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Merge pull request #1 from douglaz/fixed_estimates
chore: improving estimates
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‎README.md‎

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@@ -147,37 +147,37 @@ The table below shows realistic scenarios:
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* 🖥️ **16 threads** (e.g. 16-core/64GB RAM desktop machine)
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* 🏭 **2048 threads** (e.g. 64×32-core/128GB RAM machines on some cloud provider)
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| Bits | 16 threads 🖥️<br>(**systematic search**) | 2048 threads 🏭<br>(**systematic search**) | 2048 threads 🏭<br>(**random search**) | | |
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|------|------------------------------------------|---------------------------------------------|----------------------------------------|-------------------|---------------------|
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| | Worst-case time | Worst-case time | Expected time | 99th percentile | 99.9th percentile |
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| 1‑5 | 30 s | 30 s | 30 s | 2 min 19 s | 3 min 27 s |
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| 6 | 1 min 0 s | 30 s | 30 s | 2 min 19 s | 3 min 27 s |
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| 7 | 2 min 0 s | 30 s | 30 s | 2 min 19 s | 3 min 27 s |
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| 8 | 4 min 8 s | 30 s | 30 s | 2 min 19 s | 3 min 27 s |
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| 9 | 8 min 0 s | 30 s | 30 s | 2 min 19 s | 3 min 27 s |
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| 10 | 16 min 30 s | 30 s | 31 s | 2 min 23 s | 3 min 33 s |
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| 11 | 33 min 1 s | 30 s | 35 s | 2 min 41 s | 4 min 1 s |
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| 12 | 1 h 6 min | 30 s | 47 s | 3 min 36 s | 5 min 24 s |
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| 13 | 2 h 12 min | 1 min 0 s | 1 min 17 s | 5 min 55 s | 8 min 53 s |
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| 14 | 4 h 24 min | 2 min 0 s | 2 min 17 s | 10 min 31 s | 15 min 47 s |
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| 15 | 8 h 48 min | 4 min 0 s | 4 min 17 s | 19 min 44 s | 29 min 36 s |
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| 16 | 17 h 36 min | 8 min 0 s | 8 min 20 s | 38 min 24 s | 57 min 36 s |
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| 17 | 1 d 11 h | 16 min 0 s | 16 min 19 s | 1 h 15 m | 1 h 52 m |
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| 18 | 2 d 22 h | 32 min 0 s | 32 min 20 s | 2 h 29 m | 3 h 43 m |
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| 19 | 5 d 21 h | 1 h 4 m | 1 h 4 m | 4 h 55 m | 7 h 22 m |
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| 20 | 11 d 9 h | 2 h 8 m | 2 h 8 m | 9 h 52 m | 14 h 48 m |
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| 21 | 23 d 11 h | 4 h 16 m | 4 h 16 m | 19 h 44 m | 1 d 5 h |
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| 22 | 46 d 23 h | 8 h 32 m | 8 h 32 m | 1 d 15 h | 2 d 11 h |
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| 23 | 91 d 1 h | 17 h 4 m | 17 h 4 m | 3 d 6 h | 4 d 21 h |
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| 24 | 182 d 1 h | 1 d 10 h | 1 d 10 h | 6 d 13 h | 9 d 18 h |
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| 25 | 364 d 2 h | 2 d 20 h | 2 d 20 h | 13 d 2 h | 19 d 12 h |
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| 26 | 728 d 4 h | 5 d 17 h | 5 d 17 h | 26 d 1 h | 39 d 1 h |
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| 27 | 1456 d 8 h | 11 d 9 h | 11 d 9 h | 52 d 4 h | 78 d 6 h |
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| 28 | 8 y 83 d | 22 d 18 h | 22 d 18 h | 104 d 8 h | 156 d 12 h |
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| 29 | 16 y 165 d | 45 d 12 h | 45 d 12 h | 208 d 16 h | 312 d 24 h |
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| 30 | 32 y 331 d | 91 d | 91 d | 417 d 8 h | 1 y 261 d |
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| 31 | 65 y 297 d | 182 d | 182 d | 2 y 105 d | 3 y 157 d |
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| 32 | 131 y 228 d | 364 d | 364 d | 4 y 212 d | 6 y 318 d |
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| Bits | 16 threads 🖥️<br>(**systematic search**) | 2048 threads 🏭<br>(**systematic search**) | 2048 threads 🏭<br>(**random search**) | | |
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|------|------------------------------------------|---------------------------------------------|----------------------------------------|-----------------------|-----------------------|
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| | Worst-case time | Worst-case time | Expected time | 99th percentile | 99.9th percentile |
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| 1-5 | 30 s | 30 s | 30 s | 2 min 18 s | 3 min 27 s |
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| 6 | 1 min 0 s | 30 s | 30 s | 2 min 18 s | 3 min 27 s |
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| 7 | 2 min 0 s | 30 s | 30 s | 2 min 18 s | 3 min 27 s |
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| 8 | 4 min 0 s | 30 s | 30 s | 2 min 18 s | 3 min 27 s |
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| 9 | 8 min 0 s | 30 s | 30 s | 2 min 18 s | 3 min 27 s |
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| 10 | 16 min 0 s | 30 s | 30 s | 2 min 18 s | 3 min 27 s |
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| 11 | 32 min 0 s | 30 s | 30 s | 2 min 18 s | 3 min 27 s |
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| 12 | 1 h 4 min | 30 s | 30 s | 2 min 18 s | 3 min 27 s |
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| 13 | 2 h 8 min | 1 min 0 s | 1 min 0 s | 4 min 36 s | 6 min 54 s |
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| 14 | 4 h 16 min | 2 min 0 s | 2 min 0 s | 9 min 13 s | 13 min 49 s |
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| 15 | 8 h 32 min | 4 min 0 s | 4 min 0 s | 18 min 25 s | 27 min 38 s |
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| 16 | 17 h 4 min | 8 min 0 s | 8 min 0 s | 36 min 50 s | 55 min 16 s |
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| 17 | 1 d 10 h | 16 min 0 s | 16 min 0 s | 1 h 14 min | 1 h 51 min |
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| 18 | 2 d 20 h | 32 min 0 s | 32 min 0 s | 2 h 27 min | 3 h 41 min |
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| 19 | 5 d 17 h | 1 h 4 min | 1 h 4 min | 4 h 55 min | 7 h 22 min |
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| 20 | 11 d 9 h | 2 h 8 min | 2 h 8 min | 9 h 49 min | 14 h 44 min |
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| 21 | 22 d 18 h | 4 h 16 min | 4 h 16 min | 19 h 39 min | 1 d 5 h |
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| 22 | 45 d 12 h | 8 h 32 min | 8 h 32 min | 1 d 15 h | 2 d 11 h |
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| 23 | 91 d 0 h | 17 h 4 min | 17 h 4 min | 3 d 7 h | 4 d 22 h |
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| 24 | 182 d 0 h | 1 d 10 h | 1 d 10 h | 6 d 13 h | 9 d 20 h |
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| 25 | 364 d 0 h | 2 d 20 h | 2 d 20 h | 13 d 2 h | 19 d 16 h |
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| 26 | 1 y 363 d | 5 d 17 h | 5 d 17 h | 26 d 5 h | 39 d 7 h |
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| 27 | 3 y 361 d | 11 d 9 h | 11 d 9 h | 52 d 10 h | 78 d 14 h |
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| 28 | 7 y 358 d | 22 d 18 h | 22 d 18 h | 104 d 19 h | 157 d 5 h |
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| 29 | 15 y 351 d | 45 d 12 h | 45 d 12 h | 209 d 14 h | 314 d 9 h |
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| 30 | 31 y 338 d | 91 d 1 h | 91 d 1 h | 1 y 54 d | 1 y 264 d |
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| 31 | 63 y 311 d | 182 d 1 h | 182 d 1 h | 2 y 108 d | 3 y 163 d |
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| 32 | 127 y 257 d | 364 d 2 h | 364 d 2 h | 4 y 217 d | 6 y 325 d |
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## Understanding Random Search Variance
@@ -203,65 +203,66 @@ For planning purposes, consider the 99th percentile times shown in the table abo
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### Real world example using the `benchmark` command
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The following is an **example output**. Run this command on your own hardware to get accurate time estimates for your machine.
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```bash
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$ cargo run --release -F alkali -- benchmark -i 1 -t 16
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Using 16 threads for benchmark
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Starting benchmark with 1 iterations across 16 threads...
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Benchmark results:
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Threads: 16
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Total time: 35.48s
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Total time: 29.63s
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Total iterations: 16
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Global average time per derivation: 2217.33ms
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Global derivations per second: 0.45
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Thread average time per derivation: 35.48s
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Global average time per derivation: 1851.87ms
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Global derivations per second: 0.54
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Thread average time per derivation: 29.63s
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Thread derivations per second: 0.03
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Estimated time to brute-force one preimage/key pair:
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Note: This benchmark uses 16 threads with systematic search
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For comparison with random search percentiles, see README table
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bits │ systematic (worst) │ systematic (expected)
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-----┼--------------------┼-------------------
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1 │ 35s │ 35s
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2 │ 35s │ 35s
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3 │ 35s │ 35s
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4 │ 35s │ 35s
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5 │ 35s │ 35s
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6 │ 1min 11s │ 35s
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7 │ 2min 22s │ 1min 11s
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8 │ 4min 44s │ 2min 22s
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9 │ 9min 28s │ 4min 44s
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10 │ 18min 55s │ 9min 28s
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11 │ 37min 51s │ 18min 55s
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12 │ 1h 16min │ 37min 51s
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13 │ 2h 31min │ 1h 16min
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14 │ 5h 3min │ 2h 31min
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15 │ 10h 5min │ 5h 3min
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16 │ 20h 11min │ 10h 5min
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17 │ 1d 16h │ 20h 11min
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18 │ 3d 9h │ 1d 16h
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19 │ 6d 17h │ 3d 9h
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20 │ 13d 11h │ 6d 17h
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21 │ 26d 22h │ 13d 11h
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22 │ 53d 20h │ 26d 22h
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23 │ 107d 15h │ 53d 20h
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24 │ 215d 7h │ 107d 15h
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25 │ 1y 66d │ 215d 7h
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26 │ 2y 131d │ 1y 66d
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27 │ 4y 262d │ 2y 131d
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28 │ 9y 159d │ 4y 262d
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29 │ 18y 319d │ 9y 159d
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30 │ 37y 273d │ 18y 319d
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31 │ 75y 181d │ 37y 273d
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32 │ 150y 362d │ 75y 181d
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Systematic search explanation:
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• Worst-case: One thread gets unlucky and searches entire partition
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• Expected case: Threads find target halfway through their partitions on average
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• No variance: Deterministic partitioning means predictable bounds
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For random search with percentiles, see the README table comparing
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systematic (16 threads) vs random search (2048 threads)
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Estimated time to brute-force with measured derivation time:
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Average derivation time: 29.63s
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Thread count: 16
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bits │ systematic-16t │ systematic-16t │ random-16t │ random-16t │ random-16t
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│ (expected) │ (worst case) │ (expected)│ (99th %) │ (99.9th %)
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-----┼----------------┼----------------┼-----------┼-----------┼------------
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1 │ 30s │ 30s │ 30s │ 2min 16s │ 3min 25s
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2 │ 30s │ 30s │ 30s │ 2min 16s │ 3min 25s
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3 │ 30s │ 30s │ 30s │ 2min 16s │ 3min 25s
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4 │ 30s │ 30s │ 30s │ 2min 16s │ 3min 25s
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5 │ 30s │ 30s │ 30s │ 2min 16s │ 3min 25s
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6 │ 30s │ 59s │ 59s │ 4min 33s │ 6min 49s
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7 │ 59s │ 1min 59s │ 1min 59s │ 9min 6s │ 13min 39s
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8 │ 1min 59s │ 3min 57s │ 3min 57s │ 18min 12s │ 27min 17s
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9 │ 3min 57s │ 7min 54s │ 7min 54s │ 36min 23s │ 54min 35s
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10 │ 7min 54s │ 15min 48s │ 15min 48s │ 1h 13min │ 1h 49min
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11 │ 15min 48s │ 31min 36s │ 31min 36s │ 2h 26min │ 3h 38min
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12 │ 31min 36s │ 1h 3min │ 1h 3min │ 4h 51min │ 7h 17min
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13 │ 1h 3min │ 2h 6min │ 2h 6min │ 9h 42min │ 14h 33min
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14 │ 2h 6min │ 4h 13min │ 4h 13min │ 19h 24min │ 1d 5h
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15 │ 4h 13min │ 8h 26min │ 8h 26min │ 1d 15h │ 2d 10h
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16 │ 8h 26min │ 16h 51min │ 16h 51min │ 3d 6h │ 4d 20h
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17 │ 16h 51min │ 1d 10h │ 1d 10h │ 6d 11h │ 9d 17h
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18 │ 1d 10h │ 2d 19h │ 2d 19h │ 12d 23h │ 19d 10h
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19 │ 2d 19h │ 5d 15h │ 5d 15h │ 25d 21h │ 38d 20h
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20 │ 5d 15h │ 11d 6h │ 11d 6h │ 51d 18h │ 77d 15h
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21 │ 11d 6h │ 22d 11h │ 22d 11h │ 103d 12h │ 155d 6h
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22 │ 22d 11h │ 44d 23h │ 44d 23h │ 207d 0h │ 310d 12h
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23 │ 44d 23h │ 89d 22h │ 89d 22h │ 1y 49d │ 1y 256d
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24 │ 89d 22h │ 179d 19h │ 179d 19h │ 2y 98d │ 3y 147d
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25 │ 179d 19h │ 359d 14h │ 359d 14h │ 4y 196d │ 6y 294d
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26 │ 359d 14h │ 1y 354d │ 1y 354d │ 9y 27d │ 13y 223d
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27 │ 1y 354d │ 3y 343d │ 3y 343d │ 18y 54d │ 27y 81d
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28 │ 3y 343d │ 7y 322d │ 7y 322d │ 36y 108d │ 54y 162d
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29 │ 7y 322d │ 15y 279d │ 15y 279d │ 72y 216d │ 108y 324d
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30 │ 15y 279d │ 31y 192d │ 31y 192d │ 145y 67d │ 217y 283d
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31 │ 31y 192d │ 63y 19d │ 63y 19d │ 290y 135d │ 435y 202d
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32 │ 63y 19d │ 126y 38d │ 126y 38d │ 580y 269d │ 871y 39d
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Explanation:
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• Systematic (expected): Average case with 16 threads, each searching half their partition
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• Systematic (worst): One thread searches entire partition of 2^(n-1) / 16 candidates
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• Random (expected): 16 threads with expected 2^(n-1) / 16 trials per thread
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• Random (99th %): 99% chance completion is faster than this
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• Random (99.9th %): 99.9% chance completion is faster than this
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```
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---

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