crypto: Use Newton–Raphson for modinv in modexp #1420
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## master #1420 +/- ##
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- Coverage 81.64% 81.64% -0.01%
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Lines 13550 13548 -2
Branches 3217 3217
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Pull request overview
This PR optimizes the modular inverse computation in the modexp precompile by replacing a bit-by-bit algorithm with the Newton-Raphson method. The change significantly improves performance for modexp operations with even moduli, especially when the power-of-two factor is large.
Changes:
- Replaced the iterative bit-by-bit modular inversion algorithm with Newton-Raphson doubling method
- Reuses the existing
inv_mod()function from ModArith to compute an initial 64-bit inverse - Added documentation note about the return value potentially exceeding
kbits
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Use the Newton–Raphson method to compute the modular inverse of the
odd part of the modulus in the modexp for even modulus.
This reuses the inv_mod() procedure from ModArith to compute initial
64-bit value of the inversion.
Benchmarks of modified modexp cases with big `k` in the decomposition
to `mod_odd * 2^k`:
```
│ before │ after │
│ gas/s │ gas/s vs base │
modexp<expmod_execute>/mod_len:8/exp_bits:33-14 722.7M ± 0% 870.1M ± 0% +20.39% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:16/exp_bits:33-14 863.9M ± 0% 868.3M ± 0% +0.50% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:24/exp_bits:33-14 206.1M ± 0% 217.0M ± 0% +5.24% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:32/exp_bits:33-14 217.7M ± 0% 218.1M ± 0% +0.16% (p=0.034 n=11)
modexp<expmod_execute>/mod_len:40/exp_bits:11-14 136.5M ± 0% 181.0M ± 0% +32.65% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:48/exp_bits:8-14 211.5M ± 0% 237.4M ± 0% +12.24% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:56/exp_bits:6-14 210.2M ± 0% 296.2M ± 0% +40.89% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:64/exp_bits:5-14 33.74M ± 0% 324.07M ± 0% +860.53% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:72/exp_bits:4-14 76.66M ± 0% 116.36M ± 0% +51.79% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:80/exp_bits:4-14 91.70M ± 0% 139.26M ± 0% +51.87% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:88/exp_bits:4-14 70.52M ± 0% 167.91M ± 0% +138.11% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:96/exp_bits:4-14 171.1M ± 0% 192.2M ± 0% +12.30% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:112/exp_bits:4-14 106.2M ± 0% 239.8M ± 16% +125.91% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:136/exp_bits:3-14 53.91M ± 0% 86.57M ± 0% +60.58% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:192/exp_bits:2-14 83.53M ± 0% 107.25M ± 0% +28.39% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:200/exp_bits:2-14 2.302M ± 0% 95.886M ± 0% +4065.86% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:256/exp_bits:2-14 50.46M ± 0% 180.23M ± 1% +257.16% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:264/exp_bits:2-14 3.710M ± 0% 12.260M ± 1% +230.45% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:504/exp_bits:2-14 10.74M ± 0% 43.81M ± 1% +307.90% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:512/exp_bits:2-14 25.28M ± 0% 48.86M ± 1% +93.28% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:520/exp_bits:2-14 11.43M ± 0% 46.62M ± 0% +307.95% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:1016/exp_bits:2-14 43.47M ± 0% 175.31M ± 0% +303.26% (p=0.000 n=11)
modexp<expmod_execute>/mod_len:1024/exp_bits:2-14 145.6M ± 81% 190.8M ± 12% +31.10% (p=0.000 n=11)
geomean 69.00M 150.5M +118.12%
```
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Use the Newton–Raphson method to compute the modular inverse of the odd part of the modulus in the modexp for even modulus. This reuses the inv_mod() procedure from ModArith to compute initial 64-bit value of the inversion.
Benchmarks of modified modexp cases with big
kin the decomposition tomod_odd * 2^k: