chore: consider worst cases

Author: douglaz

README.md

@@ -162,53 +162,50 @@ For planning purposes, consider the 99th percentile times shown in the table abo
 ### Real world example using the `benchmark` command
 ```bash
 $ cargo run --release -F alkali -- benchmark -i 1 -t 16
-Using 16 threads for benchmark
-Starting benchmark with 1 iterations across 16 threads...
-
 Benchmark results:
 Threads: 16
-Total time: 30.95s
+Total time: 30.79s
 Total iterations: 16
-Global average time per derivation: 1934.24ms
+Global average time per derivation: 1924.35ms
 Global derivations per second: 0.52
-Thread average time per derivation: 30.95s
+Thread average time per derivation: 30.79s
 Thread derivations per second: 0.03
 
 Estimated time to brute-force one preimage/key pair:
-bits │ systematic (worst) │  random (expected) │ random (99th %ile)
------┼--------------------┼--------------------┼-------------------
-   1 │                31s │                31s │           2min 23s
-   2 │                31s │                31s │           2min 23s
-   3 │                31s │                31s │           2min 23s
-   4 │                31s │                31s │           2min 23s
-   5 │                31s │                31s │           2min 23s
-   6 │            1min 2s │                31s │           2min 23s
-   7 │            2min 4s │            1min 2s │           4min 45s
-   8 │            4min 8s │            2min 4s │           9min 30s
-   9 │           8min 15s │            4min 8s │           19min 0s
-  10 │          16min 30s │           8min 15s │           38min 0s
-  11 │           33min 1s │          16min 30s │           1h 16min
-  12 │            1h 6min │           33min 1s │           2h 32min
-  13 │           2h 12min │            1h 6min │            5h 4min
-  14 │           4h 24min │           2h 12min │           10h 8min
-  15 │           8h 48min │           4h 24min │          20h 16min
-  16 │          17h 36min │           8h 48min │             1d 17h
-  17 │             1d 11h │          17h 36min │              3d 9h
-  18 │             2d 22h │             1d 11h │             6d 18h
-  19 │             5d 21h │             2d 22h │            13d 12h
-  20 │            11d 18h │             5d 21h │             27d 1h
-  21 │            23d 11h │            11d 18h │             54d 1h
-  22 │            46d 23h │            23d 11h │            108d 2h
-  23 │            93d 22h │            46d 23h │            216d 5h
-  24 │           187d 19h │            93d 22h │             1y 67d
-  25 │             1y 10d │           187d 19h │            2y 134d
-  26 │             2y 21d │             1y 10d │            4y 269d
-  27 │             4y 41d │             2y 21d │            9y 172d
-  28 │             8y 83d │             4y 41d │           18y 344d
-  29 │           16y 165d │             8y 83d │           37y 323d
-  30 │           32y 331d │           16y 165d │           75y 281d
-  31 │           65y 297d │           32y 331d │          151y 197d
-  32 │          131y 228d │           65y 297d │           303y 28d
+bits │ systematic (worst) │  random (expected) │ random (99th %ile) │ random (99.9th %ile)
+-----┼--------------------┼--------------------┼--------------------┼-------------------
+   1 │                31s │                31s │           2min 22s │           3min 33s
+   2 │                31s │                31s │           2min 22s │           3min 33s
+   3 │                31s │                31s │           2min 22s │           3min 33s
+   4 │                31s │                31s │           2min 22s │           3min 33s
+   5 │                31s │                31s │           2min 22s │           3min 33s
+   6 │            1min 2s │                31s │           2min 22s │           3min 33s
+   7 │            2min 3s │            1min 2s │           4min 44s │            7min 5s
+   8 │            4min 6s │            2min 3s │           9min 27s │          14min 11s
+   9 │           8min 13s │            4min 6s │          18min 54s │          28min 21s
+  10 │          16min 25s │           8min 13s │          37min 49s │          56min 43s
+  11 │          32min 51s │          16min 25s │           1h 16min │           1h 53min
+  12 │            1h 6min │          32min 51s │           2h 31min │           3h 47min
+  13 │           2h 11min │            1h 6min │            5h 2min │           7h 34min
+  14 │           4h 23min │           2h 11min │           10h 5min │           15h 7min
+  15 │           8h 45min │           4h 23min │          20h 10min │              1d 6h
+  16 │          17h 31min │           8h 45min │             1d 16h │             2d 12h
+  17 │             1d 11h │          17h 31min │              3d 9h │              5d 1h
+  18 │             2d 22h │             1d 11h │             6d 17h │             10d 2h
+  19 │             5d 20h │             2d 22h │            13d 11h │             20d 4h
+  20 │            11d 16h │             5d 20h │            26d 21h │             40d 8h
+  21 │             23d 9h │            11d 16h │            53d 19h │            80d 16h
+  22 │            46d 17h │             23d 9h │           107d 13h │            161d 8h
+  23 │            93d 10h │            46d 17h │            215d 2h │           322d 16h
+  24 │           186d 20h │            93d 10h │             1y 65d │            1y 280d
+  25 │              1y 8d │           186d 20h │            2y 130d │            3y 195d
+  26 │             2y 17d │              1y 8d │            4y 260d │             7y 24d
+  27 │             4y 34d │             2y 17d │            9y 154d │            14y 49d
+  28 │             8y 67d │             4y 34d │           18y 309d │            28y 98d
+  29 │           16y 135d │             8y 67d │           37y 252d │           56y 196d
+  30 │           32y 270d │           16y 135d │           75y 139d │           113y 27d
+  31 │           65y 174d │           32y 270d │          150y 279d │           226y 53d
+  32 │          130y 348d │           65y 174d │          301y 193d │          452y 106d
 
 Search strategy explanation:
 • Systematic search: Partitions search space among threads (worst-case time shown)
@@ -218,5 +215,6 @@ Random search variance:
 • 50th percentile (median): ~0.7× expected time
 • 90th percentile: ~2.3× expected time
 • 99th percentile: ~4.6× expected time
+• 99.9th percentile: ~6.9× expected time
 ```
 ---