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adv-mixer-3 report: Q2b day 20733 k=0..8 (finding at k=1, clean from k=2), 2^28 at k=4, Q2 day 20733 k=4

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Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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igneum-labs 2026-10-07 19:20:18 +00:00
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docs/analysis/cryptanalysis/report-mixer-3.md
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@ -25,8 +25,8 @@ Plant rule: a tool is trusted once it has fired on a known-failed shape. Which s
| Q | Method | Known-failed shape | Gate | Result (numbers) | Status |
|---|---|---|---|---|---|
| Q1 | exhaustive round-0 line-index census, all 2^32 t, k = 0..8 | k = 0 (the init: one bin holds 2^32, fired on both days) | chi-square z within 6, no empty bin | day 20729: uniform at k = 1 (z -1.13), 2 (-0.68), 3 (-0.39), 4 (-0.47), 5 (-1.47), 6 (-0.30), 7 (-1.04), 8 (1.13, the real first read); day 20733 uniform at k = 1 (z -0.71), its k = 2..8 running under the lock; day 20730 (queue 07) uniform at k = 2, 3, 4, 8 | PASS to k = 8 on day 20729 (BOUND: the index histogram is uniform from k = 1), RUNNING |
| Q2 | single-bit avalanche, random states, 2^24 (and 2^27) states | `one` at k = 8 (fired: 1959 holes); `weak` fires at k = 1 only, not at k = 8 (see Q2) | no cell beyond 6 sigma | day 20729 k = 1: 354 holes, 129,726 cells beyond 6 sigma, worst p = 1.000; day 20733 k = 1: 266 holes, 136,797 cells; day 20729 k = 2 at 2^24: 0 holes, 0 cells beyond 6 sigma, worst z -4.74 (band 0.0015); k = 3: 0 and 0, worst z -5.28; k = 4: 0 and 0, worst z 5.28; day 20733 k = 2: 0 and 0, worst z -4.59; k = 3: 0 and 0, worst z 4.61; k = 5..8 and the 2^27 rows running | FINDING at k = 1, PASS from k = 2 on both days (margin: 1 of 8 on random states) |
| Q2b | t-bit avalanche on the round-0 input (32 bits in), 2^24 (and 2^28) states | k = 0 (the init alone, fired: 12,439 holes) | no cell beyond 6 sigma | k = 1: 0 holes, 218 cells beyond 6 sigma, worst p = 0.7427 (t bit 31 to state bit 53), 18 line-index cells beyond 6 sigma. k = 2..8 at 2^24: 0 cells beyond 6 sigma, worst z 3.7 to 4.7 (the maximum of 16,384 normals is about 4.1); k = 2 and 3 at 2^28 states: 0 cells beyond 6 sigma, worst z -4.30 and 4.76, band 0.00018; k = 4 at 2^28 running | FINDING at k = 1, PASS from k = 2 (margin: 1 of 8) |
| Q2 | single-bit avalanche, random states, 2^24 (and 2^27) states | `one` at k = 8 (fired: 1959 holes); `weak` fires at k = 1 only, not at k = 8 (see Q2) | no cell beyond 6 sigma | day 20729 k = 1: 354 holes, 129,726 cells beyond 6 sigma, worst p = 1.000; day 20733 k = 1: 266 holes, 136,797 cells; day 20729 k = 2 at 2^24: 0 holes, 0 cells beyond 6 sigma, worst z -4.74 (band 0.0015); k = 3: 0 and 0, worst z -5.28; k = 4: 0 and 0, worst z 5.28; day 20733 k = 2: 0 and 0, worst z -4.59; k = 3: 0 and 0, worst z 4.61; k = 4: 0 and 0, worst z 4.67; k = 5..8 and the 2^27 rows running | FINDING at k = 1, PASS from k = 2 on both days (margin: 1 of 8 on random states) |
| Q2b | t-bit avalanche on the round-0 input (32 bits in), 2^24 (and 2^28) states | k = 0 (the init alone, fired: 12,439 holes) | no cell beyond 6 sigma | k = 1: 0 holes, 218 cells beyond 6 sigma, worst p = 0.7427 (t bit 31 to state bit 53), 18 line-index cells beyond 6 sigma. k = 2..8 at 2^24: 0 cells beyond 6 sigma, worst z 3.7 to 4.7 (the maximum of 16,384 normals is about 4.1); k = 2, 3, 4 at 2^28 states: 0 cells beyond 6 sigma, worst z -4.30, 4.76, -4.64, band 0.00018. Day 20733: k = 1 has 502 cells beyond 6 sigma, worst p = 0.7595 (t bit 31 to state bit 127); k = 2..8 at 2^24: 0 cells, worst z 3.9 to 4.6; its 2^28 rows running | FINDING at k = 1 on both days, PASS from k = 2 on both days (margin: 1 of 8) |
| Q3 | differential multiplicity, 576 low-weight input differences, 2^20 pairs each | `nomul` at k = 1 (fired: 17,289 deterministic output bits at 4,096 pairs) | no multiplicity 4 or more, no deterministic bit | k = 1: 695 deterministic output bits over the 576 differences (max 35 in one difference) on day 20729, 537 (max 40) on 20733; k = 2..7: 0 deterministic bits, max multiplicity 1, no pair with 2 zero words, both days; k = 8 running | FINDING at k = 1 (deterministic bits), PASS from k = 2 |
| Q4 | single-bit linear correlations, random states, 2^26 samples | k = 0 (the identity, fired: c = 1.0 on the diagonal) | no cell beyond 6 sigma (band 0.00073) | day 20729 k = 1..7 and day 20733 k = 1..8: worst c between 0.00055 and 0.00062 (z 4.5 to 5.1; the expected maximum of 262,144 normals is 4.8), 0 cells beyond 6 sigma on every row; day 20729 k = 8 running | PASS from k = 1 (BOUND) |
| Q4b | t-bit linear correlations on the round-0 input, 2^26 samples | k = 0 (fired: c = 1.0, t bit 0 to s[8] bit 0) | no cell beyond 6 sigma | both days, k = 1..8: worst c 0.00046 to 0.00059 (z 3.7 to 4.9 over 16,384 cells), 0 cells beyond 6 sigma | PASS from k = 1 (BOUND) |
@ -88,6 +88,7 @@ run at k = 1 fired it too: 14,364 holes). The `one` plant is the firing check of
| 20729 | 4 | 2^24 | 0 | 0 | in 295 (word 9) to out 346 (word 10) | 0.50064 (z 5.28) | 0 | inside |
| 20733 | 2 | 2^24 | 0 | 0 | in 260 (word 8) to out 450 (word 14) | 0.49944 (z -4.59) | 0 | inside |
| 20733 | 3 | 2^24 | 0 | 0 | in 61 (word 1) to out 495 (word 15) | 0.50056 (z 4.61) | 0 | inside |
| 20733 | 4 | 2^24 | 0 | 0 | in 350 (word 10) to out 23 (word 0) | 0.50057 (z 4.67) | 0 | inside |
Reading: one application on a random 512-bit state leaves 354 deterministic cells (an input bit that always
or never flips a given output bit) and 129,726 of 262,144 cells beyond 6 sigma; 7,930 of the 11,264 cells that
@ -112,6 +113,16 @@ Logs: sac0-20729-k<k>.log. Plant k = 0 (the init alone) fired: 12,439 holes of 1
| 20729 | 8 | 2^24 | 0 | 0 | t bit 13 to bit 9 | 0.49947 (z -4.33) | 0 | inside |
| 20729 | 2 | 2^28 | 0 | 0 | t bit 8 to bit 352 | 0.49987 (z -4.30) | 0 | inside (band 0.00018) |
| 20729 | 3 | 2^28 | 0 | 0 | t bit 26 to bit 97 | 0.50015 (z 4.76) | 0 | inside (band 0.00018) |
| 20729 | 4 | 2^28 | 0 | 0 | t bit 17 to bit 8 | 0.49986 (z -4.64) | 0 | inside (band 0.00018) |
| 20733 | 0 | 65,536 | 12,448 | 16,094 | t bit 0 to bit 0 | 0.0000 | 704 of 704 | DISTINGUISHED (plant) |
| 20733 | 1 | 2^24 | 0 | 502 | t bit 31 to state bit 127 (word 3) | 0.7595 | pending | DISTINGUISHED |
| 20733 | 2 | 2^24 | 0 | 0 | t bit 11 to bit 337 | 0.49946 (z -4.45) | 0 | inside |
| 20733 | 3 | 2^24 | 0 | 0 | t bit 23 to bit 219 | 0.49952 (z -3.97) | 0 | inside |
| 20733 | 4 | 2^24 | 0 | 0 | t bit 23 to bit 220 | 0.50051 (z 4.19) | 0 | inside |
| 20733 | 5 | 2^24 | 0 | 0 | t bit 29 to bit 48 | 0.49948 (z -4.25) | 0 | inside |
| 20733 | 6 | 2^24 | 0 | 0 | t bit 20 to bit 404 | 0.49950 (z -4.13) | 0 | inside |
| 20733 | 7 | 2^24 | 0 | 0 | t bit 29 to bit 239 | 0.49953 (z -3.86) | 0 | inside |
| 20733 | 8 | 2^24 | 0 | 0 | t bit 2 to bit 370 | 0.50056 (z 4.62) | 0 | inside |
Why k = 1 has deterministic cells and k = 2 has none (read from the code, `memhard::qr` and `mixer`): a
difference whose lowest set bit is at position j keeps that lowest bit through an XOR with a constant, through a