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Up to DescribeDigitalSignatures in crypto
This commit is contained in:
Grant Sanderson
parent
ef9fbd7aa9
commit
05db6174e9
4 changed files with 610 additions and 66 deletions
629
crypto.py
629
crypto.py
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@ -33,6 +33,11 @@ from mobject.tex_mobject import *
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BITCOIN_COLOR = "#f7931a"
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def get_cursive_name(name):
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result = TextMobject("\\normalfont\\calligra %s"%name)
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result.set_stroke(width = 0.5)
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return result
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##################
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class AskQuestion(Scene):
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@ -163,6 +168,9 @@ class LedgerScene(PiCreatureScene):
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PiCreatureScene.setup(self)
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self.remove(self.pi_creatures)
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def add_ledger_and_network(self):
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self.add(self.get_ledger(), self.get_network())
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def get_ledger(self):
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title = TextMobject("Ledger")
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rect = Rectangle(
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@ -206,15 +214,13 @@ class LedgerScene(PiCreatureScene):
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amount_str += " " + self.denomination
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line = TextMobject(
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from_name.capitalize(),
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"pays" if from_name.lower() is not "you" else "pay",
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"pays" if from_name.lower() != "you" else "pay",
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to_name.capitalize(),
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amount_str
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)
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for name in from_name, to_name:
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if hasattr(self, name.lower()):
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creature = getattr(self, name.lower())
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color = creature.get_color()
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line.highlight_by_tex(name.capitalize(), color)
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color = self.get_color_from_name(name)
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line.highlight_by_tex(name.capitalize(), color)
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if self.denomination == "USD":
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line.highlight_by_tex(amount_str, GREEN_D)
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elif self.denomination == "BTC":
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@ -222,11 +228,20 @@ class LedgerScene(PiCreatureScene):
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return self.add_line_to_ledger(line)
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def get_color_from_name(self, name):
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if hasattr(self, name.lower()):
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creature = getattr(self, name.lower())
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color = creature.get_color()
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if np.mean(color.get_rgb()) < 0.5:
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color = average_color(color, color, WHITE)
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return color
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return WHITE
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def animate_payment_addition(self, *args, **kwargs):
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line = self.add_payment_line_to_ledger(*args, **kwargs)
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self.play(LaggedStart(
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FadeIn,
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VGroup(*line.family_members_with_points()),
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VGroup(*it.chain(*line)),
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run_time = 1
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))
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@ -241,24 +256,24 @@ class LedgerScene(PiCreatureScene):
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for pi1, pi2 in it.combinations(creatures, 2)
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])
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labels = VGroup(*[pi.label for pi in creatures])
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return VGroup(creatures, labels, lines)
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self.network = VGroup(creatures, labels, lines)
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return self.network
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def create_pi_creatures(self):
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creatures = VGroup(*[
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PiCreature(color = color, height = 1).shift(2*vect)
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for color, vect in zip(
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[BLUE_B, MAROON_D, GREY_BROWN, BLUE_E],
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[BLUE_C, MAROON_D, GREY_BROWN, BLUE_E],
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[UP+LEFT, UP+RIGHT, DOWN+LEFT, DOWN+RIGHT],
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)
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])
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creatures.to_edge(RIGHT)
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names = ["alice", "bob", "charlie", "you"]
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names = self.get_names()
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for name, creature in zip(names, creatures):
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setattr(self, name, creature)
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label = TextMobject(name.capitalize())
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label.scale(0.5)
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label.next_to(creature, DOWN)
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label.scale(0.75)
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label.next_to(creature, DOWN, SMALL_BUFF)
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creature.label = label
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if (creature.get_center() - creatures.get_center())[0] > 0:
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creature.flip()
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@ -266,6 +281,8 @@ class LedgerScene(PiCreatureScene):
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return creatures
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def get_names(self):
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return ["alice", "bob", "charlie", "you"]
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class LayOutPlan(LedgerScene):
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def construct(self):
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@ -404,25 +421,575 @@ class UnderlyingSystemVsUserFacing(Scene):
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self.play(DrawBorderThenFill(phone))
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self.dither(2)
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class CryptoPrefix(Scene):
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def construct(self):
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cryptocurrency = TextMobject(
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"Crypto", "currency",
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arg_separator = ""
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)
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crypto = cryptocurrency.get_part_by_tex("Crypto")
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brace = Brace(crypto, UP)
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explanation = TextMobject(
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"Built using the math \\\\ from cryptography"
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)
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explanation.next_to(brace, UP)
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self.add(cryptocurrency)
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self.play(
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crypto.highlight, YELLOW,
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GrowFromCenter(brace)
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)
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self.play(Write(explanation))
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self.dither(3)
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class IntroduceLedgerSystem(LedgerScene):
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CONFIG = {
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"payments" : [
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("Alice", "Bob", 20),
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("Bob", "Charlie", 40),
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("Charlie", "You", 30),
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("You", "Alice", 10),
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]
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}
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def construct(self):
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self.add(self.get_network())
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self.exchange_money()
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self.add_ledger()
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self.tally_it_all_up()
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def exchange_money(self):
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for from_name, to_name, num in self.payments:
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from_pi = getattr(self, from_name.lower())
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to_pi = getattr(self, to_name.lower())
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cash = TexMobject("\\$"*(num/10)).highlight(GREEN)
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cash.scale_to_fit_height(0.5)
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cash.move_to(from_pi)
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self.play(
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cash.move_to, to_pi,
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to_pi.change_mode, "hooray"
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)
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self.play(FadeOut(cash))
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self.dither()
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def add_ledger(self):
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ledger = self.get_ledger()
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self.play(
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Write(ledger),
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*[
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ApplyMethod(pi.change, "pondering", ledger)
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for pi in self.pi_creatures
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]
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)
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for payment in self.payments:
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self.animate_payment_addition(*payment)
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self.dither(3)
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def tally_it_all_up(self):
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accounts = dict()
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names = "alice", "bob", "charlie", "you"
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for name in names:
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accounts[name] = 0
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for from_name, to_name, amount in self.payments:
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accounts[from_name.lower()] -= amount
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accounts[to_name.lower()] += amount
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results = VGroup()
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debtors = VGroup()
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creditors = VGroup()
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for name in names:
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amount = accounts[name]
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creature = getattr(self, name)
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creature.cash = TexMobject("\\$"*abs(amount/10))
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creature.cash.next_to(creature, UP+LEFT, SMALL_BUFF)
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creature.cash.highlight(GREEN)
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if amount < 0:
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verb = "Owes"
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debtors.add(creature)
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else:
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verb = "Gets"
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creditors.add(creature)
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if name == "you":
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verb = verb[:-1]
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result = TextMobject(
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verb, "\\$%d"%abs(amount)
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)
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result.highlight_by_tex("Owe", RED)
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result.highlight_by_tex("Get", GREEN)
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result.add_background_rectangle()
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result.scale(0.7)
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result.next_to(creature.label, DOWN)
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results.add(result)
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brace = Brace(VGroup(*self.ledger.content[1:]), RIGHT)
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tally_up = brace.get_text("Tally up")
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tally_up.add_background_rectangle()
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self.play(
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GrowFromCenter(brace),
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FadeIn(tally_up)
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)
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self.play(
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LaggedStart(FadeIn, results),
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*[
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ApplyMethod(pi.change, "happy")
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for pi in creditors
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] + [
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ApplyMethod(pi.change, "plain")
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for pi in debtors
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]
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)
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self.dither()
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debtor_cash, creditor_cash = [
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VGroup(*it.chain(*[pi.cash for pi in group]))
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for group in debtors, creditors
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]
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self.play(FadeIn(debtor_cash))
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self.play(
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debtor_cash.arrange_submobjects, RIGHT, SMALL_BUFF,
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debtor_cash.move_to, self.pi_creatures,
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)
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self.dither()
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self.play(ReplacementTransform(
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debtor_cash, creditor_cash
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))
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self.dither(2)
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class InitialProtocol(Scene):
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def construct(self):
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title = TextMobject("Protocol")
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title.scale(1.5)
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title.to_edge(UP)
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h_line = Line(LEFT, RIGHT).scale(4)
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h_line.next_to(title, DOWN)
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items = VGroup(*map(TextMobject, [
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"$\\cdot$ Anyone can add lines to the Ledger",
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"$\\cdot$ Settle up with real money each month"
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]))
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items.arrange_submobjects(
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DOWN,
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buff = MED_LARGE_BUFF,
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aligned_edge = LEFT
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)
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items.next_to(h_line, DOWN, MED_LARGE_BUFF)
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self.add(title, h_line)
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for item in items:
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self.dither()
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self.play(LaggedStart(FadeIn, item))
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self.dither(2)
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self.title = title
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self.items = items
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class AddFraudulentLine(LedgerScene):
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def construct(self):
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self.add_ledger_and_network()
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self.bob_adds_lines()
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self.alice_reacts()
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def bob_adds_lines(self):
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line = self.add_payment_line_to_ledger("Alice", "Bob", 100)
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line.save_state()
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line.scale(0.001)
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line.move_to(self.bob)
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self.play(self.bob.change, "conniving")
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self.play(line.restore)
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self.dither()
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def alice_reacts(self):
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bubble = SpeechBubble(
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height = 1.5, width = 2, direction = LEFT,
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)
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bubble.next_to(self.alice, UP+RIGHT, buff = 0)
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bubble.write("Hey!")
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self.play(
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Animation(self.bob.pupils),
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self.alice.change, "angry",
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FadeIn(bubble),
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Write(bubble.content, run_time = 1)
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)
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self.dither(3)
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self.play(
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FadeOut(bubble),
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FadeOut(bubble.content),
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self.alice.change_mode, "pondering"
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)
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class AnnounceDigitalSignatures(TeacherStudentsScene):
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def construct(self):
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words = TextMobject("Digital \\\\ signatures!")
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words.scale(1.5)
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self.force_skipping()
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self.teacher_says(
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words,
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target_mode = "hooray",
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)
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self.revert_to_original_skipping_status()
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self.change_student_modes(*["hooray"]*3)
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self.dither(2)
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class IntroduceSignatures(LedgerScene):
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CONFIG = {
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"payments" : [
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("Alice", "Bob", 100),
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("Charlie", "You", 20),
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("Bob", "You", 30),
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],
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}
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def construct(self):
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self.add_ledger_and_network()
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self.add_transactions()
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self.add_signatures()
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def add_transactions(self):
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transactions = VGroup(*[
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self.add_payment_line_to_ledger(*payment)
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for payment in self.payments
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])
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self.play(LaggedStart(FadeIn, transactions))
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self.dither()
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def add_signatures(self):
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signatures = VGroup(*[
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get_cursive_name(payments[0].capitalize())
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for payments in self.payments
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])
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for signature, transaction in zip(signatures, self.ledger.content[1:]):
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signature.next_to(transaction, RIGHT)
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signature.highlight(transaction[0].get_color())
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self.play(Write(signature, run_time = 2))
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transaction.add(signature)
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self.dither(2)
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rect = SurroundingRectangle(self.ledger.content[1])
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self.play(ShowCreation(rect))
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self.play(FadeOut(rect))
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self.dither()
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self.play(Indicate(signatures[0]))
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self.dither()
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class AskHowDigitalSignaturesArePossible(TeacherStudentsScene):
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def construct(self):
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signature = get_cursive_name("Alice")
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signature.scale(1.5)
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signature.highlight(BLUE_C)
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signature.to_corner(UP+LEFT)
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signature_copy = signature.copy()
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signature_copy.shift(3*RIGHT)
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bits = TexMobject("01100001")
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bits.next_to(signature, DOWN)
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bits.shift_onto_screen()
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bits_copy = bits.copy()
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bits_copy.next_to(signature_copy, DOWN)
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self.add(signature)
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self.student_says(
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"Couldn't you just \\\\ copy the signature?",
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target_mode = "confused",
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run_time = 1
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)
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self.change_student_modes("pondering", "confused", "erm")
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self.play(LaggedStart(FadeIn, bits, run_time = 1))
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self.dither()
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self.play(ReplacementTransform(
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bits.copy(), bits_copy,
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path_arc = np.pi/2
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))
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self.play(Write(signature_copy))
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self.dither(3)
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class DescribeDigitalSignatures(LedgerScene):
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CONFIG = {
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"public_color" : GREEN,
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"private_color" : RED,
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"signature_color" : BLUE_C,
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}
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def construct(self):
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self.reorganize_pi_creatures()
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self.generate_key_pairs()
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self.keep_secret_key_secret()
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self.show_handwritten_signatures()
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self.show_digital_signatures()
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self.show_signing_functions()
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def reorganize_pi_creatures(self):
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self.pi_creatures.remove(self.you)
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creature_groups = VGroup(*[
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VGroup(pi, pi.label).scale(1.7)
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for pi in self.pi_creatures
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])
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creature_groups.arrange_submobjects(RIGHT, buff = 2)
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creature_groups.to_edge(DOWN)
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self.add(creature_groups)
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for pi in self.pi_creatures:
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if pi.is_flipped():
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pi.flip()
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def generate_key_pairs(self):
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title = TextMobject("Private", "key /", "Public", "key")
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title.to_edge(UP)
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private, public = map(title.get_part_by_tex, ["Private", "Public"])
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private.highlight(self.private_color)
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public.highlight(self.public_color)
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secret = TextMobject("Secret")
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secret.move_to(private, RIGHT)
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secret.highlight(self.private_color)
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names = self.get_names()[:-1]
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public_key_strings = [
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bin(256+ord(name[0].capitalize()))[3:]
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for name in names
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]
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private_key_strings = [
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bin(hash(name))[2:10]
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for name in names
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]
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public_keys, private_keys = [
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VGroup(*[
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TextMobject(key_name+":"," $%s\\dots$"%key)
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for key in keys
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])
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for key_name, keys in [
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("pk", public_key_strings),
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("sk", private_key_strings)
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]
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]
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key_pairs = [
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VGroup(*pair).arrange_submobjects(DOWN, aligned_edge = LEFT)
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for pair in zip(public_keys, private_keys)
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]
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for key_pair, pi in zip(key_pairs, self.pi_creatures):
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key_pair.next_to(pi, UP, MED_LARGE_BUFF)
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for key in key_pair:
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key.highlight_by_tex("sk", self.private_color)
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key.highlight_by_tex("pk", self.public_color)
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self.play(Write(title, run_time = 2))
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self.play(ReplacementTransform(
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VGroup(VGroup(public.copy())),
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public_keys
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))
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self.play(ReplacementTransform(
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VGroup(VGroup(private.copy())),
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private_keys
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))
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self.dither()
|
||||
self.play(private.shift, DOWN)
|
||||
self.play(FadeIn(secret))
|
||||
self.play(FadeOut(private))
|
||||
self.dither()
|
||||
|
||||
title.remove(private)
|
||||
title.add(secret)
|
||||
self.title = title
|
||||
self.private_keys = private_keys
|
||||
self.public_keys = public_keys
|
||||
|
||||
def keep_secret_key_secret(self):
|
||||
keys = self.private_keys
|
||||
rects = VGroup(*map(SurroundingRectangle, keys))
|
||||
rects.highlight(self.private_color)
|
||||
lock = SVGMobject(
|
||||
file_name = "lock",
|
||||
height = rects.get_height(),
|
||||
fill_color = LIGHT_GREY,
|
||||
fill_opacity = 1,
|
||||
stroke_width = 0,
|
||||
)
|
||||
locks = VGroup(*[
|
||||
lock.copy().next_to(rect, LEFT, SMALL_BUFF)
|
||||
for rect in rects
|
||||
])
|
||||
|
||||
self.play(ShowCreation(rects))
|
||||
self.play(LaggedStart(DrawBorderThenFill, locks))
|
||||
self.dither()
|
||||
|
||||
self.private_key_rects = rects
|
||||
self.locks = locks
|
||||
|
||||
def show_handwritten_signatures(self):
|
||||
lines = VGroup(*[Line(LEFT, RIGHT) for x in range(5)])
|
||||
lines.arrange_submobjects(DOWN)
|
||||
last_line = lines[-1]
|
||||
last_line.scale(0.7, about_point = last_line.get_left())
|
||||
|
||||
signature_line = lines[0].copy()
|
||||
signature_line.set_stroke(width = 2)
|
||||
signature_line.next_to(lines, DOWN, LARGE_BUFF)
|
||||
ex = TexMobject("\\times")
|
||||
ex.scale(0.7)
|
||||
ex.next_to(signature_line, UP, SMALL_BUFF, LEFT)
|
||||
lines.add(ex, signature_line)
|
||||
|
||||
rect = SurroundingRectangle(
|
||||
lines,
|
||||
color = LIGHT_GREY,
|
||||
buff = MED_SMALL_BUFF
|
||||
)
|
||||
document = VGroup(rect, lines)
|
||||
documents = VGroup(*[
|
||||
document.copy()
|
||||
for x in range(2)
|
||||
])
|
||||
documents.arrange_submobjects(RIGHT, buff = MED_LARGE_BUFF)
|
||||
documents.to_corner(UP+LEFT)
|
||||
|
||||
signatures = VGroup()
|
||||
for document in documents:
|
||||
signature = get_cursive_name("Alice")
|
||||
signature.highlight(self.signature_color)
|
||||
line = document[1][-1]
|
||||
signature.next_to(line, UP, SMALL_BUFF)
|
||||
signatures.add(signature)
|
||||
|
||||
self.play(
|
||||
FadeOut(self.title),
|
||||
LaggedStart(FadeIn, documents, run_time = 1)
|
||||
)
|
||||
self.play(Write(signatures))
|
||||
self.dither()
|
||||
|
||||
self.signatures = signatures
|
||||
self.documents = documents
|
||||
|
||||
def show_digital_signatures(self):
|
||||
rect = SurroundingRectangle(VGroup(
|
||||
self.public_keys[0],
|
||||
self.private_key_rects[0],
|
||||
self.locks[0]
|
||||
))
|
||||
digital_signatures = VGroup()
|
||||
for i, signature in enumerate(self.signatures):
|
||||
bits = bin(hash(str(i)))[-8:]
|
||||
digital_signature = TexMobject(bits + "\\dots")
|
||||
digital_signature.scale(0.7)
|
||||
digital_signature.highlight(signature.get_color())
|
||||
digital_signature.move_to(signature, DOWN)
|
||||
digital_signatures.add(digital_signature)
|
||||
|
||||
arrows = VGroup(*[
|
||||
Arrow(
|
||||
rect.get_corner(UP), sig.get_bottom(),
|
||||
tip_length = 0.15,
|
||||
color = WHITE
|
||||
)
|
||||
for sig in digital_signatures
|
||||
])
|
||||
|
||||
words = VGroup(*map(
|
||||
TextMobject,
|
||||
["Different messages", "Completely different signatures"]
|
||||
))
|
||||
words.arrange_submobjects(DOWN, aligned_edge = LEFT)
|
||||
words.scale(1.3)
|
||||
words.next_to(self.documents, RIGHT)
|
||||
|
||||
self.play(FadeIn(rect))
|
||||
self.play(*map(ShowCreation, arrows))
|
||||
self.play(Transform(self.signatures, digital_signatures))
|
||||
self.play(*[
|
||||
ApplyMethod(pi.change, "pondering", digital_signatures)
|
||||
for pi in self.pi_creatures
|
||||
])
|
||||
for word in words:
|
||||
self.play(FadeIn(word))
|
||||
self.dither()
|
||||
self.play(FadeOut(words))
|
||||
|
||||
def show_signing_functions(self):
|
||||
sign = TextMobject(
|
||||
"Sign(", "Message", ", ", "sk", ") = ", "Signature",
|
||||
arg_separator = ""
|
||||
)
|
||||
sign.to_corner(UP+RIGHT)
|
||||
verify = TextMobject(
|
||||
"Verify(", "Message", ", ", "Signature", ", ", "pk", ") = ", "T/F",
|
||||
arg_separator = ""
|
||||
)
|
||||
for mob in sign, verify:
|
||||
mob.highlight_by_tex("sk", self.private_color)
|
||||
mob.highlight_by_tex("pk", self.public_color)
|
||||
mob.highlight_by_tex(
|
||||
"Signature", self.signature_color,
|
||||
)
|
||||
for name in "Message", "sk", "Signature", "pk":
|
||||
part = mob.get_part_by_tex(name)
|
||||
if part is not None:
|
||||
setattr(mob, name.lower(), part)
|
||||
verify.next_to(sign, DOWN, MED_LARGE_BUFF, LEFT)
|
||||
VGroup(sign, verify).to_corner(UP+RIGHT)
|
||||
|
||||
private_key = self.private_key_rects[0]
|
||||
public_key = self.public_keys[0]
|
||||
message = self.documents[0]
|
||||
signature = self.signatures[0]
|
||||
|
||||
self.play(*[
|
||||
FadeIn(part)
|
||||
for part in sign
|
||||
if part not in [sign.message, sign.sk, sign.signature]
|
||||
])
|
||||
self.play(ReplacementTransform(
|
||||
message.copy(), VGroup(sign.message)
|
||||
))
|
||||
self.dither()
|
||||
self.play(ReplacementTransform(
|
||||
private_key.copy(), sign.sk
|
||||
))
|
||||
self.dither()
|
||||
self.play(ReplacementTransform(
|
||||
VGroup(sign.sk, sign.message).copy(),
|
||||
VGroup(sign.signature)
|
||||
))
|
||||
self.dither()
|
||||
self.play(Indicate(sign.sk))
|
||||
self.dither()
|
||||
self.play(Indicate(sign.message))
|
||||
self.dither()
|
||||
self.play(*[
|
||||
FadeIn(part)
|
||||
for part in verify
|
||||
if part not in [
|
||||
verify.message, verify.signature,
|
||||
verify.pk, verify[-1]
|
||||
]
|
||||
])
|
||||
self.dither()
|
||||
self.play(
|
||||
ReplacementTransform(
|
||||
sign.message.copy(), verify.message
|
||||
),
|
||||
ReplacementTransform(
|
||||
sign.signature.copy(), verify.signature
|
||||
)
|
||||
)
|
||||
self.dither()
|
||||
self.play(ReplacementTransform(
|
||||
public_key.copy(), VGroup(verify.pk)
|
||||
))
|
||||
self.dither()
|
||||
self.play(Write(verify[-1]))
|
||||
self.dither()
|
||||
|
||||
|
||||
class TryGuessingDigitalSignature(Scene):
|
||||
def construct(self):
|
||||
pass
|
||||
|
||||
|
||||
class SupplementVideoWrapper(Scene):
|
||||
def construct(self):
|
||||
pass
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -14,16 +14,16 @@ class TexSymbol(VMobjectFromSVGPathstring):
|
|||
#TODO, this assumes a = 0
|
||||
if b < 0.5:
|
||||
b = 2*b
|
||||
width = 1
|
||||
added_width = 1
|
||||
opacity = 0
|
||||
else:
|
||||
width = 2 - 2*b
|
||||
added_width = 2 - 2*b
|
||||
opacity = 2*b - 1
|
||||
b = 1
|
||||
VMobjectFromSVGPathstring.pointwise_become_partial(
|
||||
self, mobject, 0, b
|
||||
)
|
||||
self.set_stroke(width = width)
|
||||
self.set_stroke(width = added_width + mobject.get_stroke_width())
|
||||
self.set_fill(opacity = opacity)
|
||||
|
||||
|
||||
|
|
@ -191,7 +191,6 @@ class TextMobject(TexMobject):
|
|||
"alignment" : "\\centering",
|
||||
}
|
||||
|
||||
|
||||
class Brace(TexMobject):
|
||||
CONFIG = {
|
||||
"buff" : 0.2,
|
||||
|
|
@ -254,9 +253,6 @@ class Brace(TexMobject):
|
|||
vect = self.get_tip() - self.get_center()
|
||||
return vect/np.linalg.norm(vect)
|
||||
|
||||
|
||||
|
||||
|
||||
def tex_hash(expression, template_tex_file):
|
||||
return str(hash(expression + template_tex_file))
|
||||
|
||||
|
|
|
|||
21
template.tex
21
template.tex
|
|
@ -1,4 +1,4 @@
|
|||
\documentclass[12pt]{beamer}
|
||||
\documentclass[preview]{standalone}
|
||||
|
||||
\usepackage[english]{babel}
|
||||
\usepackage[utf8x]{inputenc}
|
||||
|
|
@ -8,23 +8,12 @@
|
|||
\usepackage{setspace}
|
||||
\usepackage{tipa}
|
||||
\usepackage{relsize}
|
||||
|
||||
|
||||
\mode<presentation>
|
||||
{
|
||||
\usetheme{default} % or try Darmstadt, Madrid, Warsaw, ...
|
||||
\usecolortheme{default} % or try albatross, beaver, crane, ...
|
||||
\usefonttheme{serif} % or try serif, structurebold, ...
|
||||
\setbeamertemplate{navigation symbols}{}
|
||||
\setbeamertemplate{caption}[numbered]
|
||||
}
|
||||
\usepackage{mathrsfs}
|
||||
\usepackage{calligra}
|
||||
|
||||
\begin{document}
|
||||
\centering
|
||||
|
||||
\begin{frame}
|
||||
\begin{align*}
|
||||
YourTextHere
|
||||
\end{align*}
|
||||
\end{frame}
|
||||
$\displaystyle YourTextHere$
|
||||
|
||||
\end{document}
|
||||
|
|
@ -1,4 +1,4 @@
|
|||
\documentclass[12pt]{beamer}
|
||||
\documentclass[preview]{standalone}
|
||||
|
||||
\usepackage[english]{babel}
|
||||
\usepackage[utf8x]{inputenc}
|
||||
|
|
@ -9,19 +9,11 @@
|
|||
\usepackage{tipa}
|
||||
\usepackage{relsize}
|
||||
\usepackage{textcomp}
|
||||
\usepackage{mathrsfs}
|
||||
\usepackage{calligra}
|
||||
|
||||
\mode<presentation>
|
||||
{
|
||||
\usetheme{default} % or try Darmstadt, Madrid, Warsaw, ...
|
||||
\usecolortheme{default} % or try albatross, beaver, crane, ...
|
||||
\usefonttheme{serif} % or try serif, structurebold, ...
|
||||
\setbeamertemplate{navigation symbols}{}
|
||||
\setbeamertemplate{caption}[numbered]
|
||||
}
|
||||
\begin{document}
|
||||
|
||||
\begin{frame}
|
||||
YourTextHere
|
||||
\end{frame}
|
||||
YourTextHere
|
||||
|
||||
\end{document}
|
||||
Loading…
Add table
Reference in a new issue