# Notation question: Dividing 2 Elliptic Curve Points producing a third point

I'm working my way through some papers and ran across what seems to be division of two points that produce a third point. I'm new to ECC and am having a terrible time trying to figure out what this notation means, any thoughts? This is from the BLS paper: https://crypto.stanford.edu/~dabo/pubs/papers/aggreg.pdf

Point division appears on pages

• 6 (A potential attack on aggregate signatures)
• 18 (Ring Signing equation)
• It is not ECC notation/ it is multiplicative group notation where the division exist! Oct 26, 2021 at 15:09
• @kelalaka I think I see! so does division here actually correspond to subtraction in the exponent? i.e. if A = g^a, B = g^b then A / B = g^(a-b) ? Oct 26, 2021 at 15:21
• As I observed elsewhere, if we assume additive notation, then 'point division' corresponds to 'discrete log'. That is, if we set up the equation $x = A/B$, then this should be equivalent to $xB = A$, which is the discrete log of A to the base B - hence, it is well defined (if somewhat intractable to compute). Of course, this has nothing to do with the paper, which is written in multiplicative notation... Oct 26, 2021 at 18:38

I read $$v_B=v'_B/v'_A$$ as $$v_B=v'_B\cdot({v'_A}^{-1})$$ where $$\cdot$$ is the group law, and $${v'_A}^{-1}$$ is the inverse of $$v'_A$$ in that group, that is such that $${v'_A}\cdot{v'_A}^{-1}={v'_A}^{-1}\cdot{v'_A}=1$$, the group's neutral.
If the group was noted additively, that would be $$v_B=v'_B-v'_A$$, read as $$v_B=v'_B+(-v'_A)$$ where $$-v'_A$$ is the opposite of $$v'_A$$ in that group, that is such that $${v'_A}+(-v'_A)=(-v'_A)+{v'_A}=0$$, the group's neutral.