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adv-mixer-3 report: Q1 day 20729 closed k=1..8 (uniform at the real first read), day 20730 rows, Q2 k=4 and 20733 k=3, SAT table

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Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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igneum-labs 2026-10-07 19:14:50 +00:00
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docs/analysis/cryptanalysis/report-mixer-3.md
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@ -24,14 +24,14 @@ 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); day 20733 uniform at k = 1 (z -0.71); k = 8 and day 20733 k = 2..8 running under the lock | PASS to k = 7 (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; day 20733 k = 2: 0 and 0, worst z -4.59; k = 4..8 and the 2^27 rows running | FINDING at k = 1, PASS at k = 2 on both days (margin: 1 of 8 on random states) |
| 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) |
| 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) |
| Q5 | rotational-XOR, rotations 1, 8, 16, 2^22 samples | `weak0` at k = 1 (fired: 740 zero-difference words of 2^20 at r = 1, 245 at r = 16) | no zero-difference word above 2 of N, no repeated difference above 3 | both days, k = 1, 2, 3, 4 at 2^22 samples: 0 zero-difference words at every rotation (random expects about 0.001), most frequent per-word difference multiplicity 3 (the birthday expectation at 2^22 draws of 32 bits) | PASS from k = 1 (BOUND: the XOR constants and the odd multiply kill the rotational property inside one application) |
| Q6 | SAT (CaDiCaL) on the round-0 input: find t with a given 22-bit index after k applications | k = 1 solved and verified | solve inside one hour per k, time against the honest 2^10 x k x 130 ops | k = 1: SATISFIABLE in 137 s wall (loaded box); model t = 0x49880000 verifies to the target 0x20eb79. Honest: 2^10 trials of one application is under a millisecond. The solver is already slower than brute force at k = 1 | PASS at k = 1 (BOUND); k = 2..4 RUNNING |
| Q6 | SAT (CaDiCaL) on the round-0 input: find t with a given 22-bit index after k applications | k = 1 solved and verified | solve inside one hour per k, time against the honest 2^10 x k x 130 ops | k = 1: SATISFIABLE in 137 s wall on build-1 (load about 160) and 1,593 s on build-2 (load about 500), the same model t = 0x49880000 both times, verified to the target 0x20eb79 through the real code. Honest: 2^10 trials of one application is under a millisecond. The solver is five orders slower than brute force at k = 1 | PASS at k = 1 (BOUND); k = 2..4 RUNNING (one-hour cap each) |
| Q7 | days: 20733 on every row, 8 fixed day indices on Q1 and Q2 | as above | as above | day 20733 rows land below | RUNNING |
| GPU | any GPU row | n/a | n/a | no GPU on either box | BLOCKED |
@ -55,6 +55,11 @@ Command (build-1), per k: `adv-mixer-3 index --day 20729 --apps k --threads 64`.
| 20729 | 5 | -1.47 | 0 | 872 | 1202 | 0.99 | -0.11 | pending | uniform |
| 20729 | 6 | -0.30 | 0 | 867 | 1185 | 0.01 | -1.62 | pending | uniform |
| 20729 | 7 | -1.04 | 0 | 862 | 1191 | -0.45 | -0.88 | pending | uniform |
| 20729 | 8 | 1.13 | 0 | 863 | 1202 | 1.46 | -0.63 | pending | uniform (the real first read) |
| 20730 | 2 | -0.53 | 0 | 864 | 1217 | -0.36 | -0.19 | pending | uniform (queue 07, run by adv-mixer) |
| 20730 | 3 | -0.78 | 0 | 866 | 1189 | -0.26 | 1.05 | pending | uniform |
| 20730 | 4 | 0.25 | 0 | 865 | 1187 | -0.01 | -0.30 | pending | uniform |
| 20730 | 8 | -1.29 | 0 | 867 | 1188 | 0.73 | 1.00 | pending | uniform |
| 20733 | 0 | 6.2e12 | 4194303 | 0 | 2^32 | 7.8e11 | 2.4e10 | n/a | NON-UNIFORM (plant) |
| 20733 | 1 | -0.71 | 0 | 863 | 1202 | 0.11 | -0.60 | pending | uniform |
@ -80,7 +85,9 @@ run at k = 1 fired it too: 14,364 holes). The `one` plant is the firing check of
| 20729 | 2 | 2^24 | 0 | 0 | in 322 (word 10) to out 373 (word 11) | 0.49942 (z -4.74) | 0 | inside the band |
| 20729 | 3 | 2^24 | 0 | 0 | in 370 (word 11) to out 88 (word 2) | 0.49936 (z -5.28) | 0 | inside |
| 20733 | 1 | 2^24 | 266 | 136,797 | in 30 (word 0) to out 32 (word 1) | 1.0000 | pending | DISTINGUISHED |
| 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 |
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
@ -227,8 +234,18 @@ are wires; constants are folded). Result: `s SATISFIABLE`, 137.06 s wall on the
t = 0x49880000; `adv-mixer-3 verify --day 20729 --apps 1 --t 0x49880000` prints index 0x20eb79, the target.
Honest cost of the same task: about 2^10 random t each through one application, under 2^18 integer operations,
under a millisecond on one core. The solver at k = 1 is five orders slower than the honest search. The queue 08
rows (k = 1..4, both days, one-hour cap) land below.
under a millisecond on one core. The solver at k = 1 is five orders slower than the honest search.
| Day | k | CNF variables | CNF clauses | result | wall | model verified |
|---|---|---|---|---|---|---|
| 20729 | 1 (smoke, build-1) | 33,873 | 112,328 | SATISFIABLE | 137 s | t = 0x49880000, index 0x20eb79 = target |
| 20729 | 1 (queue 08, build-2) | 33,873 | 112,328 | SATISFIABLE | 1,593 s (box at load 500) | the same t |
| 20729 | 2 | pending | pending | running | | |
Reading: the one-application model is a 32-variable problem with 112 k clauses of ripple-carry adders (16
constant multiplies of up to 32 adders each dominate). CaDiCaL needs minutes on it where the honest search needs
a millisecond, and the k = 2 model doubles the clause count. The SAT route to the first read's address is not a
shortcut at k = 1; the rows for k = 2 to 4 say how fast it gets worse.
## Box-hours