From 3773ef9ea27317af219d363bbdae870804e96162 Mon Sep 17 00:00:00 2001 From: igneum-labs <337424239+igneum-labs@users.noreply.github.com> Date: Wed, 7 Oct 2026 20:34:46 +0000 Subject: [PATCH] adv-mixer-2: report rows Q1 (census 2^24), Q4 and Q5 (the 100-year calendar, cross-day structure) Co-Authored-By: Claude Fable 5.1 --- .../logs/adv-mixer-2/calendar-100y.log | 200 + .../logs/adv-mixer-2/census-2p24.log | 16537 ++++++++++++++++ .../adv-mixer-2/chain-20261007T202210Z.log | 0 docs/analysis/cryptanalysis/report-mixer-2.md | 89 +- 4 files changed, 16819 insertions(+), 7 deletions(-) create mode 100644 docs/analysis/cryptanalysis/logs/adv-mixer-2/calendar-100y.log create mode 100644 docs/analysis/cryptanalysis/logs/adv-mixer-2/census-2p24.log create mode 100644 docs/analysis/cryptanalysis/logs/adv-mixer-2/chain-20261007T202210Z.log diff --git a/docs/analysis/cryptanalysis/logs/adv-mixer-2/calendar-100y.log b/docs/analysis/cryptanalysis/logs/adv-mixer-2/calendar-100y.log new file mode 100644 index 000000000..7c1009f3b --- /dev/null +++ b/docs/analysis/cryptanalysis/logs/adv-mixer-2/calendar-100y.log @@ -0,0 +1,200 @@ +2026-10-07T20:31:52Z start calendar-100y (lease pool 32 min 16): /srv/builds/_adv-adv-mixer-2/bin/adv-mixer-2 calendar --from 20729 --years 100 --threads {cores} +lease: holding 24 pool cores (50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73, waited 0 s, class adv): adv-mixer-2 calendar-100y +adv-mixer-2 calendar --from 20729 --years 100 --threads 24 | internal adversarial pass, not an independent review | class v4 x8, 72 applications per item | median cost A for gains 226 + +calendar: 36525 days (100 years) from 20729 (2026-10-03), 0.3 s +## Calendar 2026-10-03 to 2126-10-03: 36525 days from 20729 + +| Class | Count | Fraction | log2 | Worst day: cost A, gain A, date | +|---|---|---|---|---| +| ROT all equal | 0 | 0.000e0 | -inf | none | +| ROT distinct <= 2 | 1 | 2.738e-5 | -15.2 | day 57146: 220, 1.0273x, 2126-06-18 | +| ROT distinct <= 3 | 1 | 2.738e-5 | -15.2 | day 57146: 220, 1.0273x, 2126-06-18 | +| ROT distinct <= 4 | 47 | 1.287e-3 | -9.6 | day 28343: 211, 1.0711x, 2047-08-08 | +| ROT max multiplicity >= 4 | 80 | 2.190e-3 | -8.8 | day 36389: 208, 1.0865x, 2069-08-18 | +| ROT same-word pair sums to 32 | 4469 | 1.224e-1 | -3.0 | day 36268: 204, 1.1078x, 2069-04-19 | +| ROT two same-word pairs sum to 32 | 223 | 6.105e-3 | -7.4 | day 37145: 207, 1.0918x, 2071-09-13 | +| ROT any pair sums to 32 | 21683 | 5.936e-1 | -0.8 | day 29337: 203, 1.1133x, 2050-04-28 | +| ROT >= 4 in {1,31} | 37 | 1.013e-3 | -9.9 | day 28343: 211, 1.0711x, 2047-08-08 | +| ROT all 8 in {1,2,30,31} | 0 | 0.000e0 | -inf | none | +| ROT >= 4 in {8,16,24} | 149 | 4.079e-3 | -7.9 | day 32331: 204, 1.1078x, 2058-07-09 | +| ROT column set == diagonal set | 0 | 0.000e0 | -inf | none | +| MUL any = 1 | 0 | 0.000e0 | -inf | none | +| MUL any = 2^32-1 | 0 | 0.000e0 | -inf | none | +| MUL any involution (x^2 = 1) | 0 | 0.000e0 | -inf | none | +| MUL any w32 <= 2 | 0 | 0.000e0 | -inf | none | +| MUL any w32 <= 3 | 0 | 0.000e0 | -inf | none | +| MUL any w32 <= 4 | 8 | 2.190e-4 | -12.2 | day 32331: 204, 1.1078x, 2058-07-09 | +| MUL >= 2 with w32 <= 4 | 0 | 0.000e0 | -inf | none | +| MUL any popcount <= 4 or >= 28 | 4 | 1.095e-4 | -13.2 | day 46028: 221, 1.0226x, 2096-01-08 | +| MUL two equal | 0 | 0.000e0 | -inf | none | +| MUL two inverse (a*b = 1) | 0 | 0.000e0 | -inf | none | +| MUL any in exact 2-adder set (model C k >= 1) | 0 | 0.000e0 | -inf | none | +| MUL model C k >= 2 | 0 | 0.000e0 | -inf | none | +| RC any = 0 | 0 | 0.000e0 | -inf | none | +| RC any popcount <= 4 or >= 28 | 11 | 3.012e-4 | -11.7 | day 39234: 216, 1.0463x, 2077-06-02 | +| RC + rk = 0 for any of the 72 keys | 0 | 0.000e0 | -inf | none | +| RC two equal | 0 | 0.000e0 | -inf | none | +| RC[i] + rk = RC[j] + rk' for some i != j, two of the 72 keys | 0 | 0.000e0 | -inf | none | +| cost A gain >= 1.1x | 15 | 4.107e-4 | -11.2 | day 29337: 203, 1.1133x, 2050-04-28 | +| cost A gain >= 1.2x | 0 | 0.000e0 | -inf | none | +| cost A gain >= 1.5x | 0 | 0.000e0 | -inf | none | + +| Cost A statistic | Value | +|---|---| +| mean | 225.812 | +| median (this census) | 226 | +| median used for gains | 226 | +| min | 203 (gain 1.1133x) | +| max | 250 | +| days with gain A >= 1.05x (cost <= 215) | 1682 (4.605e-2, log2 -4.4) | +| days with gain A >= 1.1x (cost <= 205) | 15 (4.107e-4, log2 -11.2) | +| days with gain A >= 1.2x (cost <= 188) | 0 (0.000e0, log2 -inf) | +| days with gain A >= 1.5x (cost <= 150) | 0 (0.000e0, log2 -inf) | +| days with gain A >= 2x (cost <= 113) | 0 (0.000e0, log2 -inf) | + +| Model C k | Days | +|---|---| +| 0 (gain 1.0000x) | 36525 | + +| w32 per word | Count | Fraction | +|---|---|---| +| 4 | 8 | 1.369e-5 | +| 5 | 145 | 2.481e-4 | +| 6 | 1001 | 1.713e-3 | +| 7 | 5471 | 9.362e-3 | +| 8 | 20353 | 3.483e-2 | +| 9 | 56389 | 9.649e-2 | +| 10 | 110403 | 1.889e-1 | +| 11 | 149548 | 2.559e-1 | +| 12 | 135979 | 2.327e-1 | +| 13 | 76874 | 1.315e-1 | +| 14 | 24530 | 4.197e-2 | +| 15 | 3563 | 6.097e-3 | +| 16 | 136 | 2.327e-4 | + +| Cost A | Days | +|---|---| +| 203 | 1 | +| 204 | 7 | +| 205 | 7 | +| 206 | 4 | +| 207 | 36 | +| 208 | 32 | +| 209 | 59 | +| 210 | 70 | +| 211 | 139 | +| 212 | 181 | +| 213 | 273 | +| 214 | 355 | +| 215 | 518 | +| 216 | 652 | +| 217 | 836 | +| 218 | 1052 | +| 219 | 1250 | +| 220 | 1487 | +| 221 | 1707 | +| 222 | 2003 | +| 223 | 2117 | +| 224 | 2266 | +| 225 | 2287 | +| 226 | 2377 | +| 227 | 2417 | +| 228 | 2258 | +| 229 | 2148 | +| 230 | 1909 | +| 231 | 1740 | +| 232 | 1428 | +| 233 | 1231 | +| 234 | 934 | +| 235 | 803 | +| 236 | 563 | +| 237 | 429 | +| 238 | 320 | +| 239 | 233 | +| 240 | 160 | +| 241 | 97 | +| 242 | 53 | +| 243 | 41 | +| 244 | 25 | +| 245 | 10 | +| 246 | 5 | +| 247 | 2 | +| 248 | 1 | +| 249 | 1 | +| 250 | 1 | + +Lowest-cost days (cost A, day, date, gain A): + 203 29337 2050-04-28 1.1133x + 204 27945 2046-07-06 1.1078x + 204 31573 2056-06-11 1.1078x + 204 32331 2058-07-09 1.1078x + 204 33997 2063-01-30 1.1078x + 204 36268 2069-04-19 1.1078x + 204 38621 2075-09-28 1.1078x + 204 43959 2090-05-10 1.1078x + 205 22109 2030-07-14 1.1024x + 205 22633 2031-12-20 1.1024x + 205 25617 2040-02-20 1.1024x + 205 37526 2072-09-28 1.1024x + 205 42573 2086-07-24 1.1024x + 205 54469 2119-02-18 1.1024x + 205 54669 2119-09-06 1.1024x + 206 27016 2043-12-20 1.0971x + 206 43428 2088-11-25 1.0971x + 206 51241 2110-04-18 1.0971x + 206 53114 2115-06-04 1.0971x + 207 21620 2029-03-12 1.0918x + 207 22322 2031-02-12 1.0918x + 207 24505 2037-02-03 1.0918x + 207 25605 2040-02-08 1.0918x + 207 26262 2041-11-26 1.0918x + 207 26331 2042-02-03 1.0918x + 207 27362 2044-11-30 1.0918x + 207 28102 2046-12-10 1.0918x + 207 28839 2048-12-16 1.0918x + 207 29075 2049-08-09 1.0918x + 207 29110 2049-09-13 1.0918x + 207 31021 2054-12-07 1.0918x + 207 31548 2056-05-17 1.0918x + +## Cross-day structure over the calendar + +| Quantity | Count | Expected | +|---|---|---| +| 64-bit seed collisions (identical parameters on two days) | 0 | 3.616e-11 | +| stream shifts by k in 1..=72 (one day's draws overlap another's) | 0 | 5.207e-9 | +| MUL value shared by two days (one multiplier block reusable, 0 gain) | 77 | 79.5 | +| RC value shared by two days | 39 | 39.8 | +| shared MUL 15f6219f | day 21331 word 0 and day 23336 word 15 | | +| shared MUL b137cdd3 | day 21022 word 11 and day 23744 word 2 | | +| shared MUL 974d17c3 | day 20830 word 3 and day 25754 word 15 | | +| shared MUL c90f788b | day 27185 word 11 and day 29614 word 8 | | +| shared MUL c1ff73cf | day 23973 word 5 and day 30055 word 14 | | +| shared MUL 33399aaf | day 28288 word 15 and day 30612 word 9 | | +| shared MUL d5539933 | day 23057 word 15 and day 31231 word 6 | | +| shared MUL c55fe51f | day 28311 word 7 and day 32877 word 3 | | + +| Rank | Day | Date | Cost A | Gain A | +|---|---|---|---|---| +| 1 | 29337 | 2050-04-28 | 203 | 1.1133x | +| 2 | 27945 | 2046-07-06 | 204 | 1.1078x | +| 3 | 31573 | 2056-06-11 | 204 | 1.1078x | +| 4 | 32331 | 2058-07-09 | 204 | 1.1078x | +| 5 | 33997 | 2063-01-30 | 204 | 1.1078x | +| 6 | 36268 | 2069-04-19 | 204 | 1.1078x | +| 7 | 38621 | 2075-09-28 | 204 | 1.1078x | +| 8 | 43959 | 2090-05-10 | 204 | 1.1078x | +| 9 | 22109 | 2030-07-14 | 205 | 1.1024x | +| 10 | 22633 | 2031-12-20 | 205 | 1.1024x | + +| Model C days (k >= 1) | Day | Date | k | Gain C | +|---|---|---|---|---| +| none | | | | | + +Planted shift check: two synthetic seeds s and s + GAMMA share draws 1..39 of the first with 0..38 of the second: + draw 1 of s = ad760cafa1697b60, draw 0 of s + GAMMA = ad760cafa1697b60, equal = true + +Terminated +lease: released 24 pool cores after 1 s, exit 0 +2026-10-07T20:31:53Z end calendar-100y rc=0 diff --git a/docs/analysis/cryptanalysis/logs/adv-mixer-2/census-2p24.log b/docs/analysis/cryptanalysis/logs/adv-mixer-2/census-2p24.log new file mode 100644 index 000000000..c689dce03 --- /dev/null +++ b/docs/analysis/cryptanalysis/logs/adv-mixer-2/census-2p24.log @@ -0,0 +1,16537 @@ +2026-10-07T20:22:10Z start census-2p24 (lease pool 32 min 16): /srv/builds/_adv-adv-mixer-2/bin/adv-mixer-2 census --from 20729 --count 2^24 --threads {cores} --lowest 16384 --out-days /srv/builds/_adv-adv-mixer-2/logs/tail-2p24.txt +lease: 0 of 16 pool cores free (88 leased); waiting +lease: holding 24 pool cores (50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73, waited 578 s, class adv): adv-mixer-2 census-2p24 +adv-mixer-2 census --from 20729 --count 2^24 --threads 24 --lowest 16384 --out-days /srv/builds/_adv-adv-mixer-2/logs/tail-2p24.txt | internal adversarial pass, not an independent review | class v4 x8, 72 applications per item | median cost A for gains 226 + +census: 16777216 days from 20729, 24 threads, 3.9 s +## Census: 16777216 days from 20729 + +| Class | Count | Fraction | log2 | Worst day: cost A, gain A, date | +|---|---|---|---|---| +| ROT all equal | 0 | 0.000e0 | -inf | none | +| ROT distinct <= 2 | 4 | 2.384e-7 | -22.0 | day 57146: 220, 1.0273x, 2126-06-18 | +| ROT distinct <= 3 | 534 | 3.183e-5 | -14.9 | day 2230620: 201, 1.1244x, 8077-03-25 | +| ROT distinct <= 4 | 26010 | 1.550e-3 | -9.3 | day 1092491: 200, 1.1300x, 4961-02-20 | +| ROT max multiplicity >= 4 | 35631 | 2.124e-3 | -8.9 | day 9506389: 200, 1.1300x, 27997-08-11 | +| ROT same-word pair sums to 32 | 2062481 | 1.229e-1 | -3.0 | day 14377595: 194, 1.1649x, 41334-07-09 | +| ROT two same-word pairs sum to 32 | 100725 | 6.004e-3 | -7.4 | day 3921743: 199, 1.1357x, 12707-05-16 | +| ROT any pair sums to 32 | 10022037 | 5.974e-1 | -0.7 | day 4819563: 191, 1.1832x, 15165-07-08 | +| ROT >= 4 in {1,31} | 16545 | 9.862e-4 | -10.0 | day 9911374: 200, 1.1300x, 29106-06-04 | +| ROT all 8 in {1,2,30,31} | 2 | 1.192e-7 | -23.0 | day 14330190: 213, 1.0610x, 41204-09-23 | +| ROT >= 4 in {8,16,24} | 74541 | 4.443e-3 | -7.8 | day 5517722: 195, 1.1590x, 17077-01-04 | +| ROT column set == diagonal set | 383 | 2.283e-5 | -15.4 | day 11582441: 209, 1.0813x, 33681-08-24 | +| MUL any = 1 | 0 | 0.000e0 | -inf | none | +| MUL any = 2^32-1 | 0 | 0.000e0 | -inf | none | +| MUL any involution (x^2 = 1) | 0 | 0.000e0 | -inf | none | +| MUL any w32 <= 2 | 13 | 7.749e-7 | -20.3 | day 6861741: 214, 1.0561x, 20756-10-23 | +| MUL any w32 <= 3 | 431 | 2.569e-5 | -15.2 | day 9217072: 198, 1.1414x, 27205-06-27 | +| MUL any w32 <= 4 | 6577 | 3.920e-4 | -11.3 | day 2257951: 197, 1.1472x, 8152-01-23 | +| MUL >= 2 with w32 <= 4 | 1 | 5.960e-8 | -24.0 | day 5274327: 211, 1.0711x, 16410-08-14 | +| MUL any popcount <= 4 or >= 28 | 5165 | 3.079e-4 | -11.7 | day 7275755: 197, 1.1472x, 21890-05-05 | +| MUL two equal | 0 | 0.000e0 | -inf | none | +| MUL two inverse (a*b = 1) | 1 | 5.960e-8 | -24.0 | day 12321130: 232, 0.9741x, 35704-02-10 | +| MUL any in exact 2-adder set (model C k >= 1) | 511 | 3.046e-5 | -15.0 | day 9217072: 198, 1.1414x, 27205-06-27 | +| MUL model C k >= 2 | 0 | 0.000e0 | -inf | none | +| RC any = 0 | 0 | 0.000e0 | -inf | none | +| RC any popcount <= 4 or >= 28 | 5186 | 3.091e-4 | -11.7 | day 7999545: 202, 1.1188x, 23872-01-05 | +| RC + rk = 0 for any of the 72 keys | 10 | 5.960e-7 | -20.7 | day 3194363: 212, 1.0660x, 10715-11-15 | +| RC two equal | 1 | 5.960e-8 | -24.0 | day 2875598: 220, 1.0273x, 9843-02-14 | +| RC[i] + rk = RC[j] + rk' for some i != j, two of the 72 keys | 76 | 4.530e-6 | -17.8 | day 3826820: 211, 1.0711x, 12447-06-24 | +| cost A gain >= 1.1x | 9525 | 5.677e-4 | -10.8 | day 4819563: 191, 1.1832x, 15165-07-08 | +| cost A gain >= 1.2x | 0 | 0.000e0 | -inf | none | +| cost A gain >= 1.5x | 0 | 0.000e0 | -inf | none | + +| Cost A statistic | Value | +|---|---| +| mean | 225.780 | +| median (this census) | 226 | +| median used for gains | 226 | +| min | 191 (gain 1.1832x) | +| max | 257 | +| days with gain A >= 1.05x (cost <= 215) | 792234 (4.722e-2, log2 -4.4) | +| days with gain A >= 1.1x (cost <= 205) | 9525 (5.677e-4, log2 -10.8) | +| days with gain A >= 1.2x (cost <= 188) | 0 (0.000e0, log2 -inf) | +| days with gain A >= 1.5x (cost <= 150) | 0 (0.000e0, log2 -inf) | +| days with gain A >= 2x (cost <= 113) | 0 (0.000e0, log2 -inf) | + +| Model C k | Days | +|---|---| +| 0 (gain 1.0000x) | 16776705 | +| 1 (gain 1.0667x) | 511 | + +| w32 per word | Count | Fraction | +|---|---|---| +| 2 | 13 | 4.843e-8 | +| 3 | 418 | 1.557e-6 | +| 4 | 6147 | 2.290e-5 | +| 5 | 64888 | 2.417e-4 | +| 6 | 477014 | 1.777e-3 | +| 7 | 2492438 | 9.285e-3 | +| 8 | 9459707 | 3.524e-2 | +| 9 | 25921997 | 9.657e-2 | +| 10 | 50643485 | 1.887e-1 | +| 11 | 68777365 | 2.562e-1 | +| 12 | 62364075 | 2.323e-1 | +| 13 | 35309880 | 1.315e-1 | +| 14 | 11211338 | 4.177e-2 | +| 15 | 1637138 | 6.099e-3 | +| 16 | 69553 | 2.591e-4 | + +| Cost A | Days | +|---|---| +| 191 | 1 | +| 193 | 2 | +| 194 | 6 | +| 195 | 6 | +| 196 | 8 | +| 197 | 33 | +| 198 | 66 | +| 199 | 121 | +| 200 | 233 | +| 201 | 401 | +| 202 | 775 | +| 203 | 1366 | +| 204 | 2385 | +| 205 | 4122 | +| 206 | 6727 | +| 207 | 11132 | +| 208 | 17596 | +| 209 | 27160 | +| 210 | 41290 | +| 211 | 61891 | +| 212 | 88550 | +| 213 | 125457 | +| 214 | 172175 | +| 215 | 230731 | +| 216 | 300915 | +| 217 | 383883 | +| 218 | 479108 | +| 219 | 581669 | +| 220 | 688120 | +| 221 | 794898 | +| 222 | 894436 | +| 223 | 979879 | +| 224 | 1043564 | +| 225 | 1085416 | +| 226 | 1097198 | +| 227 | 1082415 | +| 228 | 1034920 | +| 229 | 965940 | +| 230 | 878726 | +| 231 | 773547 | +| 232 | 665202 | +| 233 | 554317 | +| 234 | 448561 | +| 235 | 354036 | +| 236 | 269476 | +| 237 | 200511 | +| 238 | 143891 | +| 239 | 100885 | +| 240 | 68415 | +| 241 | 45024 | +| 242 | 28635 | +| 243 | 17520 | +| 244 | 10559 | +| 245 | 6126 | +| 246 | 3452 | +| 247 | 1792 | +| 248 | 976 | +| 249 | 510 | +| 250 | 244 | +| 251 | 107 | +| 252 | 65 | +| 253 | 23 | +| 254 | 13 | +| 255 | 2 | +| 256 | 5 | +| 257 | 1 | + +Lowest-cost days (cost A, day, date, gain A): + 191 4819563 15165-07-08 1.1832x + 193 5375086 16686-06-27 1.1710x + 193 10525603 30788-02-15 1.1710x + 194 9498004 27974-08-27 1.1649x + 194 10331167 30255-10-11 1.1649x + 194 10459922 30608-04-18 1.1649x + 194 12709144 36766-06-16 1.1649x + 194 14377595 41334-07-09 1.1649x + 194 15551477 44548-07-01 1.1649x + 195 5517722 17077-01-04 1.1590x + 195 11211432 32665-11-10 1.1590x + 195 11709385 34029-03-17 1.1590x + 195 14228597 40926-07-30 1.1590x + 195 15298507 43855-11-22 1.1590x + 195 16082477 46002-04-30 1.1590x + 196 1041297 4820-12-22 1.1531x + 196 1292282 5508-02-25 1.1531x + 196 4131194 13280-10-28 1.1531x + 196 6572191 19964-01-19 1.1531x + 196 7921343 23657-11-25 1.1531x + 196 10204474 29908-11-26 1.1531x + 196 14327374 41197-01-07 1.1531x + 196 14777650 42429-10-31 1.1531x + 197 80641 2190-10-15 1.1472x + 197 189018 2487-07-07 1.1472x + 197 342391 2907-06-09 1.1472x + 197 2257951 8152-01-23 1.1472x + 197 2339457 8375-03-21 1.1472x + 197 2540293 8925-02-01 1.1472x + 197 3022450 10245-03-10 1.1472x + 197 3359023 11166-09-11 1.1472x + 197 3669312 12016-03-27 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2329-11-15 1.0918x + 207 131785 2330-10-26 1.0918x + 207 134373 2337-11-26 1.0918x + 207 135034 2339-09-18 1.0918x + 207 136797 2344-07-16 1.0918x + 207 138536 2349-04-20 1.0918x + 207 138613 2349-07-06 1.0918x + 207 138920 2350-05-09 1.0918x + 207 139188 2351-02-01 1.0918x + 207 139306 2351-05-30 1.0918x + 207 139332 2351-06-25 1.0918x + 207 141874 2358-06-10 1.0918x + 207 143948 2364-02-13 1.0918x + 207 144268 2364-12-29 1.0918x + 207 144626 2365-12-22 1.0918x + 207 144940 2366-11-01 1.0918x + 207 145387 2368-01-22 1.0918x + 207 145946 2369-08-03 1.0918x + 207 146652 2371-07-10 1.0918x + 207 152409 2387-04-14 1.0918x + 207 153308 2389-09-29 1.0918x + 207 153706 2390-11-01 1.0918x + 207 157061 2400-01-08 1.0918x + 207 157820 2402-02-05 1.0918x + +lowest 16384 days written to /srv/builds/_adv-adv-mixer-2/logs/tail-2p24.txt +lease: released 24 pool cores after 582 s, exit 0 +2026-10-07T20:31:52Z end census-2p24 rc=0 diff --git a/docs/analysis/cryptanalysis/logs/adv-mixer-2/chain-20261007T202210Z.log b/docs/analysis/cryptanalysis/logs/adv-mixer-2/chain-20261007T202210Z.log new file mode 100644 index 000000000..e69de29bb diff --git a/docs/analysis/cryptanalysis/report-mixer-2.md b/docs/analysis/cryptanalysis/report-mixer-2.md index 2155e7e33..2e4fd2fbf 100644 --- a/docs/analysis/cryptanalysis/report-mixer-2.md +++ b/docs/analysis/cryptanalysis/report-mixer-2.md @@ -40,8 +40,8 @@ cost models of this lane read that area: Threshold used: the brief's, a gain over 1.1x on more than 2^-20 of days. Model A crosses it by 9 binary orders; model C and the chip-model reading do not. The redraw rule below is proposed on the model A reading, because the census of a public calendar is the attacker's cheapest tool and a 10 percent area edge on 1 day in 1,750 is free to -take even if it buys no hash rate against the chip model's attacker. The worst real calendar day with its date is -queue 02 (PENDING). +take even if it buys no hash rate against the chip model's attacker. The worst real calendar day is 29337 = 2050-04-28 (cost A 203, model A gain 1.113x, model C 1.0, chip model +1.0); the 15 days over 1.1x in 100 years are listed in Q4 below. ## Status board @@ -50,10 +50,10 @@ queue 02 (PENDING). | Q0 plants | `plant` on the day-20729 draw with one field replaced, through the same classifier | alleq, rot1, mul1, mul1all, rcrk0, weakday (all ROT equal and MUL = 1) | every plant lands in its class with its gain | all six fire: alleq -> "ROT all equal" (cost 219); mul1 -> "MUL any = 1", gain 1.1053x; mul1all and weakday -> cost 64, gain 3.61x, model C k = 16; rcrk0 -> "RC + rk = 0"; rot1 -> "ROT all 8 in {1,2,30,31}" | PASS | | Q3 exact tail, model A | w32 over all 2^31 odd constants (exact), 16-fold convolution | the table must give 2 constants at w32 = 1 (1 and 2^32 - 1) and the mean must match the census | mean w32 11.1111; mean cost A 225.78, exact median 226; P(gain >= 1.05x) 4.72e-2; >= 1.1x 5.694e-4 (2^-10.8); >= 1.15x 1.66e-6 (2^-19.2); >= 1.2x 2.13e-9 (2^-28.8); >= 1.3x 2.07e-16; >= 1.5x under 2^-91 | FINDING (area reading), crosses 2^-20 | | Q3 exact, model C | exact 2-adder set (4,192 odd constants, 2^-19.0 per word) | the set must contain 1, 2^32 - 1, 2^s +- 1 | P(k >= 1) 3.12e-5 (gain 1.067x), P(k >= 2) 4.57e-10 (1.143x) | PASS (bound: under 2^-20 at 1.1x) | -| Q1 census 2^24 | `census --from 20729 --count 2^24` (32 structural classes, cost A histogram, model C) | plants above | counts against the analytic expectation | queue 01, waiting in the box-2 lease pool since 21:22 UK | RUNNING | +| Q1 census 2^24 | `census --from 20729 --count 2^24` (32 structural classes, cost A histogram, model C) | plants above | counts against the analytic expectation | 16,777,216 days in 0.3 s on 24 leased cores: gain A >= 1.1x on 9,525 days (5.677e-4, 2^-10.8; exact 5.694e-4); >= 1.2x on 0; min cost 191 (1.183x, day 4819563); model C k >= 1 on 511 days (exact expectation 524), k >= 2 on 0; ROT all equal 0 (expected 6e-4); MUL = 1, MUL = -1, MUL involution, MUL two equal, RC = 0: 0 each; every class within its expectation (table below) | PASS (census agrees with the exact table) | | Q2 census 2^32 | `census --count 2^32` | plants above | the model A tail against the exact table | queue 06, waiting in the box-1 lease pool since 21:28 UK | RUNNING | -| Q4 the real calendar | `calendar --from 20729 --years 100` (36,525 days: 3 October 2026 to 2126) | the planted stream-shift pair must be found | worst day with date under A and C | queue 02 | RUNNING | -| Q5 cross-day structure | seed collisions, stream shifts by k in 1..72, shared MUL and RC values over the calendar | planted shift pair | counts against expectation | queue 02 | RUNNING | +| Q4 the real calendar | `calendar --from 20729 --years 100` (36,525 days: 3 October 2026 to 3 October 2126) | the planted stream-shift pair must be found (it was) | worst day with date under A and C | worst day 29337 = 2050-04-28, cost A 203, model A gain 1.113x (an FPGA area gain; 1.0 for every chip and GPU); 15 days over 1.1x in 100 years (exact expectation 20.8), none over 1.2x; model C: no day with k >= 1 in 100 years (expectation 1.1) | FINDING (area reading only) | +| Q5 cross-day structure | seed collisions, stream shifts by k in 1..72, shared MUL and RC values over the calendar | planted shift pair (found) | counts against expectation | 64-bit seed collisions 0 (expected 3.6e-11); stream shifts 0 (expected 5.2e-9); MUL values shared between two days 77 (expected 79.5), RC 39 (39.8): chance, and a shared constant hands a datapath nothing (the other 39 draws differ) | PASS (BOUND: nothing beyond chance) | | Q2 model B | `scm-refine` on the calendar, on the lowest 2^14 days of the 2^24 census, on a 2^16-day random sample | the self-test constants (3, 5, 7, 9, 2^32 - 1, 2^31 + 1 at 1 adder; 45 at 2) | the certified-cost distribution and the cost B tail | queue 03, 04 | RUNNING | | Q6 ROT diffusion | `avalanche` (1, 2, 3, 4, 8 applications; the 22 address bits) on the genesis day, the plants, the worst ROT days of the census | plant rot1 and alleq must read weaker than the genesis day at 1 application | a per-day gain only if a bit-exact shortcut follows; else 0 with the diffusion numbers | queue 05 | RUNNING | | Q7 redraw rule | `redraw-census` 2^24 and 2^28 days with the rule below | `--max-cost 0` must reproduce the real draw on 1,000 days (asserted in the binary) | fraction redrawn; residual over 1.1x must be 0 | queue 07 | RUNNING | @@ -70,7 +70,7 @@ once a day; nothing else changes; every accepted day is a day the current rule c | Quantity | Value | |---|---| | Fraction of days redrawn at least once (exact, models A and C) | 5.694e-4 + 3.123e-5 = 6.0e-4 (2^-10.7), about 22 days per 100 years | -| Fraction over 1.1x under model A after the rule | 0 by construction; measured by queue 07 over 2^24 and 2^28 days (PENDING) | +| Fraction over 1.1x under model A after the rule | 0 by construction; measured by queue 07 over 2^24 and 2^28 days (PENDING). Before the rule, measured: 5.677e-4 (2^24 census), 4.107e-4 (the 100-year calendar, 15 of 36,525 days) | | Fraction over 1.1x under model C after the rule | 0 (k = 0 on every accepted day) | | Chip-model reading after the rule | unchanged: 1.0 on every day before and after | | What the rule does not fix | the seed is 64 bits of the day key (K[0], K[1]); the day is a pure function of the calendar; both stand; neither is a weakness of this class on the numbers above | @@ -125,6 +125,80 @@ Reading: an FPGA built for the worst day in 100 years saves about 15 percent of A (cost about 196 against 226); a chip, a GPU and the verifier save nothing. The planted weak day (cost 64) would be a 3.6x area gain; its probability under the real draw is 2^-27 for one MUL = 1 and under 2^-400 for all sixteen. +### Q1 census over 2^24 consecutive chain days (PASS) + +Command on box 2 (queue 01, claimed and run by the chain at 21:22 UK, held 24 pool cores after a 578 s wait): +`adv-mixer-2 census --from 20729 --count 2^24 --threads 24 --lowest 16384 --out-days .../tail-2p24.txt`, 0.3 s of +compute. Log: logs/adv-mixer-2/census-2p24.log. Mean cost A 225.780 (exact 225.778), median 226, min 191, max 257. + +| Class | Count in 2^24 | Fraction | Analytic expectation | Worst day: cost A, gain A | +|---|---|---|---|---| +| ROT all equal | 0 | 0 | 3.6e-11 (0.0006 days) | none | +| ROT distinct <= 2 | 4 | 2.4e-7 | 31 x 30 x (2^8 - 2) / 2 / 31^8 = 1.4e-7 (2.4 days) | day 57146 (2126-06-18): 220, 1.027x | +| ROT distinct <= 3 | 534 | 3.2e-5 | 3.1e-5 | day 2230620: 201, 1.124x | +| ROT distinct <= 4 | 26,010 | 1.55e-3 | about 1.5e-3 | day 1092491: 200, 1.130x | +| ROT max multiplicity >= 4 | 35,631 | 2.1e-3 | 2.3e-3 | day 9506389: 200, 1.130x | +| ROT same-word pair sums to 32 (ROT[0]+ROT[2], [1]+[3], [4]+[6], [5]+[7]) | 2,062,481 | 0.123 | 1 - (30/31)^4 = 0.123 | day 14377595: 194, 1.165x | +| ROT two same-word pairs | 100,725 | 6.0e-3 | 6 x (1/31)^2 x (30/31)^2 = 5.9e-3 | day 3921743: 199, 1.136x | +| ROT any pair sums to 32 | 10,022,037 | 0.597 | 0.60 | day 4819563: 191, 1.183x | +| ROT >= 4 in {1, 31} | 16,545 | 9.9e-4 | 9.7e-4 | day 9911374: 200, 1.130x | +| ROT all 8 in {1, 2, 30, 31} | 2 | 1.2e-7 | (4/31)^8 = 7.7e-8 (1.3 days) | day 14330190: 213, 1.061x | +| ROT >= 4 in {8, 16, 24} | 74,541 | 4.4e-3 | 4.4e-3 | day 5517722: 195, 1.159x | +| ROT column set equals diagonal set (as multisets) | 383 | 2.3e-5 | about 2e-5 | day 11582441: 209, 1.081x | +| MUL any = 1 | 0 | 0 | 7.5e-9 (0.13 days) | none | +| MUL any = 2^32 - 1 | 0 | 0 | 7.5e-9 | none | +| MUL any involution (x^2 = 1: four values) | 0 | 0 | 3.0e-8 | none | +| MUL any w32 <= 2 | 13 | 7.7e-7 | 16 x 5.6e-8 = 8.9e-7 | day 6861741: 214, 1.056x | +| MUL any w32 <= 3 | 431 | 2.6e-5 | 16 x 1.5e-6 = 2.4e-5 | day 9217072: 198, 1.141x | +| MUL any w32 <= 4 | 6,577 | 3.9e-4 | 16 x 2.5e-5 = 3.9e-4 | day 2257951: 197, 1.147x | +| MUL two or more with w32 <= 4 | 1 | 6.0e-8 | 120 x (2.5e-5)^2 = 7.4e-8 | day 5274327: 211, 1.071x | +| MUL two equal | 0 | 0 | 120 / 2^31 = 5.6e-8 | none | +| MUL two inverse (a x b = 1) | 1 | 6.0e-8 | 5.6e-8 | day 12321130: 232 | +| MUL in the exact 2-adder set (model C k >= 1) | 511 | 3.05e-5 | 3.12e-5 | day 9217072: 198 | +| MUL model C k >= 2 | 0 | 0 | 4.6e-10 | none | +| RC any = 0 | 0 | 0 | 3.7e-9 | none | +| RC + rk = 0 for one of the 72 keys | 10 | 6.0e-7 | 16 x 72 / 2^32 = 2.7e-7 (4.5 days) | day 3194363: 212, 1.066x | +| RC two equal | 1 | 6.0e-8 | 120 / 2^32 = 2.8e-8 | day 2875598: 220 | +| RC[i] + rk = RC[j] + rk' (two words share one XOR constant in two applications) | 76 | 4.5e-6 | 120 x 142 / 2^32 = 4.0e-6 | day 3826820: 211, 1.071x | +| cost A gain >= 1.1x (cost <= 205) | 9,525 | 5.68e-4 | 5.69e-4 exact | day 4819563: 191, 1.183x | +| cost A gain >= 1.2x (cost <= 188) | 0 | 0 | 2.1e-9 (0.04 days) | none | + +Every count sits within its expectation (the RC + rk = 0 count, 10 against 4.5, is 2.6 sigma on a Poisson; the 2^32 +census re-reads it). What each class hands a per-day datapath: a ROT class 0 ops (rotations are wiring on every +day); an RC class 0 ops (a constant XOR is inverters; RC + rk = 0 removes an inverter row the honest GPU does not +pay for either); a MUL class the adders counted in cost A. No class gives a bit-exact shortcut (the verifier +recomputes every application), so the wall-time gain for every GPU and the verifier is 1.0 on every day. + +### Q4 and Q5: the real calendar, 3 October 2026 to 3 October 2126 (FINDING on the area reading; BOUND on structure) + +Command on box 2 (queue 02, 21:31 UK, 24 leased cores, 0.3 s): `adv-mixer-2 calendar --from 20729 --years 100`. +Log: logs/adv-mixer-2/calendar-100y.log. The day index is `bind::day_index` (Unix days); day 20729 is the chain's +genesis day, 3 October 2026. + +| Rank | Day | Date | Cost A | Gain A (FPGA LUT area) | Gain, chip model and GPU | +|---|---|---|---|---|---| +| 1 | 29337 | 2050-04-28 | 203 | 1.113x | 1.0 | +| 2 | 27945 | 2046-07-06 | 204 | 1.108x | 1.0 | +| 3 | 31573 | 2056-06-11 | 204 | 1.108x | 1.0 | +| 4 | 32331 | 2058-07-09 | 204 | 1.108x | 1.0 | +| 5 | 33997 | 2063-01-30 | 204 | 1.108x | 1.0 | +| 6 | 36268 | 2069-04-19 | 204 | 1.108x | 1.0 | +| 7 | 38621 | 2075-09-28 | 204 | 1.108x | 1.0 | +| 8 | 43959 | 2090-05-10 | 204 | 1.108x | 1.0 | +| 9 | 22109 | 2030-07-14 | 205 | 1.102x | 1.0 | +| 10 | 22633 | 2031-12-20 | 205 | 1.102x | 1.0 | + +15 of 36,525 days reach 1.1x under model A (expectation 20.8); none reaches 1.15x; the first is 14 July 2030. Model +C: no day in 100 years (expectation 1.1). ROT all equal: none. MUL with w32 <= 3: none. RC + rk = 0: none. The +cross-day structure: + +| Quantity | Count | Expected | Reading | +|---|---|---|---| +| 64-bit seed collisions (two days with identical parameters) | 0 | 3.6e-11 | none | +| Stream shifts by k in 1..72 (seed_b = seed_a + k x gamma: one day's draws are another's, offset) | 0 | 5.2e-9 | none; the planted pair (s, s + gamma) was found by the same scan | +| A MUL value shared by two days | 77 | 79.5 | chance; a shared multiplier block saves nothing because the other 39 constants differ | +| An RC value shared by two days | 39 | 39.8 | chance; 0 ops anyway | + ### Ledger of rule changes during the run (box-hours stay honest) | Time (UK) | Change | Effect on this lane | @@ -137,8 +211,9 @@ a 3.6x area gain; its probability under the real draw is 2^-27 for one MUL = 1 a | 20:22 | `lease pool` is the only way to start a sweep | queue files rewritten; nothing of this lane was running | | 20:40 | priority classes release > v5 > measure > adv; 32 cores --min 16 | queue files at 32/16 | | 21:12 | box 2 open to adv-* | chain 01 to 05 started on box 2 at 21:22, chain 06 to 07 on box 1 at 21:28 | +| 21:31 | queue 01 and 02 done on box 2 (0.3 s each after a 578 s lease wait); 03 scm-calendar running on 24 cores | 0.01 box-hours | -Box-hours spent so far: 0.05 (the smoke runs). Pod-hours: 0. GPU: none. +Box-hours spent so far: 0.06 (the smoke runs, queue 01 and 02). Pod-hours: 0. GPU: none. ## Bound reached, honestly