What does (the point at infinity) even means? That's an abstract point/concept required so that the addition of points on the Elliptic Curve is a group law; including: Addition of any two elements $P$ and $Q$ of the group is an element of the group There is a neutral element $\mathcal O$ such that for all $P$, $P+\mathcal O=P=\mathcal O+P$. A possible ...


Theorem 2 in [Dussé et al. 1991] states that, if we skip the final subtraction, then, for $N < R / 4$ and $0 \leq A, B < 2 N$, we have $0 \leq C = \text{MonMul}(A B) < 2 N$, while keeping $C \equiv A B R^{-1} \pmod N$. I think the condition $N < R / 4$ inherently holds in your case e.g. you are using larger $R$ value acutually.


For ECC you are probably better off just using ECDSA or, if you're adventurous, the BLS signature scheme. ECDSA has a signature size / overhead of 4x the security strength (say 128 bit), or two times the key size (a 256 bit curve). BLS has a signature size / overhead of about three times the security strength (say 128 bit) or once the key size - it requires ...

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