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Learning the basics of elliptic curve cryptography. The question is a mathematical one.


While finding the points in the elliptic group $E_{23}(1,1)$,this is how one proceeds :


How is $y^2= 7$ giving $y = 7$? or $y^2 = 8$ giving $y=10$. The perfect squares I can understand but how are the others being calculated? Is it because of $\mod 23$? I am studying the topic from here.

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Before starting to learn about elliptic-curve cryptography, it is a good idea to (at least) get the hang of the basics of modular arithmetic.

We can compute that

\begin{align} 7^2&=49=3+2\cdot 23\equiv 3\bmod{23}\\ 16^2&=256=3+11\cdot 23\equiv 3\bmod{23}\\ 10^2&=100=8+4\cdot 23\equiv 8\bmod{23}\\ 13^2&=169=8+7\cdot 23\equiv 8\bmod{23} \end{align}

These values in the table are therefore correct.

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