Hi Niels,

I tried to apply your method but can't get it work, while applying it one
question came to my mind.


> First, compute b_0(x) / x^64 (mod P(x)), which expands it from 64 bits to
> 128,
>
>   c_1(x) x^64 + c_0(x) = b_0(x) / x^64 (mod P(x))
>

Here you are trying to get partially reduced product by computing b_0(x) /
x^64 (mod P(x)) but since the degree of input is 127,  we can use the
polynomial defining the finite field with x^64 elements, in this case P(x)
= X^64+X^4+X^3+X+1 and P' = P^-1 (mod X^64) = X^63+X^61+X^60+1 which is the
same constant 0xB0 and the function now: c_1(x) x^64 + c_0(x) = ((b_0 mod
X^64) * p') mod X^64
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