[curves] Microsoft ECCLib for "NUMS" curves

[Samuel Neves]

Here are the remaining numbers:

> BENCHMARKING
> --------------------------------------------------------------------------------------------------------
>
> Curve arithmetic: Weierstrass a=-3 over GF(2^256-189)
>
>   Point doubling runs in ..........................................      687 cycles
>   (Complete) point addition runs in ...............................     1788 cycles
>   Variable-base scalar mul runs in ................................   282593 cycles
>   Fixed-base scalar mul (memory model=MEM_LARGE) runs in ..........   109593 cycles
>   Double-base scalar mul (memory model=MEM_LARGE) runs in .........   299468 cycles
>
> --------------------------------------------------------------------------------------------------------
>
> Curve arithmetic: twisted Edwards a=-1 over GF(2^256-189)
>
>   Point doubling runs in ..........................................      561 cycles
>   (Complete) point addition runs in ...............................      932 cycles
>   Variable-base scalar mul runs in ................................   228468 cycles
>   Fixed-base scalar mul (memory model=MEM_LARGE) runs in ..........    84344 cycles
>   Double-base scalar mul (memory model=MEM_LARGE) runs in .........   242463 cycles
>
> --------------------------------------------------------------------------------------------------------
>
> Curve arithmetic: Weierstrass a=-3 over GF(2^384-317)
>
>   Point doubling runs in ..........................................     1291 cycles
>   (Complete) point addition runs in ...............................     3160 cycles
>   Variable-base scalar mul runs in ................................   756699 cycles
>   Fixed-base scalar mul (memory model=MEM_LARGE) runs in ..........   260110 cycles
>   Double-base scalar mul (memory model=MEM_LARGE) runs in .........   795440 cycles
>
> --------------------------------------------------------------------------------------------------------
>
> Curve arithmetic: twisted Edwards a=-1 over GF(2^384-317)
>
>   Point doubling runs in ..........................................     1048 cycles
>   (Complete) point addition runs in ...............................     1738 cycles
>   Variable-base scalar mul runs in ................................   612372 cycles
>   Fixed-base scalar mul (memory model=MEM_LARGE) runs in ..........   206029 cycles
>   Double-base scalar mul (memory model=MEM_LARGE) runs in .........   644065 cycles
>
> --------------------------------------------------------------------------------------------------------
>
> Curve arithmetic: Weierstrass a=-3 over GF(2^512-569)
>
>   Point doubling runs in ..........................................     1995 cycles
>   (Complete) point addition runs in ...............................     4798 cycles
>   Variable-base scalar mul runs in ................................  1560055 cycles
>   Fixed-base scalar mul (memory model=MEM_LARGE) runs in ..........   505452 cycles
>   Double-base scalar mul (memory model=MEM_LARGE) runs in .........  1643738 cycles
>
> --------------------------------------------------------------------------------------------------------
>
> Curve arithmetic: twisted Edwards a=-1 over GF(2^512-569)
>
>   Point doubling runs in ..........................................     1697 cycles
>   (Complete) point addition runs in ...............................     2832 cycles
>   Variable-base scalar mul runs in ................................  1287500 cycles
>   Fixed-base scalar mul (memory model=MEM_LARGE) runs in ..........   399970 cycles
>   Double-base scalar mul (memory model=MEM_LARGE) runs in .........  1346718 cycles