Goldreich-Goldwasser-Halevi/main.py

from consts import *
from components import *

import numpy as np
from manim import *


class Introduction(TitledScene):
    def construct(self):
        self.add_title("Goldreich--Goldwasser--Halevi")
        self.wait()

        text_1 = Tex(
            r"""
            \begin{itemize} 
                \item Lattice-based cryptosystem.
                \item Devised in 1997 by Goldreich, Goldwasser, and Halevi.
                \item Broken in 1999 by Nguyen.
            \end{itemize}
            """,
            font_size=MEDIUM_FONT,
        )
        self.add(text_1)
        self.play(Write(text_1, run_time=4.0))
        self.wait()


class Premise(TitledScene):
    def construct(self):
        self.add_title("Lattices")

        # A lattice is a subspace of a vector space that is constructed by taking integer multiples of some basis
        # vectors.
        # For example, take the real plane R2.
        plane = NumberPlane(axis_config={"stroke_width": 0.0})
        plane.set_z_index(-10)
        plane.set_opacity(0.75)
        dot = Dot(ORIGIN)
        self.add(dot, plane)
        self.play(Create(dot), Create(plane))
        self.wait()

        # We can construct the 2D grid of integers with the elementary basis
        lattice_1 = VGroup()
        arrow_1 = Arrow(ORIGIN, [1, 0, 0], buff=0)
        arrow_2 = Arrow(ORIGIN, [0, 1, 0], buff=0)

        self.play(Create(arrow_1), Create(arrow_2))
        self.wait()

        for i in range(-7, 8):
            for j in range(-6, 7):
                lattice_1.add(Dot([i, j, 0]))

        self.play(Create(lattice_1))

        # By moving these basis vectors but maintaining their linear independency, other lattices can be formed
        self.play(
            Transform(arrow_1, Arrow(ORIGIN, [1.5, 0, 0], buff=0)),
            *[
                Transform(
                    dot,
                    Dot(
                        dot.get_center()
                        * np.matrix([[1.5, 0, 0], [0, 1, 0], [0, 0, 1]])
                    ),
                )
                for dot in lattice_1
            ]
        )
        self.wait()

        self.play(
            Transform(arrow_1, Arrow(ORIGIN, [1, -0.5, 0], buff=0)),
            *[
                Transform(
                    dot,
                    Dot(
                        dot.get_center()
                        * np.matrix([[2 / 3, 0, 0], [0, 1, 0], [0, 0, 1]])
                        * np.matrix([[1, -0.5, 0], [0, 1, 0], [0, 0, 1]])
                    ),
                )
                for dot in lattice_1
            ]
        )
        self.wait()

        self.play(
            Transform(arrow_1, Arrow(ORIGIN, [1, -1, 0], buff=0)),
            Transform(arrow_2, Arrow(ORIGIN, [1, 1, 0], buff=0)),
            *[
                Transform(
                    dot,
                    Dot(
                        dot.get_center()
                        * np.matrix([[1, 0.5, 0], [0, 1, 0], [0, 0, 1]])
                        * np.matrix([[1, -1, 0], [1, 1, 0], [0, 0, 1]])
                    ),
                )
                for dot in lattice_1
            ]
        )
        self.wait()