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How do you figure out the multiplicative and additive identity with respects to R?
I pick some R such that gcd(R, N) = 1 where N is the size of the group.
Given some field element x in the group, I do x' = xR mod N
How would I figure out the multiplicative identity m such that x' * m = x'
and the additive identity a such that x' + a = x'` ?
The additive identity is $0$, as usual.
The multiplicative identity is the Montgomery representative for $1$, namely $1\cdot R \bmod N = R \bmod N$, just like the Montgomery representative for any other element $x$ is $x\cdot R \bmod N$.
