Introduction to Cryptography with Coding Theory, 3rd Edition

C.11 Examples for Chapter 21

Example 40

We want to graph the elliptic curve $y^2=x(x-1)(x+1)$.

First, we create a string $v$ that contains the equation we wish to graph.

>> v=’y^2 - x*(x-1)*(x+1)’;

Next we use the ezplot command to plot the elliptic curve.

>> ezplot(v,[-1,3,-5,5])

The plot appears in Figure C.1. The use of $[-1\text{,}3\text{,}-5\text{,}5]$ in the preceding command is to define the limits of the $x$-axis and $y$-axis in the plot.

Figure C.1 Graph of the Elliptic Curve $y^2=x(x-1)(x+1)$.

Figure C.1 Full Alternative Text

Example 41

Add the points (1,3) and (3,5) on the elliptic curve $y^2\equiv x^3+24x+13(\text{mod}29)$.

>> addell([1,3],[3,5],24,13,29)

ans =
    26    1

You can ...