Manim animation of the double-and-add algorithm for elliptic curve point multiplication

double_add.py

#!/usr/bin/env python

from manim import *

# usage: python3 -m manim double_add.py DoubleAdd -p

class DoubleAdd(Scene):
    def construct(self):
        n_bin = Text("n = 101010")
        self.play(Write(n_bin))
        self.wait(1)
        Q = MathTex(r"Q = P", substrings_to_isolate="Q") \
            .next_to(n_bin, 7*LEFT+3*DOWN) \
            .set_color_by_tex("Q", ORANGE)
        R = MathTex(r"R = \mathcal{O}", substrings_to_isolate="R") \
            .next_to(Q, 3*DOWN) \
            .set_color_by_tex("R", PINK)
        self.play(
            Write(Q),
            Write(R)
        )
        up_arrow = Arrow(
            n_bin[-1].get_center()+1.5*DOWN,
            n_bin[-1].get_center()+0.25*DOWN
        )
        odd = Text("1?").next_to(up_arrow, DOWN).set_color(YELLOW)
        yes = Text("✓").next_to(up_arrow, DOWN).set_color(GREEN)
        no  = Text("✗").next_to(up_arrow, DOWN).set_color(RED)
        arrow_and_checker = Group(up_arrow, odd)
        self.play(
            FadeIn(arrow_and_checker)
        )
        q = 1
        r = 0
        for idx in range(1, 7):
            self.wait(1)
            self.play(Wiggle(odd))
            if idx % 2 == 1:
                self.play(Transform(odd, no))
                self.wait(1)
            else:
                self.play(Transform(odd, yes))
                self.wait(1)
                R_text = r'\mathcal{O}' if r == 0 else f'{q}P'
                new_R = MathTex(f"R = {R_text} + Q", substrings_to_isolate=["R", "Q"]) \
                    .next_to(R, ORIGIN).set_color_by_tex("R", PINK).set_color_by_tex("Q", ORANGE)
                self.play(
                    Transform(R, new_R)
                )
                self.wait(1)
                r += q
                self.play(Transform(R, 
                    MathTex(f"R = {r}P", substrings_to_isolate=["R", "Q"]) \
                        .next_to(R, ORIGIN).set_color_by_tex("R", PINK).set_color_by_tex("Q", ORANGE)
                ))
                self.wait(1)
            self.play(
                n_bin[:-idx].animate.shift(n_bin[-idx].get_center()-n_bin[-idx-1].get_center()),
                n_bin[-idx].animate.set_color(BLACK).shift(IN)
            )
            self.wait(1)
            self.play(Transform(Q, 
                MathTex(fr"Q = {'' if q == 1 else q}P \cdot 2", substrings_to_isolate="Q")
                .next_to(Q, ORIGIN).set_color_by_tex("Q", ORANGE)
            ))
            q *= 2
            self.wait(1)
            self.play(Transform(Q, 
                MathTex(fr"Q = {q}P", substrings_to_isolate="Q")
                .next_to(Q, ORIGIN).set_color_by_tex("Q", ORANGE)
            ))
            self.wait(1)
            self.play(Transform(odd, Text("1?").next_to(up_arrow, DOWN).set_color(YELLOW)))