, rng, duration_ms, genesis_d, rules=None, log=None):
"""Mine duration_ms of chain. Rows: (t, h, D, H, r, finder, active names)."""
rules = rules or Rules()
t = 0.0
target = ONE / genesis_d
ctrl.push(0, target)
h = 1
rows = []
avg = AvgD()
st = {"t": 0.0, "h": 1, "D": genesis_d, "avgD": genesis_d, "k": 1}
while t < duration_ms:
target = ctrl.next_target()
D = ONE / target
st.update(t=t, h=h, D=D, k=h % EPOCH, avgD=avg.value(genesis_d))
for m in miners:
want = bool(m.policy(st))
if want != m.on:
m.on = want
m.last_switch = t
work = rng.expovariate(1.0) * D
tt = t
while True:
live = [m for m in miners if m.live(tt)]
hr = sum(m.hash for m in live)
nxt = None
for m in miners:
for x in ([m.start_ms] if m.start_ms > tt else []) + ([m.schedule(tt)] if m.schedule else []):
if x is not None and x > tt and (nxt is None or x < nxt):
nxt = x
if hr > 0 and (nxt is None or work <= hr * (nxt - tt)):
dt = work / hr
for m in live:
m.hashes += m.hash * dt
tt += dt
break
if nxt is None:
tt = duration_ms + 1
break
dt = nxt - tt
for m in live:
m.hashes += m.hash * dt
work -= hr * dt
tt = nxt
if tt > duration_ms:
break
gap = max(tt - t, 1.0)
t += gap
live = [m for m in miners if m.live(t)]
tot = sum(m.hash for m in live)
u = rng.random() * tot
finder = live[-1]
acc = 0.0
for m in live:
acc += m.hash
if u <= acc:
finder = m
break
for m in live:
m.exp_blocks += m.hash / tot
finder.blocks += 1
lo, hi = rules.bounds(ctrl.ts, h, int(t))
ts = min(max(finder.stamp_for(t, lo, hi), lo), hi)
ctrl.push(ts, target)
avg.add(t, D, gap)
rows.append((t, h, D, tot, tot * T / D, finder.name, tuple(m.name for m in live)))
if log is not None:
log.append((t, h, D, tot, finder.name, ts, int(t)))
h += 1
return rows
# ---------------------------------------------------------------- metrics
def bph(rows, name, t_from=0):
"""Expected blocks per hash of a miner over the blocks it was on for after t_from: sum(1/H) / sum(D/H)."""
num = den = 0.0
for r in rows:
if r[0] >= t_from and name in r[6]:
num += 1.0 / r[3]
den += r[2] / r[3]
return num / den if den > 0 else float("nan")
def on_frac(rows, name, t_from):
act = tot = 0.0
prev = None
for r in rows:
if prev is not None and r[0] >= t_from:
g = r[0] - prev
tot += g
if name in r[6]:
act += g
prev = r[0]
return act / tot if tot else 0.0
def rate_stats(rows, t_from, t_to):
seg = [r for r in rows if t_from <= r[0] < t_to]
if len(seg) < 10:
return None, None, None, None
rs = [r[4] for r in seg]
mean = sum(rs) / len(rs)
std = math.sqrt(sum((x - mean) ** 2 for x in rs) / len(rs))
gaps = [seg[i][0] - seg[i - 1][0] for i in range(1, len(seg))]
return mean, std, max(gaps) / 1000, len(seg) / ((t_to - t_from) / 1000)
def max_blocks_in(rows, t0, bin_ms):
bins = {}
for r in rows:
if r[0] >= t0:
b = int(r[0] // bin_ms)
bins[b] = bins.get(b, 0) + 1
return max(bins.values()) if bins else 0
# ---------------------------------------------------------------- scenarios
def scen_hop(rule, seed, x_pct, dwell_s=0, hours=24):
"""Pool hopper with x% of the honest base, on only while D is below its trailing 6-hour mean (1% band),
base constant. Starts at hour 2; measured from hour 3."""
rng = random.Random(seed)
base = Miner("base", 1.0)
band = 0.01
def policy(st):
m = hopper
if st["t"] < m.start_ms:
return False
if st["t"] - m.last_switch < dwell_s * 1000:
return m.on
if m.on:
return st["D"] <= st["avgD"] * (1 + band)
return st["D"] < st["avgD"] * (1 - band)
hopper = Miner("hopper", x_pct / 100.0, policy=policy, start_ms=2 * HOUR)
rows = run([base, hopper], make(rule, SCALE), rng, hours * HOUR, SCALE)
t0 = 3 * HOUR
switches = 0
on = False
for r in rows:
if r[0] >= t0 and ("hopper" in r[6]) != on:
switches += 1
on = not on
_, std, gap, bps = rate_stats(rows, t0, rows[-1][0])
return {"rule": rule, "seed": seed, "x": x_pct, "dwell": dwell_s, "adv": bph(rows, "hopper", t0) / bph(rows, "base", t0) - 1,
"hop_on_frac": on_frac(rows, "hopper", t0), "switches": switches, "std": std, "worst_gap": gap, "blocks_per_s": bps}
def scen_pulse(rule, seed, mult=50.0, burst_s=600, period_s=3600, hours=8):
"""A rented burst of mult x the base for burst_s every period_s from hour 2 (period_s >= hours*3600: once)."""
rng = random.Random(seed)
base = Miner("base", 1.0)
pulser = Miner("pulser", mult, start_ms=2 * HOUR)
P = period_s * 1000
B = burst_s * 1000
s0 = pulser.start_ms
pulser.gate = lambda t: t >= s0 and ((t - s0) % P) < B
pulser.schedule = lambda t: s0 if t < s0 else s0 + ((t - s0) // P) * P + (B if ((t - s0) % P) < B else P)
rows = run([base, pulser], make(rule, SCALE), rng, hours * HOUR, SCALE)
t0 = 2 * HOUR
seg = [r for r in rows if r[0] >= t0]
b_base = bph(rows, "base", t0)
b_pulse = bph(rows, "pulser", t0)
steady = bph([r for r in rows if HOUR <= r[0] < 2 * HOUR], "base")
share_blocks = sum(1 for r in seg if r[5] == "pulser") / len(seg)
share_hash = pulser.hashes / (pulser.hashes + sum(base.hash * (seg[i][0] - seg[i - 1][0]) for i in range(1, len(seg))))
_, std, gap, bps = rate_stats(rows, t0, rows[-1][0])
return {"rule": rule, "seed": seed, "period_s": period_s, "pulse_vs_base": b_pulse / b_base - 1, "pulse_vs_steady": b_pulse / steady - 1,
"base_vs_steady": b_base / steady - 1, "weight_per_hash": share_blocks / share_hash, "pulse_block_share": share_blocks,
"pulse_hash_share": share_hash, "peak_blocks_per_min": max_blocks_in(rows, t0, 60000), "worst_gap": gap, "blocks_per_s": bps}
def scen_ts(rule, seed, share_pct, stamp, hours=6, rules="kaspa"):
"""A miner with share_pct of the total hash rate stamping every block at the latest allowed future offset
(future), the earliest allowed (past) or alternating (alt) from hour 2; honest for the first 2 hours. Base
honest and constant; genesis sized for both."""
rng = random.Random(seed)
a = share_pct / (100.0 - share_pct)
base = Miner("base", 1.0)
att = Miner("forger", a)
gd = SCALE * (1 + a)
orig = att.stamp_for
def stamp_for(t, lo, hi):
if t < 2 * HOUR:
return max(int(t), lo)
att.stamp = stamp
return orig(t, lo, hi)
att.stamp_for = stamp_for
log = []
rows = run([base, att], make(rule, gd), rng, hours * HOUR, gd, TS_RULES[rules](), log)
pre = rate_stats(rows, 1 * HOUR, 2 * HOUR)
post = rate_stats(rows, 3 * HOUR, hours * HOUR)
tail = rate_stats(rows, (hours - 1) * HOUR, hours * HOUR)
seg = [r for r in rows if r[0] >= 3 * HOUR]
mean_D = sum(r[2] for r in seg) / len(seg) if seg else float("nan")
offs = [l[5] - l[6] for l in log if l[0] >= 3 * HOUR and l[4] == "forger"]
return {"rule": rule, "seed": seed, "ts_rules": rules, "share": share_pct, "stamp": stamp, "forger_offset_s": (sum(offs) / len(offs) / 1000) if offs else 0.0,
"rate_pre": pre[3], "rate_post": post[3], "rate_last_hour": tail[3], "drift": post[3] - 1.0, "D_ratio": mean_D / gd,
"std": post[1], "worst_gap": post[2], "forger_adv": bph(rows, "forger", 3 * HOUR) / bph(rows, "base", 3 * HOUR) - 1}
def scen_osc(rule, seed, share_pct=25, period_blocks=120, hours=6):
"""A miner of share_pct of the full hash rate on and off every period_blocks from hour 2."""
rng = random.Random(seed)
a = share_pct / (100.0 - share_pct)
base = Miner("base", 1.0)
osc = Miner("osc", a, start_ms=2 * HOUR)
osc.policy = lambda st: st["t"] >= 2 * HOUR and ((st["h"] // period_blocks) % 2 == 0)
rows = run([base, osc], make(rule, SCALE), rng, hours * HOUR, SCALE)
pre = rate_stats(rows, 1 * HOUR, 2 * HOUR)
post = rate_stats(rows, 3 * HOUR, hours * HOUR)
t0 = 3 * HOUR
seg = [r for r in rows if r[0] >= t0]
hrs = [r[3] for r in seg]
mh = sum(hrs) / len(hrs)
floor = math.sqrt(sum((x / mh - 1) ** 2 for x in hrs) / len(hrs))
return {"rule": rule, "seed": seed, "share": share_pct, "period": period_blocks, "std_pre": pre[1], "std_post": post[1],
"std_ratio": post[1] / pre[1], "std_floor": floor, "worst_gap_pre": pre[2], "worst_gap_post": post[2],
"blocks_per_s": post[3], "osc_adv": bph(rows, "osc", t0) / bph(rows, "base", t0) - 1}
def scen_epoch(rule, seed, kind, share_pct=30, hours=8):
"""Epoch-boundary games from hour 2. dodge: a share_pct miner is off for the 8 hold blocks of each epoch.
flood: a 10x miner is on only for the hold blocks. flood30: a share_pct miner on only for the hold blocks."""
rng = random.Random(seed)
a = share_pct / (100.0 - share_pct)
base = Miner("base", 1.0)
if kind == "dodge":
g = Miner("gamer", a, start_ms=2 * HOUR)
g.policy = lambda st: st["t"] >= 2 * HOUR and st["k"] >= 8
gd = SCALE * (1 + a)
elif kind == "flood":
g = Miner("gamer", 10.0, start_ms=2 * HOUR)
g.policy = lambda st: st["t"] >= 2 * HOUR and st["k"] < 8
gd = SCALE
elif kind == "flood30":
g = Miner("gamer", a, start_ms=2 * HOUR)
g.policy = lambda st: st["t"] >= 2 * HOUR and st["k"] < 8
gd = SCALE
else:
raise ValueError(kind)
rows = run([base, g], make(rule, gd), rng, hours * HOUR, gd)
t0 = 3 * HOUR
post = rate_stats(rows, t0, hours * HOUR)
return {"rule": rule, "seed": seed, "kind": kind, "gamer_adv": bph(rows, "gamer", t0) / bph(rows, "base", t0) - 1,
"gamer_on_frac": on_frac(rows, "gamer", t0), "std": post[1], "worst_gap": post[2], "blocks_per_s": post[3]}
def scen_pollute(rule, seed, mult=10.0, join_k=0, leave_k=600, hours=4):
"""A mult x miner joins at block join_k of epoch 2 and leaves at block leave_k of the same epoch (600 is where
the reference lane switches from the epoch window to the sampled long lane)."""
rng = random.Random(seed)
base = Miner("base", 1.0)
big = Miner("big", mult)
e = 2 * EPOCH
big.policy = lambda st: e + join_k <= st["h"] < e + leave_k
rows = run([base, big], make(rule, SCALE), rng, hours * HOUR, SCALE)
t_join = next((r[0] for r in rows if r[1] >= e + join_k), None)
t_leave = next((r[0] for r in rows if r[1] >= e + leave_k), None)
blocks = [r[:5] for r in rows]
m_leave = S.metrics(blocks, None, t_step=t_leave) if t_leave else {}
m_join = S.metrics(blocks, None, t_step=t_join, t_end=t_leave) if t_join else {}
return {"rule": rule, "seed": seed, "mult": mult, "join_k": join_k, "leave_k": leave_k,
"join_first10_s": m_join.get("first10_s"), "join_settled_s": m_join.get("recover_s"),
"leave_first10_s": m_leave.get("first10_s"), "leave_settled_s": m_leave.get("recover_s"),
"leave_worst_gap_s": m_leave.get("worst_gap_s"), "leave_below05": m_leave.get("below05"), "leave_above2x": m_leave.get("above2x")}
def base_profiles(rule, seed):
"""The base simulator's synthetic profiles through one controller (its own metrics)."""
out = []
for p in S.synthetic_profiles(seed):
if p.name in ("up50", "down50", "epoch30", "walk10", "hop10", "polluted", "warmup-hard"):
r = S.run_profile(p, [rule], seed, 0)[0]
out.append({"rule": rule, "seed": seed, "profile": p.name, "first10_s": r.get("first10_s"), "settled_s": r.get("recover_s"),
"worst_gap_s": r.get("worst_gap_s") or r.get("ss_worst_gap_s"), "steady_std": r.get("ss_std"),
"peak_rate": r.get("peak_rate"), "not_recovered": r.get("recover_fail")})
return out
# ---------------------------------------------------------------- driver
def job(args):
fn, kw = args
return globals()[fn](**kw)
def fmt(x):
if x is None:
return "none"
if isinstance(x, float):
if math.isnan(x):
return "nan"
return ("%.3f" % x) if abs(x) < 10 else ("%.1f" % x)
return str(x)
def table(title, rows, cols):
print("\n### " + title + "\n")
print("| " + " | ".join(cols) + " |")
print("|" + "---|" * len(cols))
for r in rows:
print("| " + " | ".join(fmt(r.get(c)) for c in cols) + " |")
def mean_rows(rows, keys, worst=()):
groups = {}
for r in rows:
groups.setdefault(tuple(r[x] for x in keys), []).append(r)
out = []
for k, rs in groups.items():
m = dict(rs[0])
m["seeds"] = len(rs)
for f in rs[0]:
if f in keys or f == "seed":
continue
vals = [r[f] for r in rs if isinstance(r[f], (int, float)) and not (isinstance(r[f], float) and math.isnan(r[f]))]
if len(vals) == len(rs):
m[f] = sum(vals) / len(vals)
if f in worst:
m[f + "_worst"] = max(vals, key=abs)
else:
m[f] = None if not vals else sum(vals) / len(vals)
m[f + "_none"] = len(rs) - len(vals)
out.append(m)
return out
def main():
ap = argparse.ArgumentParser()
ap.add_argument("--scenario", default="all")
ap.add_argument("--seeds", type=int, default=3)
ap.add_argument("--rules", default="igneum,kaspa")
ap.add_argument("--base", action="store_true", help="also run the base simulator's profiles through each rule")
ap.add_argument("--jobs", type=int, default=4)
ap.add_argument("--hop-hours", type=int, default=24)
ap.add_argument("--ts-rules", default="kaspa", help="timestamp rules the forger obeys: kaspa or tight (README.md)")
args = ap.parse_args()
seeds = list(range(7, 7 + args.seeds))
rules = args.rules.split(",")
want = args.scenario.split(",") if args.scenario != "all" else ["hop", "pulse", "ts", "osc", "epoch", "pollute"]
jobs = []
for rule in rules:
for seed in seeds:
if "hop" in want:
for x in (10, 30, 50, 100):
for dwell in (0, 60):
jobs.append(("scen_hop", dict(rule=rule, seed=seed, x_pct=x, dwell_s=dwell, hours=args.hop_hours)))
if "pulse" in want:
jobs.append(("scen_pulse", dict(rule=rule, seed=seed)))
jobs.append(("scen_pulse", dict(rule=rule, seed=seed, period_s=10 ** 6, hours=4)))
if "ts" in want:
for share in (30, 50):
for stamp in ("future", "past", "alt"):
jobs.append(("scen_ts", dict(rule=rule, seed=seed, share_pct=share, stamp=stamp, rules=args.ts_rules)))
if "osc" in want:
jobs.append(("scen_osc", dict(rule=rule, seed=seed)))
if "epoch" in want:
for kind in ("dodge", "flood", "flood30"):
jobs.append(("scen_epoch", dict(rule=rule, seed=seed, kind=kind)))
if "pollute" in want:
for join_k, leave_k in ((0, 600), (480, 600), (480, 720), (0, 1200)):
jobs.append(("scen_pollute", dict(rule=rule, seed=seed, join_k=join_k, leave_k=leave_k)))
if args.base:
jobs.append(("base_profiles", dict(rule=rule, seed=seed)))
try:
os.nice(19)
except OSError:
pass
with Pool(args.jobs) as pool:
results = pool.map(job, jobs)
by = {}
for (fn, _), r in zip(jobs, results):
by.setdefault(fn, []).extend(r if isinstance(r, list) else [r])
print("# Difficulty attacks, seeds %s, rules %s\n" % (seeds, rules))
if "scen_hop" in by:
table("1. Pool hopping: hopper's blocks per hash against the always-on base (adv = ratio - 1), %d h" % args.hop_hours,
mean_rows(by["scen_hop"], ["rule", "x", "dwell"], worst=("adv",)),
["rule", "x", "dwell", "adv", "adv_worst", "hop_on_frac", "switches", "std", "worst_gap", "blocks_per_s", "seeds"])
if "scen_pulse" in by:
table("2. Pulsed hash rate: 50x for 10 min, every hour (period 3600) and once (period 1000000); weight_per_hash = block share / hash share",
mean_rows(by["scen_pulse"], ["rule", "period_s"], worst=("pulse_vs_base", "weight_per_hash")),
["rule", "period_s", "pulse_vs_base", "pulse_vs_base_worst", "weight_per_hash", "weight_per_hash_worst", "pulse_vs_steady", "base_vs_steady",
"pulse_block_share", "pulse_hash_share", "peak_blocks_per_min", "worst_gap", "blocks_per_s", "seeds"])
if "scen_ts" in by:
table("3. Timestamp stretching inside the rules: block rate after 1 h of forging (drift = rate - 1), 6 h runs",
mean_rows(by["scen_ts"], ["rule", "ts_rules", "share", "stamp"], worst=("drift",)),
["rule", "ts_rules", "share", "stamp", "forger_offset_s", "rate_pre", "rate_post", "rate_last_hour", "drift", "drift_worst", "D_ratio", "std", "worst_gap", "forger_adv", "seeds"])
if "scen_osc" in by:
table("4. Short-lane oscillation: 25% miner on and off every 120 blocks (std_floor = the hash square wave at a fixed D)",
mean_rows(by["scen_osc"], ["rule", "share", "period"], worst=("std_ratio",)),
["rule", "share", "period", "std_pre", "std_post", "std_ratio", "std_ratio_worst", "std_floor", "worst_gap_pre", "worst_gap_post", "blocks_per_s", "osc_adv", "seeds"])
if "scen_epoch" in by:
table("5. Epoch-boundary games: hold dodger (30%, off for blocks 0 to 7), hold flooder (10x, on for blocks 0 to 7), 30% flooder",
mean_rows(by["scen_epoch"], ["rule", "kind"], worst=("gamer_adv",)),
["rule", "kind", "gamer_adv", "gamer_adv_worst", "gamer_on_frac", "std", "worst_gap", "blocks_per_s", "seeds"])
if "scen_pollute" in by:
table("6. Polluted window under adversarial timing: 10x miner joins at block join_k of an epoch and leaves at leave_k (600 = long lane takes over)",
mean_rows(by["scen_pollute"], ["rule", "join_k", "leave_k"]),
["rule", "join_k", "leave_k", "join_first10_s", "join_settled_s", "leave_first10_s", "leave_settled_s", "leave_worst_gap_s", "leave_below05", "leave_above2x", "seeds"])
if "base_profiles" in by:
table("Base profiles (sim.py metrics) through each rule",
mean_rows(by["base_profiles"], ["rule", "profile"]),
["rule", "profile", "first10_s", "settled_s", "settled_s_none", "worst_gap_s", "steady_std", "peak_rate", "not_recovered", "seeds"])
if __name__ == "__main__":
main()

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# Raw simulator output behind README.md (4 October 2026)
Seeds 7, 8, 9 unless stated. Tables are attacks.py output; the candidate igneum-san is the sanitised clock with the 60 s lag bound (README.md, Part B) unless stated.
## Full suite, Kaspa's timestamp rules (the forger under 132 s and the past median)
# Difficulty attacks, seeds [7, 8, 9], rules ['igneum', 'igneum-san', 'kaspa']
### 1. Pool hopping: hopper's blocks per hash against the always-on base (adv = ratio - 1), 24 h
| rule | x | dwell | adv | adv_worst | hop_on_frac | switches | std | worst_gap | blocks_per_s | seeds |
|---|---|---|---|---|---|---|---|---|---|---|
| igneum | 10 | 0 | 0.015 | 0.015 | 0.432 | 301.0 | 0.072 | 12.7 | 0.998 | 3 |
| igneum | 10 | 60 | 0.013 | 0.014 | 0.437 | 227.0 | 0.072 | 12.6 | 0.998 | 3 |
| igneum | 30 | 0 | 0.010 | 0.011 | 0.216 | 492.0 | 0.135 | 12.8 | 0.994 | 3 |
| igneum | 30 | 60 | 0.001 | 0.003 | 0.283 | 394.0 | 0.140 | 13.9 | 0.992 | 3 |
| igneum | 50 | 0 | 0.009 | 0.010 | 0.149 | 616.7 | 0.197 | 13.8 | 0.992 | 3 |
| igneum | 50 | 60 | -0.017 | -0.022 | 0.283 | 544.7 | 0.211 | 13.8 | 0.984 | 3 |
| igneum | 100 | 0 | 0.007 | 0.007 | 0.085 | 741.0 | 0.339 | 13.3 | 0.990 | 3 |
| igneum | 100 | 60 | -0.040 | -0.054 | 0.378 | 818.0 | 0.349 | 16.9 | 0.968 | 3 |
| igneum-san | 10 | 0 | 0.015 | 0.015 | 0.432 | 301.0 | 0.072 | 12.7 | 0.998 | 3 |
| igneum-san | 10 | 60 | 0.013 | 0.014 | 0.437 | 227.0 | 0.072 | 12.6 | 0.998 | 3 |
| igneum-san | 30 | 0 | 0.010 | 0.011 | 0.216 | 492.0 | 0.135 | 12.8 | 0.994 | 3 |
| igneum-san | 30 | 60 | 0.001 | 0.003 | 0.283 | 394.0 | 0.140 | 13.9 | 0.992 | 3 |
| igneum-san | 50 | 0 | 0.009 | 0.010 | 0.149 | 616.7 | 0.197 | 13.8 | 0.992 | 3 |
| igneum-san | 50 | 60 | -0.017 | -0.022 | 0.283 | 544.7 | 0.211 | 13.8 | 0.984 | 3 |
| igneum-san | 100 | 0 | 0.007 | 0.007 | 0.085 | 741.0 | 0.339 | 13.3 | 0.990 | 3 |
| igneum-san | 100 | 60 | -0.040 | -0.054 | 0.378 | 818.0 | 0.349 | 16.9 | 0.968 | 3 |
| kaspa | 10 | 0 | 0.008 | 0.009 | 0.367 | 63.7 | 0.054 | 11.8 | 1.000 | 3 |
| kaspa | 10 | 60 | 0.008 | 0.009 | 0.367 | 63.7 | 0.054 | 11.8 | 1.000 | 3 |
| kaspa | 30 | 0 | 0.006 | 0.007 | 0.181 | 88.0 | 0.124 | 12.3 | 1.001 | 3 |
| kaspa | 30 | 60 | 0.006 | 0.007 | 0.181 | 88.0 | 0.124 | 12.3 | 1.001 | 3 |
| kaspa | 50 | 0 | 0.005 | 0.006 | 0.116 | 112.3 | 0.180 | 12.7 | 1.001 | 3 |
| kaspa | 50 | 60 | 0.005 | 0.006 | 0.115 | 111.3 | 0.179 | 12.6 | 1.001 | 3 |
| kaspa | 100 | 0 | 0.005 | 0.006 | 0.061 | 122.7 | 0.304 | 12.5 | 1.001 | 3 |
| kaspa | 100 | 60 | 0.004 | 0.005 | 0.068 | 132.0 | 0.315 | 12.5 | 1.001 | 3 |
### 2. Pulsed hash rate: 50x for 10 min, every hour (period 3600) and once (period 1000000); weight_per_hash = block share / hash share
| rule | period_s | pulse_vs_base | pulse_vs_base_worst | weight_per_hash | weight_per_hash_worst | pulse_vs_steady | base_vs_steady | pulse_block_share | pulse_hash_share | peak_blocks_per_min | worst_gap | blocks_per_s | seeds |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| igneum | 3600 | -0.963 | -0.964 | 0.263 | 0.267 | -0.977 | -0.375 | 0.234 | 0.893 | 183.7 | 152.5 | 0.824 | 3 |
| igneum | 1000000 | -0.971 | -0.972 | 0.131 | 0.138 | -0.976 | -0.186 | 0.106 | 0.806 | 177.0 | 81.3 | 0.920 | 3 |
| igneum-san | 3600 | -0.964 | -0.965 | 0.262 | 0.267 | -0.977 | -0.362 | 0.234 | 0.893 | 182.3 | 221.4 | 0.823 | 3 |
| igneum-san | 1000000 | -0.971 | -0.972 | 0.130 | 0.136 | -0.976 | -0.179 | 0.105 | 0.806 | 177.0 | 78.4 | 0.927 | 3 |
| kaspa | 3600 | -0.145 | -0.159 | 0.983 | 0.984 | -0.898 | -0.880 | 0.878 | 0.893 | 1734.0 | 102.7 | 0.979 | 3 |
| kaspa | 1000000 | -0.432 | -0.443 | 0.871 | 0.879 | -0.884 | -0.796 | 0.703 | 0.806 | 1734.0 | 68.4 | 0.686 | 3 |
### 3. Timestamp stretching inside the rules: block rate after 1 h of forging (drift = rate - 1), 6 h runs
| rule | ts_rules | share | stamp | forger_offset_s | rate_pre | rate_post | rate_last_hour | drift | drift_worst | D_ratio | std | worst_gap | forger_adv | seeds |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| igneum | kaspa | 30 | future | 132.0 | 0.994 | 0.656 | 0.658 | -0.344 | -0.350 | 1.549 | 0.136 | 15.6 | 0.000 | 3 |
| igneum | kaspa | 30 | past | -439.1 | 0.994 | 0.415 | 0.428 | -0.585 | -0.597 | 2.421 | 0.243 | 44.8 | 0.000 | 3 |
| igneum | kaspa | 30 | alt | -70.3 | 0.994 | 0.514 | 0.513 | -0.486 | -0.545 | 1.966 | 0.381 | 37.0 | 0.000 | 3 |
| igneum | kaspa | 50 | future | 132.0 | 0.994 | 0.563 | 0.573 | -0.437 | -0.449 | 1.796 | 0.103 | 17.1 | 0.000 | 3 |
| igneum | kaspa | 50 | past | -2122.9 | 0.994 | 0.116 | 0.119 | -0.884 | -0.925 | 9.886 | 0.186 | 233.8 | 0.000 | 3 |
| igneum | kaspa | 50 | alt | -289.0 | 0.994 | 0.231 | 0.221 | -0.769 | -0.804 | 4.393 | 0.257 | 83.5 | 0.000 | 3 |
| igneum-san | kaspa | 30 | future | 132.0 | 0.994 | 0.091 | 0.100 | -0.909 | -0.911 | 10.9 | 0.055 | 119.1 | 0.000 | 3 |
| igneum-san | kaspa | 30 | past | -195.5 | 0.994 | 0.931 | 0.874 | -0.069 | -0.092 | 1.084 | 0.228 | 20.4 | 0.000 | 3 |
| igneum-san | kaspa | 30 | alt | -786.0 | 0.994 | 0.087 | 0.091 | -0.913 | -0.918 | 11.6 | 0.058 | 126.6 | 0.000 | 3 |
| igneum-san | kaspa | 50 | future | 132.0 | 0.994 | 0.166 | 0.188 | -0.834 | -0.860 | 6.046 | 0.173 | 102.4 | 0.000 | 3 |
| igneum-san | kaspa | 50 | past | -4510.6 | 0.994 | 0.033 | 0.009 | -0.967 | -0.992 | 64.0 | 0.098 | 607.0 | 0.000 | 3 |
| igneum-san | kaspa | 50 | alt | -2039.9 | 0.994 | 0.038 | 0.036 | -0.962 | -0.968 | 25.6 | 0.024 | 439.2 | 0.000 | 3 |
| kaspa | kaspa | 30 | future | 132.0 | 0.993 | 1.049 | 1.049 | 0.049 | 0.052 | 0.959 | 0.018 | 8.825 | 0.000 | 3 |
| kaspa | kaspa | 30 | past | -170.2 | 0.993 | 1.069 | 1.073 | 0.069 | 0.072 | 0.941 | 0.021 | 8.675 | 0.000 | 3 |
| kaspa | kaspa | 30 | alt | 6.993 | 0.993 | 1.090 | 1.092 | 0.090 | 0.092 | 0.923 | 0.023 | 8.463 | 0.000 | 3 |
| kaspa | kaspa | 50 | future | 132.0 | 0.993 | 1.050 | 1.052 | 0.050 | 0.054 | 0.958 | 0.018 | 8.840 | 0.000 | 3 |
| kaspa | kaspa | 50 | past | -235.6 | 0.993 | 1.113 | 1.113 | 0.113 | 0.116 | 0.904 | 0.027 | 8.353 | 0.000 | 3 |
| kaspa | kaspa | 50 | alt | 8.892 | 0.993 | 1.098 | 1.100 | 0.098 | 0.100 | 0.916 | 0.021 | 8.451 | 0.000 | 3 |
### 4. Short-lane oscillation: 25% miner on and off every 120 blocks (std_floor = the hash square wave at a fixed D)
| rule | share | period | std_pre | std_post | std_ratio | std_ratio_worst | std_floor | worst_gap_pre | worst_gap_post | blocks_per_s | osc_adv | seeds |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| igneum | 25 | 120 | 0.045 | 0.160 | 3.753 | 4.815 | 0.143 | 8.789 | 11.0 | 0.980 | -0.014 | 3 |
| igneum-san | 25 | 120 | 0.045 | 0.160 | 3.753 | 4.815 | 0.143 | 8.789 | 11.0 | 0.980 | -0.014 | 3 |
| kaspa | 25 | 120 | 0.010 | 0.147 | 16.4 | 23.5 | 0.143 | 8.906 | 10.3 | 1.001 | 0.000 | 3 |
### 5. Epoch-boundary games: hold dodger (30%, off for blocks 0 to 7), hold flooder (10x, on for blocks 0 to 7), 30% flooder
| rule | kind | gamer_adv | gamer_adv_worst | gamer_on_frac | std | worst_gap | blocks_per_s | seeds |
|---|---|---|---|---|---|---|---|---|
| igneum | dodge | 0.000 | 0.000 | 0.997 | 0.054 | 9.598 | 1.002 | 3 |
| igneum | flood | 0.007 | 0.024 | 0.000 | 0.470 | 9.986 | 0.995 | 3 |
| igneum | flood30 | 0.003 | 0.021 | 0.001 | 0.054 | 9.811 | 0.997 | 3 |
| igneum-san | dodge | 0.000 | 0.000 | 0.997 | 0.054 | 9.598 | 1.002 | 3 |
| igneum-san | flood | 0.007 | 0.024 | 0.000 | 0.470 | 9.986 | 0.995 | 3 |
| igneum-san | flood30 | 0.003 | 0.021 | 0.001 | 0.054 | 9.811 | 0.997 | 3 |
| kaspa | dodge | 0.000 | 0.000 | 0.997 | 0.026 | 9.360 | 1.001 | 3 |
| kaspa | flood | 0.000 | 0.005 | 0.000 | 0.482 | 9.293 | 1.001 | 3 |
| kaspa | flood30 | -0.001 | 0.004 | 0.002 | 0.030 | 9.278 | 1.001 | 3 |
### 6. Polluted window under adversarial timing: 10x miner joins at block join_k of an epoch and leaves at leave_k (600 = long lane takes over)
| rule | join_k | leave_k | join_first10_s | join_settled_s | leave_first10_s | leave_settled_s | leave_worst_gap_s | leave_below05 | leave_above2x | seeds |
|---|---|---|---|---|---|---|---|---|---|---|
| igneum | 0 | 600 | 88.6 | 134.8 | 303.1 | 303.1 | 16.9 | 55.3 | 0.000 | 3 |
| igneum | 480 | 600 | none | none | 291.9 | 291.9 | 15.2 | 50.3 | 0.000 | 3 |
| igneum | 480 | 720 | 76.3 | 58.3 | 321.4 | 321.4 | 28.4 | 56.7 | 0.000 | 3 |
| igneum | 0 | 1200 | 88.6 | 134.8 | 312.2 | 334.0 | 24.5 | 56.7 | 0.000 | 3 |
| igneum-san | 0 | 600 | 88.6 | 134.8 | 296.8 | 296.8 | 16.4 | 55.3 | 0.000 | 3 |
| igneum-san | 480 | 600 | none | none | 286.7 | 286.7 | 14.8 | 47.3 | 0.000 | 3 |
| igneum-san | 480 | 720 | 76.3 | 58.3 | 312.0 | 312.0 | 28.4 | 54.3 | 0.000 | 3 |
| igneum-san | 0 | 1200 | 88.6 | 134.8 | 304.7 | 328.7 | 24.5 | 55.7 | 0.000 | 3 |
| kaspa | 0 | 600 | none | none | 2910.0 | 2910.0 | 9.954 | 0.000 | 0.000 | 3 |
| kaspa | 480 | 600 | none | none | 0.000 | 0.000 | 8.600 | 0.000 | 0.000 | 3 |
| kaspa | 480 | 720 | none | none | 135.3 | 135.3 | 8.838 | 0.000 | 0.000 | 3 |
| kaspa | 0 | 1200 | none | none | 3539.6 | 3539.6 | 13.1 | 0.000 | 0.000 | 3 |
## Timestamp stretching under the tight rules (README.md, Part A: 10 s ahead, selected parent minus 10 s)
# Difficulty attacks, seeds [7, 8, 9], rules ['igneum', 'igneum-san', 'kaspa']
### 3. Timestamp stretching inside the rules: block rate after 1 h of forging (drift = rate - 1), 6 h runs
| rule | ts_rules | share | stamp | forger_offset_s | rate_pre | rate_post | rate_last_hour | drift | drift_worst | D_ratio | std | worst_gap | forger_adv | seeds |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| igneum | tight | 30 | future | 10.0 | 0.994 | 1.008 | 1.006 | 0.008 | 0.018 | 0.999 | 0.067 | 9.662 | 0.000 | 3 |
| igneum | tight | 30 | past | -16.6 | 0.994 | 0.636 | 0.649 | -0.364 | -0.381 | 1.597 | 0.201 | 32.5 | 0.000 | 3 |
| igneum | tight | 30 | alt | 1.012 | 0.994 | 0.975 | 0.968 | -0.025 | -0.035 | 1.030 | 0.067 | 10.7 | 0.000 | 3 |
| igneum | tight | 50 | future | 10.0 | 0.994 | 1.009 | 1.001 | 0.009 | 0.021 | 0.997 | 0.071 | 9.792 | 0.000 | 3 |
| igneum | tight | 50 | past | -30.3 | 0.994 | 0.170 | 0.132 | -0.830 | -0.850 | 5.917 | 0.115 | 106.0 | 0.000 | 3 |
| igneum | tight | 50 | alt | 1.975 | 0.994 | 0.949 | 0.936 | -0.051 | -0.057 | 1.059 | 0.088 | 11.6 | 0.000 | 3 |
| igneum-san | tight | 30 | future | 10.0 | 0.994 | 1.008 | 1.006 | 0.008 | 0.018 | 0.999 | 0.067 | 9.662 | 0.000 | 3 |
| igneum-san | tight | 30 | past | -15.8 | 0.994 | 1.008 | 1.006 | 0.008 | 0.024 | 0.998 | 0.077 | 9.920 | 0.000 | 3 |
| igneum-san | tight | 30 | alt | 1.036 | 0.994 | 1.004 | 1.001 | 0.004 | 0.012 | 1.001 | 0.052 | 9.826 | 0.000 | 3 |
| igneum-san | tight | 50 | future | 10.0 | 0.994 | 1.009 | 1.001 | 0.009 | 0.021 | 0.997 | 0.071 | 9.792 | 0.000 | 3 |
| igneum-san | tight | 50 | past | -21.9 | 0.994 | 1.007 | 1.012 | 0.007 | 0.027 | 1.000 | 0.147 | 10.1 | 0.000 | 3 |
| igneum-san | tight | 50 | alt | 2.017 | 0.994 | 1.011 | 1.005 | 0.011 | 0.022 | 0.995 | 0.071 | 9.996 | 0.000 | 3 |
| kaspa | tight | 30 | future | 10.0 | 0.993 | 1.000 | 1.003 | 0.000 | 0.005 | 1.005 | 0.017 | 9.249 | 0.000 | 3 |
| kaspa | tight | 30 | past | -15.8 | 0.993 | 1.002 | 1.002 | 0.002 | 0.007 | 1.002 | 0.018 | 9.239 | 0.000 | 3 |
| kaspa | tight | 30 | alt | 1.036 | 0.993 | 1.001 | 1.003 | 0.001 | 0.005 | 1.004 | 0.017 | 9.220 | 0.000 | 3 |
| kaspa | tight | 50 | future | 10.0 | 0.993 | 1.001 | 1.002 | 0.001 | 0.005 | 1.004 | 0.017 | 9.252 | 0.000 | 3 |
| kaspa | tight | 50 | past | -21.9 | 0.993 | 1.009 | 1.012 | 0.009 | 0.015 | 0.996 | 0.019 | 9.152 | 0.000 | 3 |
| kaspa | tight | 50 | alt | 1.987 | 0.993 | 1.001 | 1.002 | 0.001 | 0.005 | 1.004 | 0.017 | 9.238 | 0.000 | 3 |
## Base profiles (sim.py metrics) through each rule
# Difficulty attacks, seeds [7, 8, 9], rules ['igneum', 'igneum-san', 'kaspa']
### Base profiles (sim.py metrics) through each rule
| rule | profile | first10_s | settled_s | settled_s_none | worst_gap_s | steady_std | peak_rate | not_recovered | seeds |
|---|---|---|---|---|---|---|---|---|---|
| igneum | up50 | 56.1 | 154.4 | none | 9.719 | 0.042 | none | none | 3 |
| igneum | down50 | 782.3 | 782.3 | none | 78.3 | 0.042 | none | none | 3 |
| igneum | epoch30 | 44.6 | 87.6 | none | 10.8 | 0.039 | none | 0.000 | 3 |
| igneum | walk10 | none | none | 3 | 10.7 | 0.058 | none | none | 3 |
| igneum | hop10 | 213.8 | 239.4 | none | 31.9 | 0.042 | none | 0.000 | 3 |
| igneum | polluted | 70.1 | 70.1 | none | 10.2 | 0.041 | 7.969 | none | 3 |
| igneum | warmup-hard | 381.3 | 381.3 | none | 34.6 | 0.039 | none | none | 3 |
| igneum-san | up50 | 56.1 | 154.4 | none | 9.719 | 0.042 | none | none | 3 |
| igneum-san | down50 | 728.5 | 762.2 | none | 73.9 | 0.042 | none | none | 3 |
| igneum-san | epoch30 | 44.6 | 87.6 | none | 10.8 | 0.039 | none | 0.000 | 3 |
| igneum-san | walk10 | none | none | 3 | 10.7 | 0.058 | none | none | 3 |
| igneum-san | hop10 | 210.3 | 245.1 | none | 35.6 | 0.042 | none | 0.000 | 3 |
| igneum-san | polluted | 74.9 | 74.9 | none | 10.2 | 0.041 | 11.4 | none | 3 |
| igneum-san | warmup-hard | 305.8 | 326.5 | none | 34.6 | 0.039 | none | none | 3 |
| kaspa | up50 | 1764.8 | 1764.8 | none | 9.869 | 0.014 | none | none | 3 |
| kaspa | down50 | 12306.2 | 12306.2 | none | 155.2 | 0.014 | none | none | 3 |
| kaspa | epoch30 | 1663.5 | 1663.5 | none | 10.9 | 0.023 | none | 0.000 | 3 |
| kaspa | walk10 | none | none | 3 | 10.8 | 0.044 | none | none | 3 |
| kaspa | hop10 | none | none | 3 | 45.6 | 0.014 | none | 12.0 | 3 |
| kaspa | polluted | 695.0 | 2713.3 | none | 11.4 | 0.013 | 8.225 | none | 3 |
| kaspa | warmup-hard | 5975.0 | none | 3 | 68.8 | 43.4 | none | none | 3 |
## Lag bound of the sanitised clock (older naming: igneum-san = 120 s bound, igneum-san-j60 = 60 s bound; 60 s was adopted)
# Difficulty attacks, seeds [7, 8, 9], rules ['igneum-san', 'igneum-san-j60']
### Base profiles (sim.py metrics) through each rule
| rule | profile | first10_s | settled_s | settled_s_none | worst_gap_s | steady_std | peak_rate | not_recovered | seeds |
|---|---|---|---|---|---|---|---|---|---|
| igneum-san | up50 | 56.1 | 154.4 | none | 9.719 | 0.042 | none | none | 3 |
| igneum-san | down50 | 720.9 | 758.9 | none | 73.9 | 0.042 | none | none | 3 |
| igneum-san | epoch30 | 44.6 | 87.6 | none | 10.8 | 0.039 | none | 0.000 | 3 |
| igneum-san | walk10 | none | none | 3 | 10.7 | 0.058 | none | none | 3 |
| igneum-san | hop10 | 210.3 | 245.1 | none | 35.6 | 0.042 | none | 0.000 | 3 |
| igneum-san | polluted | 83.6 | 83.6 | none | 10.2 | 0.041 | 17.8 | none | 3 |
| igneum-san | warmup-hard | 305.8 | 326.5 | none | 34.6 | 0.039 | none | none | 3 |
| igneum-san-j60 | up50 | 56.1 | 154.4 | none | 9.719 | 0.042 | none | none | 3 |
| igneum-san-j60 | down50 | 728.5 | 762.2 | none | 73.9 | 0.042 | none | none | 3 |
| igneum-san-j60 | epoch30 | 44.6 | 87.6 | none | 10.8 | 0.039 | none | 0.000 | 3 |
| igneum-san-j60 | walk10 | none | none | 3 | 10.7 | 0.058 | none | none | 3 |
| igneum-san-j60 | hop10 | 210.3 | 245.1 | none | 35.6 | 0.042 | none | 0.000 | 3 |
| igneum-san-j60 | polluted | 74.9 | 74.9 | none | 10.2 | 0.041 | 11.4 | none | 3 |
| igneum-san-j60 | warmup-hard | 305.8 | 326.5 | none | 34.6 | 0.039 | none | none | 3 |
# Difficulty attacks, seeds [7], rules ['igneum-san', 'igneum-san-j60']
### 3. Timestamp stretching inside the rules: block rate after 1 h of forging (drift = rate - 1), 6 h runs
| rule | ts_rules | share | stamp | forger_offset_s | rate_pre | rate_post | rate_last_hour | drift | drift_worst | D_ratio | std | worst_gap | forger_adv | seeds |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| igneum-san | tight | 30 | future | 10.0 | 0.978 | 1.010 | 0.998 | 0.010 | 0.010 | 0.989 | 0.084 | 10.3 | 0.000 | 1 |
| igneum-san | tight | 30 | past | -15.9 | 0.978 | 1.014 | 1.000 | 0.014 | 0.014 | 0.984 | 0.097 | 11.1 | 0.000 | 1 |
| igneum-san | tight | 30 | alt | 1.051 | 0.978 | 1.009 | 0.999 | 0.009 | 0.009 | 0.989 | 0.068 | 10.9 | 0.000 | 1 |
| igneum-san | tight | 50 | future | 10.0 | 0.978 | 1.009 | 0.986 | 0.009 | 0.009 | 0.989 | 0.086 | 10.7 | 0.000 | 1 |
| igneum-san | tight | 50 | past | -22.1 | 0.978 | 1.040 | 1.030 | 0.040 | 0.040 | 0.960 | 0.190 | 10.7 | 0.000 | 1 |
| igneum-san | tight | 50 | alt | 2.023 | 0.978 | 1.014 | 0.991 | 0.014 | 0.014 | 0.984 | 0.097 | 11.3 | 0.000 | 1 |
| igneum-san-j60 | tight | 30 | future | 10.0 | 0.978 | 1.010 | 0.998 | 0.010 | 0.010 | 0.989 | 0.084 | 10.3 | 0.000 | 1 |
| igneum-san-j60 | tight | 30 | past | -15.9 | 0.978 | 1.012 | 0.995 | 0.012 | 0.012 | 0.986 | 0.096 | 11.1 | 0.000 | 1 |
| igneum-san-j60 | tight | 30 | alt | 1.051 | 0.978 | 1.009 | 0.999 | 0.009 | 0.009 | 0.989 | 0.068 | 10.9 | 0.000 | 1 |
| igneum-san-j60 | tight | 50 | future | 10.0 | 0.978 | 1.009 | 0.986 | 0.009 | 0.009 | 0.989 | 0.086 | 10.7 | 0.000 | 1 |
| igneum-san-j60 | tight | 50 | past | -22.2 | 0.978 | 1.002 | 1.013 | 0.002 | 0.002 | 0.999 | 0.181 | 10.7 | 0.000 | 1 |
| igneum-san-j60 | tight | 50 | alt | 2.023 | 0.978 | 1.014 | 0.991 | 0.014 | 0.014 | 0.984 | 0.097 | 11.3 | 0.000 | 1 |
## Clock without a lag bound (first candidate): base profiles, seed 7 to 9
# Difficulty attacks, seeds [7, 8, 9], rules ['igneum', 'igneum-san']
### Base profiles (sim.py metrics) through each rule
| rule | profile | first10_s | settled_s | settled_s_none | worst_gap_s | steady_std | peak_rate | not_recovered | seeds |
|---|---|---|---|---|---|---|---|---|---|
| igneum | up50 | 56.1 | 154.4 | none | 9.719 | 0.042 | none | none | 3 |
| igneum | down50 | 782.3 | 782.3 | none | 78.3 | 0.042 | none | none | 3 |
| igneum | epoch30 | 44.6 | 87.6 | none | 10.8 | 0.039 | none | 0.000 | 3 |
| igneum | walk10 | none | none | 3 | 10.7 | 0.058 | none | none | 3 |
| igneum | hop10 | 213.8 | 239.4 | none | 31.9 | 0.042 | none | 0.000 | 3 |
| igneum | polluted | 70.1 | 70.1 | none | 10.2 | 0.041 | 7.969 | none | 3 |
| igneum | warmup-hard | 381.3 | 381.3 | none | 34.6 | 0.039 | none | none | 3 |
| igneum-san | up50 | 56.1 | 154.4 | none | 9.719 | 0.042 | none | none | 3 |
| igneum-san | down50 | 718.8 | 757.2 | none | 73.9 | 0.042 | none | none | 3 |
| igneum-san | epoch30 | 44.6 | 87.6 | none | 10.8 | 0.039 | none | 0.000 | 3 |
| igneum-san | walk10 | none | none | 3 | 10.7 | 0.058 | none | none | 3 |
| igneum-san | hop10 | 210.3 | 245.1 | none | 35.6 | 0.042 | none | 0.000 | 3 |
| igneum-san | polluted | 75.5 | 75.5 | none | 10.2 | 0.041 | 274.4 | none | 3 |
| igneum-san | warmup-hard | 305.8 | 326.5 | none | 34.6 | 0.039 | none | none | 3 |
## Early variant study, clock without a lag bound, Kaspa's timestamp rules, seed 7 (flat weights, lag, 10 T cap)
# Difficulty attacks, seeds [7], rules ['igneum-san-flat-lag0', 'igneum-san-flat-lag1', 'igneum-san-flat-lag2', 'igneum-san-lwma-lag1', 'igneum-san-lwma-lag2', 'igneum-san-flat-lag1-cap10']
### 3. Timestamp stretching inside the rules: block rate after 1 h of forging (drift = rate - 1), 6 h runs
| rule | share | stamp | forger_offset_s | rate_pre | rate_post | rate_last_hour | drift | drift_worst | D_ratio | std | worst_gap | forger_adv | seeds |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| igneum-san-flat-lag0 | 30 | future | 132.0 | 0.979 | 1.070 | 1.049 | 0.070 | 0.070 | 0.935 | 0.204 | 9.132 | 0.000 | 1 |
| igneum-san-flat-lag0 | 30 | past | -168.4 | 0.979 | 1.072 | 1.073 | 0.072 | 0.072 | 0.939 | 0.244 | 13.1 | 0.000 | 1 |
| igneum-san-flat-lag0 | 30 | alt | 5.685 | 0.979 | 1.070 | 1.059 | 0.070 | 0.070 | 0.936 | 0.118 | 11.0 | 0.000 | 1 |
| igneum-san-flat-lag0 | 50 | future | 132.0 | 0.979 | 1.063 | 1.042 | 0.063 | 0.063 | 0.943 | 0.438 | 12.5 | 0.000 | 1 |
| igneum-san-flat-lag0 | 50 | past | -285.0 | 0.979 | 0.823 | 0.536 | -0.177 | -0.177 | 1.229 | 14.5 | 77.4 | 0.000 | 1 |
| igneum-san-flat-lag0 | 50 | alt | 8.669 | 0.979 | 1.094 | 1.081 | 0.094 | 0.094 | 0.918 | 0.161 | 11.1 | 0.000 | 1 |
| igneum-san-flat-lag1 | 30 | future | 132.0 | 0.979 | 1.070 | 1.048 | 0.070 | 0.070 | 0.935 | 0.200 | 9.312 | 0.000 | 1 |
| igneum-san-flat-lag1 | 30 | past | -168.4 | 0.979 | 1.072 | 1.072 | 0.072 | 0.072 | 0.939 | 0.243 | 12.8 | 0.000 | 1 |
| igneum-san-flat-lag1 | 30 | alt | 5.639 | 0.979 | 1.069 | 1.058 | 0.069 | 0.069 | 0.936 | 0.117 | 10.7 | 0.000 | 1 |
| igneum-san-flat-lag1 | 50 | future | 132.0 | 0.979 | 1.063 | 1.040 | 0.063 | 0.063 | 0.943 | 0.435 | 12.1 | 0.000 | 1 |
| igneum-san-flat-lag1 | 50 | past | -285.8 | 0.979 | 0.823 | 0.527 | -0.177 | -0.177 | 1.238 | 14.5 | 72.7 | 0.000 | 1 |
| igneum-san-flat-lag1 | 50 | alt | 8.666 | 0.979 | 1.093 | 1.081 | 0.093 | 0.093 | 0.918 | 0.163 | 10.8 | 0.000 | 1 |
| igneum-san-flat-lag2 | 30 | future | 132.0 | 0.979 | 1.069 | 1.047 | 0.069 | 0.069 | 0.936 | 0.199 | 9.121 | 0.000 | 1 |
| igneum-san-flat-lag2 | 30 | past | -168.5 | 0.979 | 1.071 | 1.071 | 0.071 | 0.071 | 0.939 | 0.243 | 15.5 | 0.000 | 1 |
| igneum-san-flat-lag2 | 30 | alt | 5.651 | 0.979 | 1.069 | 1.058 | 0.069 | 0.069 | 0.936 | 0.117 | 10.9 | 0.000 | 1 |
| igneum-san-flat-lag2 | 50 | future | 132.0 | 0.979 | 1.061 | 1.031 | 0.061 | 0.061 | 0.944 | 0.431 | 13.4 | 0.000 | 1 |
| igneum-san-flat-lag2 | 50 | past | -285.2 | 0.979 | 0.823 | 0.528 | -0.177 | -0.177 | 1.234 | 13.0 | 78.7 | 0.000 | 1 |
| igneum-san-flat-lag2 | 50 | alt | 8.680 | 0.979 | 1.094 | 1.079 | 0.094 | 0.094 | 0.918 | 0.161 | 10.5 | 0.000 | 1 |
| igneum-san-lwma-lag1 | 30 | future | 132.0 | 0.978 | 1.098 | 1.091 | 0.098 | 0.098 | 0.911 | 0.353 | 9.727 | 0.000 | 1 |
| igneum-san-lwma-lag1 | 30 | past | -162.2 | 0.978 | 1.114 | 1.139 | 0.114 | 0.114 | 0.904 | 0.290 | 12.2 | 0.000 | 1 |
| igneum-san-lwma-lag1 | 30 | alt | 5.272 | 0.978 | 1.065 | 1.053 | 0.065 | 0.065 | 0.942 | 0.132 | 10.7 | 0.000 | 1 |
| igneum-san-lwma-lag1 | 50 | future | 132.0 | 0.978 | 1.233 | 1.258 | 0.233 | 0.233 | 0.823 | 0.709 | 10.2 | 0.000 | 1 |
| igneum-san-lwma-lag1 | 50 | past | -270.0 | 0.978 | 0.934 | 0.609 | -0.066 | -0.066 | 1.076 | 1396.5 | 102.2 | 0.000 | 1 |
| igneum-san-lwma-lag1 | 50 | alt | 8.250 | 0.978 | 1.089 | 1.081 | 0.089 | 0.089 | 0.921 | 0.144 | 11.4 | 0.000 | 1 |
| igneum-san-lwma-lag2 | 30 | future | 132.0 | 0.978 | 1.096 | 1.095 | 0.096 | 0.096 | 0.912 | 0.349 | 9.663 | 0.000 | 1 |
| igneum-san-lwma-lag2 | 30 | past | -162.3 | 0.978 | 1.113 | 1.136 | 0.113 | 0.113 | 0.905 | 0.288 | 13.4 | 0.000 | 1 |
| igneum-san-lwma-lag2 | 30 | alt | 5.288 | 0.978 | 1.064 | 1.055 | 0.064 | 0.064 | 0.943 | 0.131 | 10.7 | 0.000 | 1 |
| igneum-san-lwma-lag2 | 50 | future | 132.0 | 0.978 | 1.229 | 1.257 | 0.229 | 0.229 | 0.826 | 0.699 | 10.8 | 0.000 | 1 |
| igneum-san-lwma-lag2 | 50 | past | -270.4 | 0.978 | 0.931 | 0.600 | -0.069 | -0.069 | 1.085 | 1068.9 | 97.6 | 0.000 | 1 |
| igneum-san-lwma-lag2 | 50 | alt | 8.606 | 0.978 | 1.097 | 1.111 | 0.097 | 0.097 | 0.916 | 0.155 | 9.717 | 0.000 | 1 |
| igneum-san-flat-lag1-cap10 | 30 | future | 132.0 | 0.979 | 1.052 | 1.024 | 0.052 | 0.052 | 0.950 | 0.113 | 9.696 | 0.000 | 1 |
| igneum-san-flat-lag1-cap10 | 30 | past | -175.7 | 0.979 | 1.031 | 0.999 | 0.031 | 0.031 | 0.974 | 0.185 | 13.3 | 0.000 | 1 |
| igneum-san-flat-lag1-cap10 | 30 | alt | 5.566 | 0.979 | 1.068 | 1.058 | 0.068 | 0.068 | 0.938 | 0.119 | 10.7 | 0.000 | 1 |
| igneum-san-flat-lag1-cap10 | 50 | future | 132.0 | 0.979 | 0.938 | 0.918 | -0.062 | -0.062 | 1.071 | 0.404 | 22.1 | 0.000 | 1 |
| igneum-san-flat-lag1-cap10 | 50 | past | -853.2 | 0.979 | 0.226 | 0.019 | -0.774 | -0.774 | 4.585 | 40314.5 | 268.5 | 0.000 | 1 |
| igneum-san-flat-lag1-cap10 | 50 | alt | 7.507 | 0.979 | 1.077 | 1.071 | 0.077 | 0.077 | 0.932 | 0.135 | 11.0 | 0.000 | 1 |
## First run, realised-count estimator (superseded; shows the block-count noise on the epoch flooders)
# Difficulty attacks, seeds [7, 8, 9], rules ['igneum', 'kaspa']
### 1. Pool hopping: hopper's blocks per hash against the always-on base (adv = ratio - 1), 24 h
| rule | x | dwell | adv | adv_worst | hop_on_frac | switches | std | worst_gap | blocks_per_s | seeds |
|---|---|---|---|---|---|---|---|---|---|---|
| igneum | 10 | 0 | 0.011 | 0.013 | 0.432 | 301.0 | 0.072 | 12.7 | 0.998 | 3 |
| igneum | 10 | 60 | 0.010 | 0.011 | 0.437 | 227.0 | 0.072 | 12.6 | 0.998 | 3 |
| igneum | 30 | 0 | 0.006 | 0.014 | 0.216 | 492.0 | 0.135 | 12.8 | 0.994 | 3 |
| igneum | 30 | 60 | -0.002 | -0.008 | 0.283 | 394.0 | 0.140 | 13.9 | 0.992 | 3 |
| igneum | 50 | 0 | 0.006 | 0.015 | 0.149 | 616.7 | 0.197 | 13.8 | 0.992 | 3 |
| igneum | 50 | 60 | -0.015 | -0.022 | 0.283 | 544.7 | 0.211 | 13.8 | 0.984 | 3 |
| igneum | 100 | 0 | 0.012 | 0.024 | 0.085 | 741.0 | 0.339 | 13.3 | 0.990 | 3 |
| igneum | 100 | 60 | -0.038 | -0.050 | 0.378 | 818.0 | 0.349 | 16.9 | 0.968 | 3 |
| kaspa | 10 | 0 | 0.005 | 0.009 | 0.367 | 63.7 | 0.054 | 11.8 | 1.000 | 3 |
| kaspa | 10 | 60 | 0.005 | 0.009 | 0.367 | 63.7 | 0.054 | 11.8 | 1.000 | 3 |
| kaspa | 30 | 0 | 0.006 | 0.008 | 0.181 | 88.0 | 0.124 | 12.3 | 1.001 | 3 |
| kaspa | 30 | 60 | 0.006 | 0.008 | 0.181 | 88.0 | 0.124 | 12.3 | 1.001 | 3 |
| kaspa | 50 | 0 | 0.012 | 0.015 | 0.116 | 112.3 | 0.180 | 12.7 | 1.001 | 3 |
| kaspa | 50 | 60 | 0.014 | 0.019 | 0.115 | 111.3 | 0.179 | 12.6 | 1.001 | 3 |
| kaspa | 100 | 0 | 0.010 | 0.029 | 0.061 | 122.7 | 0.304 | 12.5 | 1.001 | 3 |
| kaspa | 100 | 60 | 0.006 | 0.019 | 0.068 | 132.0 | 0.315 | 12.5 | 1.001 | 3 |
### 2. Pulsed hash rate: 50x for 10 min every hour, blocks per hash of the pulser against steady mining
| rule | pulse_vs_steady | pulse_vs_steady_worst | base_vs_steady | pulse_vs_base | pulse_block_share | pulse_hash_share | peak_blocks_per_min | worst_gap | blocks_per_s | seeds |
|---|---|---|---|---|---|---|---|---|---|---|
| igneum | -0.977 | -0.977 | -0.346 | -0.964 | 0.228 | 0.862 | 182.3 | 100.9 | 0.841 | 3 |
| kaspa | -0.896 | -0.897 | -0.879 | -0.139 | 0.878 | 0.862 | 1741.0 | 102.1 | 0.979 | 3 |
### 3. Timestamp stretching inside the rules: block rate after 1 h of forging (drift = rate - 1)
| rule | share | stamp | forger_offset_s | rate_pre | rate_post | rate_last_hour | drift | drift_worst | D_ratio | std | worst_gap | seeds |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| igneum | 30 | future | 132.0 | 0.994 | 0.656 | 0.658 | -0.344 | -0.350 | 1.549 | 0.136 | 15.6 | 3 |
| igneum | 30 | past | -439.1 | 0.994 | 0.415 | 0.428 | -0.585 | -0.597 | 2.421 | 0.243 | 44.8 | 3 |
| igneum | 30 | alt | -70.3 | 0.994 | 0.514 | 0.513 | -0.486 | -0.545 | 1.966 | 0.381 | 37.0 | 3 |
| igneum | 50 | future | 132.0 | 0.994 | 0.563 | 0.573 | -0.437 | -0.449 | 1.796 | 0.103 | 17.1 | 3 |
| igneum | 50 | past | -2122.9 | 0.994 | 0.116 | 0.119 | -0.884 | -0.925 | 9.886 | 0.186 | 233.8 | 3 |
| igneum | 50 | alt | -289.0 | 0.994 | 0.231 | 0.221 | -0.769 | -0.804 | 4.393 | 0.257 | 83.5 | 3 |
| kaspa | 30 | future | 132.0 | 0.993 | 1.049 | 1.049 | 0.049 | 0.052 | 0.959 | 0.018 | 8.825 | 3 |
| kaspa | 30 | past | -170.2 | 0.993 | 1.069 | 1.073 | 0.069 | 0.072 | 0.941 | 0.021 | 8.675 | 3 |
| kaspa | 30 | alt | 6.993 | 0.993 | 1.090 | 1.092 | 0.090 | 0.092 | 0.923 | 0.023 | 8.463 | 3 |
| kaspa | 50 | future | 132.0 | 0.993 | 1.050 | 1.052 | 0.050 | 0.054 | 0.958 | 0.018 | 8.840 | 3 |
| kaspa | 50 | past | -235.6 | 0.993 | 1.113 | 1.113 | 0.113 | 0.116 | 0.904 | 0.027 | 8.353 | 3 |
| kaspa | 50 | alt | 8.892 | 0.993 | 1.098 | 1.100 | 0.098 | 0.100 | 0.916 | 0.021 | 8.451 | 3 |
### 4. Short-lane oscillation: 25% miner on and off every 120 blocks
| rule | share | period | std_pre | std_post | std_ratio | std_ratio_worst | std_floor | worst_gap_pre | worst_gap_post | blocks_per_s | osc_adv | seeds |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| igneum | 25 | 120 | 0.045 | 0.160 | 3.753 | 4.815 | 0.143 | 8.789 | 11.0 | 0.980 | -0.015 | 3 |
| kaspa | 25 | 120 | 0.010 | 0.147 | 16.4 | 23.5 | 0.143 | 8.906 | 10.3 | 1.001 | 0.012 | 3 |
### 5. Epoch-boundary games: hold dodger (30%, off for blocks 0 to 7), hold flooder (10x, on for blocks 0 to 7), 30% flooder
| rule | kind | gamer_adv | gamer_adv_worst | gamer_on_frac | std | worst_gap | blocks_per_s | seeds |
|---|---|---|---|---|---|---|---|---|
| igneum | dodge | -0.000 | 0.001 | 0.997 | 0.054 | 9.598 | 1.002 | 3 |
| igneum | flood | 0.136 | 0.276 | 0.000 | 0.470 | 9.986 | 0.995 | 3 |
| igneum | flood30 | 0.131 | 0.272 | 0.001 | 0.054 | 9.811 | 0.997 | 3 |
| kaspa | dodge | -0.000 | -0.000 | 0.997 | 0.026 | 9.360 | 1.001 | 3 |
| kaspa | flood | 0.111 | 0.264 | 0.000 | 0.482 | 9.293 | 1.001 | 3 |
| kaspa | flood30 | 0.110 | 0.263 | 0.002 | 0.030 | 9.278 | 1.001 | 3 |
### 6. Polluted window under adversarial timing: 10x miner joins at block join_k of an epoch and leaves at leave_k (600 = long lane takes over)
| rule | join_k | leave_k | join_first10_s | join_settled_s | leave_first10_s | leave_settled_s | leave_worst_gap_s | leave_below05 | leave_above2x | seeds |
|---|---|---|---|---|---|---|---|---|---|---|
| igneum | 0 | 600 | 88.6 | 134.8 | 303.1 | 303.1 | 16.9 | 55.3 | 0.000 | 3 |
| igneum | 480 | 600 | none | none | 291.9 | 291.9 | 15.2 | 50.3 | 0.000 | 3 |
| igneum | 480 | 720 | 76.3 | none | 321.4 | 321.4 | 28.4 | 56.7 | 0.000 | 3 |
| igneum | 0 | 1200 | 88.6 | 134.8 | 312.2 | 334.0 | 24.5 | 56.7 | 0.000 | 3 |
| kaspa | 0 | 600 | none | none | 2910.0 | 2910.0 | 9.954 | 0.000 | 0.000 | 3 |
| kaspa | 480 | 600 | none | none | 0.000 | 0.000 | 8.600 | 0.000 | 0.000 | 3 |
| kaspa | 480 | 720 | none | none | 135.3 | 135.3 | 8.838 | 0.000 | 0.000 | 3 |
| kaspa | 0 | 1200 | none | none | 3539.6 | 3539.6 | 13.1 | 0.000 | 0.000 | 3 |
## Scenario 7, flood test output (cargo test -p kaspa-consensus --lib igneum_flood -- --nocapture, diff-attacks branch)
```
target below 2^64 at block 4142 (epoch start 3600), bits 0x900fe5b
thread 'processes::difficulty::tests::igneum_flood_at_85_blocks_per_second_drives_the_target_below_block_work_range' (36166563) panicked at consensus/src/processes/difficulty.rs:431:20:
Work should not exceed 2**192: TryFromIntError
test processes::difficulty::tests::igneum_flood_at_85_blocks_per_second_drives_the_target_below_block_work_range - should panic ... ok
test result: ok. 1 passed; 0 failed; 0 ignored; 0 measured; 81 filtered out; finished in 0.01s
```
## Ease clamp against the hopper (igneum-ease6 and igneum-ease3: the spec rule with a 6% or 3% ease clamp), seed 7, 24 h
# Difficulty attacks, seeds [7], rules ['igneum-ease6', 'igneum-ease3']
### 1. Pool hopping: hopper's blocks per hash against the always-on base (adv = ratio - 1), 24 h
| rule | x | dwell | adv | adv_worst | hop_on_frac | switches | std | worst_gap | blocks_per_s | seeds |
|---|---|---|---|---|---|---|---|---|---|---|
| igneum-ease6 | 10 | 0 | 0.015 | 0.015 | 0.517 | 330.0 | 0.073 | 12.7 | 1.000 | 1 |
| igneum-ease6 | 10 | 60 | 0.014 | 0.014 | 0.505 | 240.0 | 0.073 | 12.7 | 1.000 | 1 |
| igneum-ease6 | 30 | 0 | 0.010 | 0.010 | 0.271 | 565.0 | 0.143 | 11.7 | 0.995 | 1 |
| igneum-ease6 | 30 | 60 | 0.002 | 0.002 | 0.336 | 445.0 | 0.144 | 13.7 | 0.993 | 1 |
| igneum-ease6 | 50 | 0 | 0.009 | 0.009 | 0.185 | 718.0 | 0.209 | 13.6 | 0.992 | 1 |
| igneum-ease6 | 50 | 60 | -0.011 | -0.011 | 0.309 | 576.0 | 0.214 | 12.2 | 0.986 | 1 |
| igneum-ease6 | 100 | 0 | 0.006 | 0.006 | 0.107 | 861.0 | 0.362 | 13.9 | 0.990 | 1 |
| igneum-ease6 | 100 | 60 | -0.032 | -0.032 | 0.396 | 841.0 | 0.346 | 17.0 | 0.970 | 1 |
| igneum-ease3 | 10 | 0 | 0.015 | 0.015 | 0.529 | 308.0 | 0.072 | 11.7 | 0.999 | 1 |
| igneum-ease3 | 10 | 60 | 0.015 | 0.015 | 0.515 | 238.0 | 0.073 | 12.8 | 0.999 | 1 |
| igneum-ease3 | 30 | 0 | 0.009 | 0.009 | 0.284 | 566.0 | 0.142 | 11.7 | 0.994 | 1 |
| igneum-ease3 | 30 | 60 | 0.002 | 0.002 | 0.342 | 446.0 | 0.143 | 13.7 | 0.993 | 1 |
| igneum-ease3 | 50 | 0 | 0.008 | 0.008 | 0.190 | 698.0 | 0.208 | 12.7 | 0.991 | 1 |
| igneum-ease3 | 50 | 60 | -0.012 | -0.012 | 0.321 | 588.0 | 0.213 | 12.1 | 0.984 | 1 |
| igneum-ease3 | 100 | 0 | 0.005 | 0.005 | 0.115 | 896.0 | 0.366 | 11.9 | 0.988 | 1 |
| igneum-ease3 | 100 | 60 | -0.027 | -0.027 | 0.413 | 859.0 | 0.343 | 16.7 | 0.970 | 1 |

305
sim/difficulty/attacks/testnet.py Normal file
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#!/usr/bin/env python3
"""3-node CPU test network for the difficulty attacks (ports 27700 and above, appdir /tmp/igneum-diff-attacks).
Node 1 (gRPC 27700, P2P 27701, wRPC JSON 27702) is the honest seed, node 2 (27710/27711) honest, node 3
(27720/27721) the attacker's node: it is started with IGNEUM_ATTACK_TS_OFFSET_MS so every template it hands
out is stamped at the given offset (the diff-attacks branch of vendor/igneum-node reads that variable in the
template builder only; the validation rules are untouched). Miners are `igneum-miner mine --engine igneum-pow`
CPU miners with their own payout labels, started and stopped by pid.
python3 testnet.py --rule igneum --scenario ts --minutes 15 --out /tmp/igneum-diff-attacks/ts-igneum
python3 testnet.py --rule kaspa --scenario hop --minutes 15 --out /tmp/igneum-diff-attacks/hop-kaspa
python3 testnet.py --analyse /tmp/igneum-diff-attacks/ts-igneum
Scenarios
ts honest miner A on node 1 all run; forger F mines on node 2 (honest stamps) for the first third, then on
node 3 (stamps 130 s ahead) for the rest. Threads chosen for about a 50% share.
hop honest miner A on node 1 all run; hopper B (same threads) on node 2, on while the difficulty read from
node 1 is below its trailing mean (1% band), off when above, re-evaluated every second; from minute 3.
Everything started here is stopped at the end (SIGTERM, then SIGKILL) by pid; nothing else is touched.
"""
import argparse
import asyncio
import csv
import json
import os
import signal
import subprocess
import sys
import time
ROOT = os.path.abspath(os.path.join(os.path.dirname(__file__), "..", "..", ".."))
BIN = os.path.join(ROOT, "vendor", "igneum-node-diff-attacks", "target", "release")
IGNEUMD = os.path.join(BIN, "igneumd")
MINER = os.path.join(BIN, "igneum-miner")
GENESIS_BITS = 0x1f010000 # 2^16 expected hashes per block: about 1 block/s for one 4-thread CPU miner on this Mac
NODES = [
{"name": "node1", "grpc": 27700, "p2p": 27701, "json": 27702},
{"name": "node2", "grpc": 27710, "p2p": 27711, "json": None},
{"name": "node3", "grpc": 27720, "p2p": 27721, "json": None},
]
started = [] # Popen objects we own
def log(out, msg):
line = "%s %s" % (time.strftime("%H:%M:%S"), msg)
print(line, flush=True)
with open(os.path.join(out, "schedule.log"), "a") as f:
f.write(line + "\n")
def start_node(n, out, rule, env_extra=None):
override = os.path.join(out, "override.json")
with open(override, "w") as f:
json.dump({"difficulty_rule": rule, "genesis_bits": GENESIS_BITS}, f)
appdir = os.path.join(out, n["name"])
args = [IGNEUMD, "--devnet", "--nodnsseed", "--disable-upnp", "--enable-unsynced-mining", "--nologfiles",
"--override-params-file=" + override, "--appdir=" + appdir,
"--rpclisten=127.0.0.1:%d" % n["grpc"], "--listen=127.0.0.1:%d" % n["p2p"]]
if n["json"]:
args.append("--rpclisten-json=127.0.0.1:%d" % n["json"])
if n["name"] != "node1":
args.append("--connect=127.0.0.1:%d" % NODES[0]["p2p"])
env = dict(os.environ)
env.update(env_extra or {})
lf = open(os.path.join(out, n["name"] + ".log"), "w")
p = subprocess.Popen(["nice", "-n", "19"] + args, stdout=lf, stderr=subprocess.STDOUT, env=env)
started.append(p)
log(out, "%s pid %d gRPC %d%s" % (n["name"], p.pid, n["grpc"], " env " + json.dumps(env_extra) if env_extra else ""))
return p
def start_miner(out, label, grpc, threads, secs):
lf = open(os.path.join(out, "miner-%s.log" % label), "a")
args = ["nice", "-n", "19", MINER, "mine", "grpc://127.0.0.1:%d" % grpc, str(threads), str(secs), label,
"--engine", "igneum-pow", "--payout-label", label, "--status-secs", "10"]
p = subprocess.Popen(args, stdout=lf, stderr=subprocess.STDOUT)
started.append(p)
log(out, "miner %s pid %d on %d threads %d for %d s" % (label, p.pid, grpc, threads, secs))
return p
def stop(p, out, what):
if p.poll() is None:
p.send_signal(signal.SIGTERM)
try:
p.wait(10)
except subprocess.TimeoutExpired:
p.kill()
p.wait(5)
log(out, "stopped %s pid %d code %s" % (what, p.pid, p.returncode))
async def rpc(port, method, params=None):
import websockets
async with websockets.connect("ws://127.0.0.1:%d" % port, max_size=None) as ws:
await ws.send(json.dumps({"id": 1, "method": method, "params": params or {}}))
m = json.loads(await ws.recv())
if m.get("error"):
raise RuntimeError(m["error"])
return m["params"]
def dag_info(port):
return asyncio.run(rpc(port, "getBlockDagInfo"))
def export(port, path):
info = dag_info(port)
low = info.get("pruningPointHash") or info["pruningPointHash"]
seen = set()
rows = []
while True:
r = asyncio.run(rpc(port, "getBlocks", {"lowHash": low, "includeBlocks": True, "includeTransactions": False}))
blocks = r.get("blocks") or []
new = 0
for b in blocks:
h = b["header"]
hs = h.get("hash") or (b.get("verboseData") or {}).get("hash")
if hs in seen:
continue
seen.add(hs)
new += 1
v = b.get("verboseData") or {}
rows.append({"hash": hs, "daa_score": h["daaScore"], "blue_score": h["blueScore"], "timestamp_ms": h["timestamp"],
"bits": "0x%08x" % int(h["bits"]), "difficulty": v.get("difficulty"), "is_chain_block": 1 if v.get("isChainBlock") else 0,
"parents": len((h.get("parentsByLevel") or [[]])[0]), "selected_parent": v.get("selectedParentHash"),
"vote_key_hash": h.get("voteKeyHash"), "blue_work": h.get("blueWork")})
if not blocks or new == 0:
break
low = (blocks[-1]["header"].get("hash") or blocks[-1]["verboseData"]["hash"])
if len(blocks) < 2:
break
rows.sort(key=lambda r: (int(r["blue_score"]), int(r["daa_score"]), int(r["timestamp_ms"])))
with open(path, "w", newline="") as f:
w = csv.DictWriter(f, fieldnames=list(rows[0].keys()))
w.writeheader()
w.writerows(rows)
return rows, info
def wait_grpc(out, n, secs=60):
lp = os.path.join(out, n["name"] + ".log")
for _ in range(secs * 2):
try:
if "GRPC Server starting" in open(lp).read():
return True
except FileNotFoundError:
pass
time.sleep(0.5)
return False
def run(args):
out = args.out
os.makedirs(out, exist_ok=True)
total = args.minutes * 60
log(out, "start rule=%s scenario=%s minutes=%d genesis_bits=%#x" % (args.rule, args.scenario, args.minutes, GENESIS_BITS))
try:
env3 = {"IGNEUM_ATTACK_TS_OFFSET_MS": str(args.ts_offset_ms)} if args.scenario == "ts" else None
start_node(NODES[0], out, args.rule)
wait_grpc(out, NODES[0])
start_node(NODES[1], out, args.rule)
start_node(NODES[2], out, args.rule, env3)
for n in NODES[1:]:
wait_grpc(out, n)
time.sleep(3)
t0 = time.time()
log(out, "miners from now; block 1 expected shortly")
a = start_miner(out, "A", NODES[0]["grpc"], args.threads, total)
if args.scenario == "ts":
third = total // 3
f1 = start_miner(out, "F", NODES[1]["grpc"], args.forger_threads, third)
time.sleep(third)
stop(f1, out, "miner F (honest leg)")
f2 = start_miner(out, "F", NODES[2]["grpc"], args.forger_threads, total - third - 2)
log(out, "forger now on node3 with offset %d ms" % args.ts_offset_ms)
while time.time() - t0 < total:
time.sleep(5)
stop(f2, out, "miner F (forging leg)")
elif args.scenario == "hop":
warm = 180
time.sleep(warm)
hop = None
hist = []
on_since = None
on_total = 0.0
switches = 0
while time.time() - t0 < total:
try:
d = float(dag_info(NODES[0]["json"])["difficulty"])
except Exception as e:
log(out, "dag info failed: %s" % e)
time.sleep(1)
continue
now = time.time()
hist.append((now, d))
hist = [x for x in hist if x[0] >= now - 600]
avg = sum(x[1] for x in hist) / len(hist)
want = (d < avg * 0.99) if hop is None or hop.poll() is not None else (d <= avg * 1.01)
running = hop is not None and hop.poll() is None
if want and not running:
hop = start_miner(out, "B", NODES[1]["grpc"], args.threads, int(total - (now - t0)) + 5)
on_since = now
switches += 1
log(out, "hop ON D=%.0f avg=%.0f" % (d, avg))
elif not want and running:
stop(hop, out, "miner B")
on_total += now - on_since
on_since = None
switches += 1
log(out, "hop OFF D=%.0f avg=%.0f" % (d, avg))
with open(os.path.join(out, "hop.csv"), "a") as f:
f.write("%.3f,%.1f,%.1f,%d\n" % (now, d, avg, 1 if running else 0))
time.sleep(1)
if hop is not None and hop.poll() is None:
stop(hop, out, "miner B")
on_total += time.time() - on_since
log(out, "hopper on %.0f s of %d, %d switches" % (on_total, total - warm, switches))
else:
while time.time() - t0 < total:
time.sleep(5)
stop(a, out, "miner A")
time.sleep(2)
rows, info = export(NODES[0]["json"], os.path.join(out, "record.csv"))
log(out, "dag %s" % json.dumps({k: info.get(k) for k in ("blockCount", "headerCount", "difficulty", "tipHashes", "virtualDaaScore")}))
log(out, "wrote %d rows" % len(rows))
finally:
for p in reversed(started):
stop(p, out, "pid")
log(out, "end")
def analyse(out):
"""Per-30-s table in wall time. Honest miner A's header stamps are real time (its node's clock), so every
chain block is placed at the stamp of the nearest earlier A block in blue order; the forger's own stamps are
reported as an offset against that clock."""
rows = list(csv.DictReader(open(os.path.join(out, "record.csv"))))
rows = [r for r in rows if int(r["blue_score"]) > 0]
chain = sorted([r for r in rows if r["is_chain_block"] == "1"], key=lambda r: int(r["blue_score"]))
keys = {}
summary = {}
for fn in os.listdir(out):
if fn.startswith("miner-") and fn.endswith(".log"):
label = fn[6:-4]
for line in open(os.path.join(out, fn)):
if "vote_key_hash=" in line and label not in keys:
keys[label] = line.split("vote_key_hash=")[1].split()[0]
if "MINER SUMMARY" in line:
summary.setdefault(label, []).append(line.strip())
who = {v: k for k, v in keys.items()}
t = None
t0 = None
bins = {}
offs = []
for r in chain:
label = who.get(r["vote_key_hash"], "?")
ts = int(r["timestamp_ms"]) / 1000.0
if label == "A":
t = ts
if t is None:
continue
if t0 is None:
t0 = t
b = int((t - t0) // 30)
d = bins.setdefault(b, {"n": 0, "F": 0, "dsum": 0.0, "off": []})
d["n"] += 1
d["F"] += 1 if label == "F" else 0
d["dsum"] += float(r["difficulty"] or 0)
if label == "F":
d["off"].append(ts - t)
print("blocks %d, chain blocks %d, miners %s" % (len(rows), len(chain), sorted(keys)))
print("| from s | chain blocks | blocks/s | F share | mean difficulty | F stamp offset s |")
print("|---|---|---|---|---|---|")
for b in sorted(bins):
d = bins[b]
off = ("%.0f" % (sum(d["off"]) / len(d["off"]))) if d["off"] else ""
print("| %d | %d | %.2f | %.2f | %s | %s |" % (b * 30, d["n"], d["n"] / 30.0, d["F"] / d["n"], "{:,.0f}".format(d["dsum"] / d["n"]), off))
for k, v in sorted(summary.items()):
for line in v:
print(k, line)
def main():
ap = argparse.ArgumentParser()
ap.add_argument("--rule", default="igneum-dual", help="igneum-dual or kaspa-sampled")
ap.add_argument("--scenario", default="ts", help="ts or hop")
ap.add_argument("--minutes", type=int, default=15)
ap.add_argument("--threads", type=int, default=4)
ap.add_argument("--forger-threads", type=int, default=4)
ap.add_argument("--ts-offset-ms", type=int, default=130000)
ap.add_argument("--out", default="/tmp/igneum-diff-attacks/run")
ap.add_argument("--analyse", default="")
args = ap.parse_args()
if args.analyse:
analyse(args.analyse)
return
if args.rule == "igneum":
args.rule = "igneum-dual"
if args.rule == "kaspa":
args.rule = "kaspa-sampled"
run(args)
if __name__ == "__main__":
main()

769
sim/difficulty/attacks/testnet/ts-future-igneum.csv Normal file
View file

@ -0,0 +1,769 @@
hash,daa_score,blue_score,timestamp_ms,bits,difficulty,is_chain_block,parents,selected_parent,vote_key_hash,blue_work
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21
sim/difficulty/attacks/testnet/ts-future-igneum.schedule.log Normal file
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@ -0,0 +1,21 @@
00:39:09 start rule=igneum-dual scenario=ts minutes=15 genesis_bits=0x1f010000
00:39:09 node1 pid 27070 gRPC 27700
00:39:10 node2 pid 27071 gRPC 27710
00:39:10 node3 pid 27072 gRPC 27720 env {"IGNEUM_ATTACK_TS_OFFSET_MS": "130000"}
00:39:14 miners from now; block 1 expected shortly
00:39:14 miner A pid 27074 on 27700 threads 4 for 900 s
00:39:14 miner F pid 27075 on 27710 threads 4 for 300 s
00:44:14 stopped miner F (honest leg) pid 27075 code -15
00:44:14 miner F pid 27386 on 27720 threads 4 for 598 s
00:44:14 forger now on node3 with offset 130000 ms
00:54:14 stopped miner F (forging leg) pid 27386 code 0
00:54:14 stopped miner A pid 27074 code 0
00:54:16 dag {"blockCount": 767, "headerCount": 767, "difficulty": 192979.45326331034, "tipHashes": ["fb9474443c41d6d6604c406effdafc880bca9b725c8b9ba41ecca4bf68a2907c", "d7825a8127ea0ff6379c0c60ad26540fb77ef4ae56f51d258e67f995bc36f812"], "virtualDaaScore": 767}
00:54:16 wrote 768 rows
00:54:16 stopped pid pid 27386 code 0
00:54:16 stopped pid pid 27075 code -15
00:54:16 stopped pid pid 27074 code 0
00:54:17 stopped pid pid 27072 code 0
00:54:18 stopped pid pid 27071 code 0
00:54:18 stopped pid pid 27070 code 0
00:54:18 end

519
sim/difficulty/attacks/testnet/ts-past-igneum.csv Normal file
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@ -0,0 +1,519 @@
hash,daa_score,blue_score,timestamp_ms,bits,difficulty,is_chain_block,parents,selected_parent,vote_key_hash,blue_work
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21
sim/difficulty/attacks/testnet/ts-past-igneum.schedule.log Normal file
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@ -0,0 +1,21 @@
23:52:40 start rule=igneum-dual scenario=ts minutes=15 genesis_bits=0x1f010000
23:52:40 node1 pid 84436 gRPC 27700
23:52:41 node2 pid 84437 gRPC 27710
23:52:41 node3 pid 84438 gRPC 27720 env {"IGNEUM_ATTACK_TS_OFFSET_MS": "-1000000000"}
23:52:44 miners from now; block 1 expected shortly
23:52:44 miner A pid 84443 on 27700 threads 4 for 900 s
23:52:44 miner F pid 84444 on 27710 threads 4 for 300 s
23:57:44 stopped miner F (honest leg) pid 84444 code -15
23:57:44 miner F pid 86093 on 27720 threads 4 for 598 s
23:57:44 forger now on node3 with offset -1000000000 ms
00:07:45 stopped miner F (forging leg) pid 86093 code 0
00:07:45 stopped miner A pid 84443 code 0
00:07:47 dag {"blockCount": 517, "headerCount": 517, "difficulty": 363596.55784877454, "tipHashes": ["a0316d088b83d876451c19c671b8e06ad1c2019c62b9417283546efecd1c7b04"], "virtualDaaScore": 517}
00:07:47 wrote 518 rows
00:07:47 stopped pid pid 86093 code 0
00:07:47 stopped pid pid 84444 code -15
00:07:47 stopped pid pid 84443 code 0
00:07:48 stopped pid pid 84438 code 0
00:07:49 stopped pid pid 84437 code 0
00:07:49 stopped pid pid 84436 code 0
00:07:49 end

1456
sim/difficulty/attacks/testnet/ts-past-kaspa.csv Normal file
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File diff suppressed because it is too large Load diff

21
sim/difficulty/attacks/testnet/ts-past-kaspa.schedule.log Normal file
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@ -0,0 +1,21 @@
00:23:56 start rule=kaspa-sampled scenario=ts minutes=15 genesis_bits=0x1f010000
00:23:56 node1 pid 15909 gRPC 27700
00:23:56 node2 pid 15918 gRPC 27710
00:23:56 node3 pid 15919 gRPC 27720 env {"IGNEUM_ATTACK_TS_OFFSET_MS": "-1000000000"}
00:24:00 miners from now; block 1 expected shortly
00:24:00 miner A pid 15935 on 27700 threads 4 for 900 s
00:24:00 miner F pid 15936 on 27710 threads 4 for 300 s
00:29:00 stopped miner F (honest leg) pid 15936 code -15
00:29:00 miner F pid 16882 on 27720 threads 4 for 598 s
00:29:00 forger now on node3 with offset -1000000000 ms
00:39:01 stopped miner F (forging leg) pid 16882 code 0
00:39:01 stopped miner A pid 15935 code -15
00:39:03 dag {"blockCount": 1454, "headerCount": 1454, "difficulty": 83193.1884888781, "tipHashes": ["b18d193ba8383242ef97bf7527799fbe2ce09b8eff8a82dba399f154862eb2c8"], "virtualDaaScore": 1454}
00:39:03 wrote 1455 rows
00:39:03 stopped pid pid 16882 code 0
00:39:03 stopped pid pid 15936 code -15
00:39:03 stopped pid pid 15935 code -15
00:39:03 stopped pid pid 15919 code 0
00:39:04 stopped pid pid 15918 code 0
00:39:04 stopped pid pid 15909 code 0
00:39:04 end