Comments (2)
Two interesting papers on efficient arithmetic:
- Multiplication and Squaring on Pairing-Friendly Fields, which is mentioning the approach above.
- Efficient Multiplication over Extension Fields
from cheetah.
Also to get an idea of cost comparison between arithmetic operations, below are Fp
operations which costs are given with respect to the cost of Fp
addition (plus running time on my machine for reference). In practice for Fp6
we use internal integer values seen as u128
to reduce the number of reductions per coordinate.
Fp op. |
Timing | Relative cost |
---|---|---|
Addition | 852.7 ps | 1 A |
Subtraction | 860.1 ps | 1.01 A |
Doubling | 725.23 ps | 0.85 A |
Multiplication | 1.4133 ns | 1.66 A |
Mult. by u32 / by beta | 937.6 ps | 1.1 A |
Squaring | 1.3054 ns | 1.53 A |
Inversion | 221.6 ns | 191 A ( = 133 M) |
from cheetah.
Related Issues (17)
- Speed-up scalar multiplication in the group HOT 2
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from cheetah.