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17

By the same argument, they would have to forbid $d = 1234$; after all, an attacker can trivially compute the value of $1234 G$; and if they see it, then they can immediately infer $d$ without having to complete a discrete log over an elliptic curve. Of course, this logic would forbid all possible values of $d$... The issue is that if the attacker gets ...


3

On standard way to compute scalar multiplication is to use Double-and-add algorithm: The idea is to take the binary representation of your scalar $b = b_0 ... b_m$in your case $b = 3$ gives $b_0b_1 = 11$. First you initialize your result $Q$ with $0$. Then for each increasing bit index $i$, you set $Q = 2Q$ (computed with the doubling formula) and if ...


2

Given two points $P_1 = (x_1,y_1)$ and $P_2 = (x_2, y_2)$ on an elliptic curve $y^2 = x^3 + ax +b$, the sum $P_3$ of $P_1$ and $P_2$ is $P_3 = P_1 + P_2 = (x_3,y_3)$ where $x_3 = \lambda^2 - x_1 - x_2$ and $y_3 = y_1 + \lambda(x_3 - x_1)$ where $\lambda = (y_1 - y_2)/(x_1 - x_2)$ if $P_1 \neq P_2$ and $\lambda = (3x_1^2 + a)/(2y_1)$ if $P_1 = P_2$. The ...



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