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Bloomberg

Bloomberg

3 years ago

Expulsion of ten million Ukrainians

According to recent data from two UN agencies, ten million Ukrainians have been displaced.

The International Organization for Migration (IOM) estimates nearly 6.5 million Ukrainians have relocated. Most have fled the war zones around Kyiv and eastern Ukraine, including Dnipro, Zhaporizhzhia, and Kharkiv. Most IDPs have fled to western and central Ukraine.

Since Russia invaded on Feb. 24, 3.6 million people have crossed the border to seek refuge in neighboring countries, according to the latest UN data. While most refugees have fled to Poland and Romania, many have entered Russia.

Internally displaced figures are IOM estimates as of March 19, based on 2,000 telephone interviews with Ukrainians aged 18 and older conducted between March 9-16. The UNHCR compiled the figures for refugees to neighboring countries on March 21 based on official border crossing data and its own estimates. The UNHCR's top-line total is lower than the country totals because Romania and Moldova totals include people crossing between the two countries.

Sources: IOM, UNHCR

According to IOM estimates based on telephone interviews with a representative sample of internally displaced Ukrainians, over 53% of those displaced are women, and over 60% of displaced households have children.

More on Current Events

Will Lockett

Will Lockett

2 years ago

Russia's nukes may be useless

Russia's nuclear threat may be nullified by physics.

Putin seems nostalgic and wants to relive the Cold War. He's started a deadly war to reclaim the old Soviet state of Ukraine and is threatening the West with nuclear war. NATO can't risk starting a global nuclear war that could wipe out humanity to support Ukraine's independence as much as they want to. Fortunately, nuclear physics may have rendered Putin's nuclear weapons useless. However? How will Ukraine and NATO react?

To understand why Russia's nuclear weapons may be ineffective, we must first know what kind they are.

Russia has the world's largest nuclear arsenal, with 4,447 strategic and 1,912 tactical weapons (all of which are ready to be rolled out quickly). The difference between these two weapons is small, but it affects their use and logistics. Strategic nuclear weapons are ICBMs designed to destroy a city across the globe. Russia's ICBMs have many designs and a yield of 300–800 kilotonnes. 300 kilotonnes can destroy Washington. Tactical nuclear weapons are smaller and can be fired from artillery guns or small truck-mounted missile launchers, giving them a 1,500 km range. Instead of destroying a distant city, they are designed to eliminate specific positions, bases, or military infrastructure. They produce 1–50 kilotonnes.

These two nuclear weapons use different nuclear reactions. Pure fission bombs are compact enough to fit in a shell or small missile. All early nuclear weapons used this design for their fission bombs. This technology is inefficient for bombs over 50 kilotonnes. Larger bombs are thermonuclear. Thermonuclear weapons use a small fission bomb to compress and heat a hydrogen capsule, which undergoes fusion and releases far more energy than ignition fission reactions, allowing for effective giant bombs. 

Here's Russia's issue.

A thermonuclear bomb needs deuterium (hydrogen with one neutron) and tritium (hydrogen with two neutrons). Because these two isotopes fuse at lower energies than others, the bomb works. One problem. Tritium is highly radioactive, with a half-life of only 12.5 years, and must be artificially made.

Tritium is made by irradiating lithium in nuclear reactors and extracting the gas. Tritium is one of the most expensive materials ever made, at $30,000 per gram.

Why does this affect Putin's nukes?

Thermonuclear weapons need tritium. Tritium decays quickly, so they must be regularly refilled at great cost, which Russia may struggle to do.

Russia has a smaller economy than New York, yet they are running an invasion, fending off international sanctions, and refining tritium for 4,447 thermonuclear weapons.

The Russian military is underfunded. Because the state can't afford it, Russian troops must buy their own body armor. Arguably, Putin cares more about the Ukraine conflict than maintaining his nuclear deterrent. Putin will likely lose power if he loses the Ukraine war.

It's possible that Putin halted tritium production and refueling to save money for Ukraine. His threats of nuclear attacks and escalating nuclear war may be a bluff.

This doesn't help Ukraine, sadly. Russia's tactical nuclear weapons don't need expensive refueling and will help with the invasion. So Ukraine still risks a nuclear attack. The bomb that destroyed Hiroshima was 15 kilotonnes, and Russia's tactical Iskander-K nuclear missile has a 50-kiloton yield. Even "little" bombs are deadly.

We can't guarantee it's happening in Russia. Putin may prioritize tritium. He knows the power of nuclear deterrence. Russia may have enough tritium for this conflict. Stockpiling a material with a short shelf life is unlikely, though.

This means that Russia's most powerful weapons may be nearly useless, but they may still be deadly. If true, this could allow NATO to offer full support to Ukraine and push the Russian tyrant back where he belongs. If Putin withholds funds from his crumbling military to maintain his nuclear deterrent, he may be willing to sink the ship with him. Let's hope the former.

Jared A. Brock

Jared A. Brock

3 years ago

Here is the actual reason why Russia invaded Ukraine

Democracy's demise

Our Ukrainian brothers and sisters are being attacked by a far superior force.
It's the biggest invasion since WWII.

43.3 million peaceful Ukrainians awoke this morning to tanks, mortars, and missiles. Russia is already 15 miles away.

America and the West will not deploy troops.
They're sanctioning. Except railways. And luxuries. And energy. Diamonds. Their dependence on Russian energy exports means they won't even cut Russia off from SWIFT.

Ukraine is desperate enough to hand out guns on the street.

France, Austria, Turkey, and the EU are considering military aid, but Ukraine will fall without America or NATO.

The Russian goal is likely to encircle Kyiv and topple Zelenskyy's government. A proxy power will be reinstated once Russia has total control.

“Western security services believe Putin intends to overthrow the government and install a puppet regime,” says Financial Times foreign affairs commentator Gideon Rachman. This “decapitation” strategy includes municipalities. Ukrainian officials are being targeted for arrest or death.”

Also, Putin has never lost a war.

Why is Russia attacking Ukraine?

Putin, like a snowflake college student, “feels unsafe.”
Why?

Because Ukraine is full of “Nazi ideas.”

Putin claims he has felt threatened by Ukraine since the country's pro-Putin leader was ousted and replaced by a popular Jewish comedian.

Hee hee

He fears a full-scale enemy on his doorstep if Ukraine joins NATO. But he refuses to see it both ways. NATO has never invaded Russia, but Russia has always stolen land from its neighbors. Can you blame them for joining a mutual defense alliance when a real threat exists?
Nations that feel threatened can join NATO. That doesn't justify an attack by Russia. It allows them to defend themselves. But NATO isn't attacking Moscow. They aren't.
Russian President Putin's "special operation" aims to de-Nazify the Jewish-led nation.
To keep Crimea and the other two regions he has already stolen, he wants Ukraine undefended by NATO.

(Warlords have fought for control of the strategically important Crimea for over 2,000 years.)
Putin wants to own all of Ukraine.

Why?

The Black Sea is his goal.

Ports bring money and power, and Ukraine pipelines transport Russian energy products.
Putin wants their wheat, too — with 70% crop coverage, Ukraine would be their southern breadbasket, and Russia has no qualms about starving millions of Ukrainians to death to feed its people.

In the end, it's all about greed and power.
Putin wants to own everything Russia has ever owned. This year he turns 70, and he wants to be remembered like his hero Peter the Great.
In order to get it, he's willing to kill thousands of Ukrainians

Art imitates life

This story began when a Jewish TV comedian portrayed a teacher elected President after ranting about corruption.
Servant of the People, the hit sitcom, is now the leading centrist political party.
Right, President Zelenskyy won the hearts and minds of Ukrainians by imagining a fairer world.
A fair fight is something dictators, corporatists, monopolists, and warlords despise.
Now Zelenskyy and his people will die, allowing one of history's most corrupt leaders to amass even more power.

The poor always lose

Meanwhile, the West will impose economic sanctions on Russia.

China is likely to step in to help Russia — or at least the wealthy.

The poor and working class in Russia will suffer greatly if there is a hard crash or long-term depression.
Putin's friends will continue to drink champagne and eat caviar.

Russia cutting off oil, gas, and fertilizer could cause more inflation and possibly a recession if it cuts off supplies to the West. This causes more suffering and hardship for the Western poor and working class.

Why? a billionaire sociopath gets his dirt.

Yes, Russia is simply copying America. Some of us think all war is morally wrong, regardless of who does it.

But let's not kid ourselves right now.

The markets rallied after the biggest invasion in Europe since WWII.
Investors hope Ukraine collapses and Russian oil flows.
Unbridled capitalists value lifeless.

What we can do about Ukraine

When the Russian army invaded eastern Finland, my wife's grandmother fled as a child. 80 years later, Russia still has Karelia.
Russia invaded Ukraine today to retake two eastern provinces.
History has taught us nothing.
Past mistakes won't fix the future.

Instead, we should try:

  • Pray and/or meditate on our actions with our families.
  • Stop buying Russian products (vodka, obviously, but also pay more for hydro/solar/geothermal/etc.)
  • Stop wasting money on frivolous items and donate it to Ukrainian charities.

Here are 35+ places to donate.

  • To protest, gather a few friends, contact the media, and shake signs in front of the Russian embassy.
  • Prepare to welcome refugees.

More war won't save the planet or change hearts.

Only love can work.

Johnny Harris

Johnny Harris

3 years ago

The REAL Reason Putin is Invading Ukraine [video with transcript]

Transcript:

[Reporter] The Russian invasion of Ukraine.
Momentum is building for a war between Ukraine and Russia.
[Reporter] Tensions between Russia and the West
are growing rapidly.
[Reporter] President Biden considering deploying
thousands of troops to Eastern Europe.
There are now 100,000 troops
on the Eastern border of Ukraine.
Russia is setting up field hospitals on this border.
Like this is what preparation for war looks like.
A legitimate war.
Ukrainian troops are watching and waiting,
saying they are preparing for a fight.
The U.S. has ordered the families of embassy staff
to leave Ukraine.
Britain has sent all of their nonessential staff home.
And now the U.S. is sending tons of weapons and munitions
to Ukraine's army.
And we're even considering deploying
our own troops to the region.
I mean, this thing is heating up.
Meanwhile, Russia and the West have been in Geneva
and Brussels trying to talk it out,
and sort of getting nowhere.
The message is very clear.
Should Russia take further aggressive actions
against Ukraine the costs will be severe
and the consequences serious.
It's a scary, grim momentum that is unpredictable.
And the chances of miscalculation
and escalation are growing.

I want to explain what's going on here,
but I want to show you that this isn't just
typical geopolitical behavior.
Stuff that can just be explained on the map.
Instead, to understand why 100,000 troops are camped out
on Ukraine's Eastern border, ready for war,
you have to understand Russia
and how it's been cut down over the ages
from the Slavic empire that dominated this whole region
to then the Soviet Union,
which was defeated in the nineties.
And what you really have to understand here
is how that history is transposed
onto the brain of one man.
This guy, Vladimir Putin.
This is a story about regional domination
and struggles between big powers,
but really it's the story about
what Vladimir Putin really wants.
[Reporter] Russian troops moving swiftly
to take control of military bases in Crimea.
[Reporter] Russia has amassed more than 100,000 troops
and a lot of military hardware
at the border with Ukraine.

Let's dive back in.
Okay. Let's get up to speed on what's happening here.
And I'm just going to quickly give you the highlight version
of like the news that's happening,
because I want to get into the juicy part,
which is like why, the roots of all of this.
So let's go.
A few months ago, Russia started sending
more and more troops to this border.
It's this massive border between Ukraine and Russia.
They said they were doing a military exercise,
but the rest of the world was like,
"Yeah, we totally believe you Russia. Pshaw."
This was right before this big meeting
where North American and European countries
were coming together to talk about a lot
of different things, like these countries often do
in these diplomatic summits.
But soon, because of Russia's aggressive behavior
coming in and setting up 100,000 troops
on the border with Ukraine,
the entire summit turned into a whole, "WTF Russia,
what are you doing on the border of Ukraine," meeting.
Before the meeting Putin comes out and says,
"Listen, I have some demands for the West."
And everyone's like, "Okay, Russia, what are your demands?
You know, we have like, COVID19 right now.
And like, that's like surging.

So like, we don't need your like,
bluster about what your demands are."
And Putin's like, "No, here's my list of demands."
Putin's demands for the summit were this:
number one, that NATO, which is this big military alliance
between U.S., Canada, and Europe stop expanding,
meaning they don't let any new members in, okay.
So, Russia is like, "No more new members to your, like,
cool military club that I don't like.
You can't have any more members."
Number two, that NATO withdraw all of their troops
from anywhere in Eastern Europe.
Basically Putin is saying,
"I can veto any military cooperation
or troops going between countries
that have to do with Eastern Europe,
the place that used to be the Soviet Union."
Okay, and number three, Putin demands that America vow
not to protect its allies in Eastern Europe
with nuclear weapons.
"LOL," said all of the other countries,
"You're literally nuts, Vladimir Putin.
Like these are the most ridiculous demands, ever."
But there he is, Putin, with these demands.
These very, very aggressive demands.
And he sort of is implying that if his demands aren't met,
he's going to invade Ukraine.
I mean, it doesn't work like this.
This is not how international relations work.
You don't just show up and say like,
"I'm not gonna allow other countries to join your alliance
because it makes me feel uncomfortable."
But what I love about this list of demands
from Vladimir Putin for this summit
is that it gives us a clue
on what Vladimir Putin really wants.

What he's after here.
You read them closely and you can grasp his intentions.
But to grasp those intentions
you have to understand what NATO is.
and what Russia and Ukraine used to be.
(dramatic music)
Okay, so a while back I made this video
about why Russia is so damn big,
where I explain how modern day Russia started here in Kiev,
which is actually modern day Ukraine.
In other words, modern day Russia, as we know it,
has its original roots in Ukraine.
These places grew up together
and they eventually became a part
of the same mega empire called the Soviet Union.
They were deeply intertwined,
not just in their history and their culture,
but also in their economy and their politics.
So it's after World War II,
it's like the '50s, '60s, '70s, and NATO was formed,
the North Atlantic Treaty Organization.
This was a military alliance between all of these countries,
that was meant to sort of deter the Soviet Union
from expanding and taking over the world.
But as we all know, the Soviet Union,
which was Russia and all of these other countries,
collapsed in 1991.
And all of these Soviet republics,
including Ukraine, became independent,
meaning they were not now a part
of one big block of countries anymore.
But just because the border's all split up,
it doesn't mean that these cultural ties actually broke.
Like for example, the Soviet leader at the time
of the collapse of the Soviet Union, this guy, Gorbachev,
he was the son of a Ukrainian mother and a Russian father.
Like he grew up with his mother singing him
Ukrainian folk songs.

In his mind, Ukraine and Russia were like one thing.
So there was a major reluctance to accept Ukraine
as a separate thing from Russia.
In so many ways, they are one.
There was another Russian at the time
who did not accept this new division.
This young intelligence officer, Vladimir Putin,
who was starting to rise up in the ranks
of postSoviet Russia.
There's this amazing quote from 2005
where Putin is giving this stateoftheunionlike address,
where Putin declares the collapse of the Soviet Union,
quote, "The greatest catastrophe of the 20th century.
And as for the Russian people, it became a genuine tragedy.
Tens of millions of fellow citizens and countrymen
found themselves beyond the fringes of Russian territory."
Do you see how he frames this?
The Soviet Union were all one people in his mind.
And after it collapsed, all of these people
who are a part of the motherland were now outside
of the fringes or the boundaries of Russian territory.
First off, fact check.
Greatest catastrophe of the 20th century?
Like, do you remember what else happened
in the 20th century, Vladimir?
(ominous music)

Putin's worry about the collapse of this one people
starts to get way worse when the West, his enemy,
starts showing up to his neighborhood
to all these exSoviet countries that are now independent.
The West starts selling their ideology
of democracy and capitalism and inviting them
to join their military alliance called NATO.
And guess what?
These countries are totally buying it.
All these exSoviet countries are now joining NATO.
And some of them, the EU.
And Putin is hating this.
He's like not only did the Soviet Union divide
and all of these people are now outside
of the Russia motherland,
but now they're being persuaded by the West
to join their military alliance.
This is terrible news.
Over the years, this continues to happen,
while Putin himself starts to chip away
at Russian institutions, making them weaker and weaker.
He's silencing his rivals
and he's consolidating power in himself.
(triumphant music)

And in the past few years,
he's effectively silenced anyone who can challenge him;
any institution, any court,
or any political rival have all been silenced.
It's been decades since the Soviet Union fell,
but as Putin gains more power,
he still sees the region through the lens
of the old Cold War, Soviet, Slavic empire view.
He sees this region as one big block
that has been torn apart by outside forces.
"The greatest catastrophe of the 20th century."
And the worst situation of all of these,
according to Putin, is Ukraine,
which was like the gem of the Soviet Union.
There was tons of cultural heritage.
Again, Russia sort of started in Ukraine,
not to mention it was a very populous
and industrious, resourcerich place.
And over the years Ukraine has been drifting west.
It hasn't joined NATO yet, but more and more,
it's been electing proWestern presidents.
It's been flirting with membership in NATO.
It's becoming less and less attached
to the Russian heritage that Putin so adores.
And more than half of Ukrainians say
that they'd be down to join the EU.
64% of them say that it would be cool joining NATO.
But Putin can't handle this. He is in total denial.
Like an exboyfriend who handle his exgirlfriend
starting to date someone else,
Putin can't let Ukraine go.
He won't let go.

So for the past decade,
he's been trying to keep the West out
and bring Ukraine back into the motherland of Russia.
This usually takes the form of Putin sending
secret soldiers from Russia into Ukraine
to help the people in Ukraine who want to like separate
from Ukraine and join Russia.
It also takes the form of, oh yeah,
stealing entire parts of Ukraine for Russia.
Russian troops moving swiftly to take control
of military bases in Crimea.
Like in 2014, Putin just did this.
To what America is officially calling
a Russian invasion of Ukraine.
He went down and just snatched this bit of Ukraine
and folded it into Russia.
So you're starting to see what's going on here.
Putin's life's work is to salvage what he calls
the greatest catastrophe of the 20th century,
the division and the separation
of the Soviet republics from Russia.
So let's get to present day. It's 2022.
Putin is at it again.
And honestly, if you really want to understand
the mind of Vladimir Putin and his whole view on this,
you have to read this.
"On the History of Unity of Russians and Ukrainians,"
by Vladimir Putin.
A blog post that kind of sounds
like a ninth grade history essay.
In this essay, Vladimir Putin argues
that Russia and Ukraine are one people.
He calls them essentially the same historical
and spiritual space.

Kind of beautiful writing, honestly.
Anyway, he argues that the division
between the two countries is due to quote,
"a deliberate effort by those forces
that have always sought to undermine our unity."
And that the formula they use, these outside forces,
is a classic one: divide and rule.
And then he launches into this super indepth,
like 10page argument, as to every single historical beat
of Ukraine and Russia's history
to make this argument that like,
this is one people and the division is totally because
of outside powers, i.e. the West.
Okay, but listen, there's this moment
at the end of the post,
that actually kind of hit me in a big way.
He says this, "Just have a look at Austria and Germany,
or the U.S. and Canada, how they live next to each other.
Close in ethnic composition, culture,
and in fact, sharing one language,
they remain sovereign states with their own interests,
with their own foreign policy.
But this does not prevent them
from the closest integration or allied relations.
They have very conditional, transparent borders.
And when crossing them citizens feel at home.
They create families, study, work, do business.
Incidentally, so do millions of those born in Ukraine
who now live in Russia.
We see them as our own close people."
I mean, listen, like,
I'm not in support of what Putin is doing,
but like that, it's like a pretty solid like analogy.
If China suddenly showed up and started like
coaxing Canada into being a part of its alliance,
I would be a little bit like, "What's going on here?"
That's what Putin feels.
And so I kind of get what he means there.
There's a deep heritage and connection between these people.
And he's seen that falter and dissolve
and he doesn't like it.
He clearly genuinely feels a brotherhood
and this deep heritage connection
with the people of Ukraine.
Okay, okay, okay, okay. Putin, I get it.
Your essay is compelling there at the end.
You're clearly very smart and wellread.
But this does not justify what you've been up to. Okay?
It doesn't justify sending 100,000 troops to the border
or sending cyber soldiers to sabotage
the Ukrainian government, or annexing territory,
fueling a conflict that has killed
tens of thousands of people in Eastern Ukraine.
No. Okay.

No matter how much affection you feel for Ukrainian heritage
and its connection to Russia, this is not okay.
Again, it's like the boyfriend
who genuinely loves his girlfriend.
They had a great relationship,
but they broke up and she's free to see whomever she wants.
But Putin is not ready to let go.
[Man In Blue Shirt] What the hell's wrong with you?
I love you, Jessica.
What the hell is wrong with you?
Dude, don't fucking touch me.
I love you. Worldstar!
What is wrong with you? Just stop!
Putin has constructed his own reality here.
One in which Ukraine is actually being controlled
by shadowy Western forces
who are holding the people of Ukraine hostage.
And if that he invades, it will be a swift victory
because Ukrainians will accept him with open arms.
The great liberator.
(triumphant music)

Like, this guy's a total romantic.
He's a history buff and a romantic.
And he has a hill to die on here.
And it is liberating the people
who have been taken from the Russian motherland.
Kind of like the abusive boyfriend, who's like,
"She actually really loves me,
but it's her annoying friends
who were planting all these ideas in her head.
That's why she broke up with me."
And it's like, "No, dude, she's over you."
[Man In Blue Shirt] What the hell is wrong with you?
I love you, Jessica.
I mean, maybe this video should be called
Putin is just like your abusive exboyfriend.
[Man In Blue Shirt] What the hell is wrong with you?
I love you, Jessica!
Worldstar! What's wrong with you?
Okay. So where does this leave us?
It's 2022, Putin is showing up to these meetings in Europe
to tell them where he stands.
He says, "NATO, you cannot expand anymore. No new members.
And you need to withdraw all your troops
from Eastern Europe, my neighborhood."
He knows these demands will never be accepted
because they're ludicrous.
But what he's doing is showing a false effort to say,
"Well, we tried to negotiate with the West,
but they didn't want to."
Hence giving a little bit more justification
to a Russian invasion.
So will Russia invade? Is there war coming?
Maybe; it's impossible to know
because it's all inside of the head of this guy.
But, if I were to make the best argument
that war is not coming tomorrow,
I would look at a few things.
Number one, war in Ukraine would be incredibly costly
for Vladimir Putin.
Russia has a far superior army to Ukraine's,
but still, Ukraine has a very good army
that is supported by the West
and would give Putin a pretty bad bloody nose
in any invasion.

Controlling territory in Ukraine would be very hard.
Ukraine is a giant country.
They would fight back and it would be very hard
to actually conquer and take over territory.
Another major point here is that if Russia invades Ukraine,
this gives NATO new purpose.
If you remember, NATO was created because of the Cold War,
because the Soviet Union was big and nuclear powered.
Once the Soviet Union fell,
NATO sort of has been looking for a new purpose
over the past couple of decades.
If Russia invades Ukraine,
NATO suddenly has a brand new purpose to unite
and to invest in becoming more powerful than ever.
Putin knows that.
And it would be very bad news for him if that happened.
But most importantly, perhaps the easiest clue
for me to believe that war isn't coming tomorrow
is the Russian propaganda machine
is not preparing the Russian people for an invasion.
In 2014, when Russia was about to invade
and take over Crimea, this part of Ukraine,
there was a barrage of state propaganda
that prepared the Russian people
that this was a justified attack.
So when it happened, it wasn't a surprise
and it felt very normal.

That isn't happening right now in Russia.
At least for now. It may start happening tomorrow.
But for now, I think Putin is showing up to the border,
flexing his muscles and showing the West that he is earnest.
I'm not sure that he's going to invade tomorrow,
but he very well could.
I mean, read the guy's blog post
and you'll realize that he is a romantic about this.
He is incredibly idealistic about the glory days
of the Slavic empires, and he wants to get it back.
So there is dangerous momentum towards war.
And the way war works is even a small little, like, fight,
can turn into the other guy
doing something bigger and crazier.
And then the other person has to respond
with something a little bit bigger.
That's called escalation.
And there's not really a ceiling
to how much that momentum can spin out of control.
That is why it's so scary when two nuclear countries
go to war with each other,
because there's kind of no ceiling.
So yeah, it's dangerous. This is scary.
I'm not sure what happens next here,
but the best we can do is keep an eye on this.
At least for now, we better understand
what Putin really wants out of all of this.

Thanks for watching.

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Farhan Ali Khan

Farhan Ali Khan

2 years ago

Introduction to Zero-Knowledge Proofs: The Art of Proving Without Revealing

Zero-Knowledge Proofs for Beginners

Published here originally.

Introduction

I Spy—did you play as a kid? One person chose a room object, and the other had to guess it by answering yes or no questions. I Spy was entertaining, but did you know it could teach you cryptography?

Zero Knowledge Proofs let you show your pal you know what they picked without exposing how. Math replaces electronics in this secret spy mission. Zero-knowledge proofs (ZKPs) are sophisticated cryptographic tools that allow one party to prove they have particular knowledge without revealing it. This proves identification and ownership, secures financial transactions, and more. This article explains zero-knowledge proofs and provides examples to help you comprehend this powerful technology.

What is a Proof of Zero Knowledge?

Zero-knowledge proofs prove a proposition is true without revealing any other information. This lets the prover show the verifier that they know a fact without revealing it. So, a zero-knowledge proof is like a magician's trick: the prover proves they know something without revealing how or what. Complex mathematical procedures create a proof the verifier can verify.

Want to find an easy way to test it out? Try out with tis awesome example! ZK Crush

Describe it as if I'm 5

Alex and Jack found a cave with a center entrance that only opens when someone knows the secret. Alex knows how to open the cave door and wants to show Jack without telling him.

Alex and Jack name both pathways (let’s call them paths A and B).

  1. In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.

  2. As Alex made his decision, Jack entered the cave and asked him to exit from the B path.

  3. Jack can confirm that Alex really does know the key to open the door because he came out for the B path and used it.

To conclude, Alex and Jack repeat:

  1. Alex walks into the cave.

  2. Alex follows a random route.

  3. Jack walks into the cave.

  4. Alex is asked to follow a random route by Jack.

  5. Alex follows Jack's advice and heads back that way.

What is a Zero Knowledge Proof?

At a high level, the aim is to construct a secure and confidential conversation between the prover and the verifier, where the prover convinces the verifier that they have the requisite information without disclosing it. The prover and verifier exchange messages and calculate in each round of the dialogue.

The prover uses their knowledge to prove they have the information the verifier wants during these rounds. The verifier can verify the prover's truthfulness without learning more by checking the proof's mathematical statement or computation.

Zero knowledge proofs use advanced mathematical procedures and cryptography methods to secure communication. These methods ensure the evidence is authentic while preventing the prover from creating a phony proof or the verifier from extracting unnecessary information.

ZK proofs require examples to grasp. Before the examples, there are some preconditions.

Criteria for Proofs of Zero Knowledge

  1. Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.

  2. Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.

  3. Zero-knowledge: The verifier only realizes that the proposition being proved is true. In other words, the proof only establishes the veracity of the proposition being supported and nothing more.

The zero-knowledge condition is crucial. Zero-knowledge proofs show only the secret's veracity. The verifier shouldn't know the secret's value or other details.

Example after example after example

To illustrate, take a zero-knowledge proof with several examples:

Initial Password Verification Example

You want to confirm you know a password or secret phrase without revealing it.

Use a zero-knowledge proof:

  1. You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.

  2. The puzzle or problem is then solved using the hidden knowledge that you have learned. You may, for instance, utilize your understanding of the password to determine the components of a particular number.

  3. You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.

  4. You go through this process several times with various riddles or issues to persuade the verifier that you actually are aware of the secret knowledge.

You solved the mathematical puzzles or problems, proving to the verifier that you know the hidden information. The proof is zero-knowledge since the verifier only sees puzzle solutions, not the secret information.

In this scenario, the mathematical challenge or problem represents the secret, and solving it proves you know it. The evidence does not expose the secret, and the verifier just learns that you know it.

My simple example meets the zero-knowledge proof conditions:

  1. Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.

  2. Soundness: The proof is sound because the verifier can use a publicly known algorithm to confirm that your answer to the mathematical conundrum or difficulty is accurate.

  3. Zero-knowledge: The proof is zero-knowledge because all the verifier learns is that you are aware of the confidential information. Beyond the fact that you are aware of it, the verifier does not learn anything about the secret information itself, such as the password or the factors of the number. As a result, the proof does not provide any new insights into the secret.

Explanation #2: Toss a coin.

One coin is biased to come up heads more often than tails, while the other is fair (i.e., comes up heads and tails with equal probability). You know which coin is which, but you want to show a friend you can tell them apart without telling them.

Use a zero-knowledge proof:

  1. One of the two coins is chosen at random, and you secretly flip it more than once.

  2. You show your pal the following series of coin flips without revealing which coin you actually flipped.

  3. Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.

  4. Then, without revealing which coin is which, you can use your understanding of the secret order of coin flips to determine which coin your friend flipped.

  5. To persuade your friend that you can actually differentiate between the coins, you repeat this process multiple times using various secret coin-flipping sequences.

In this example, the series of coin flips represents the knowledge of biased and fair coins. You can prove you know which coin is which without revealing which is biased or fair by employing a different secret sequence of coin flips for each round.

The evidence is zero-knowledge since your friend does not learn anything about which coin is biased and which is fair other than that you can tell them differently. The proof does not indicate which coin you flipped or how many times you flipped it.

The coin-flipping example meets zero-knowledge proof requirements:

  1. Completeness: If you actually know which coin is biased and which is fair, you should be able to distinguish between them based on the order of coin flips, and your friend should be persuaded that you can.

  2. Soundness: Your friend may confirm that you are correctly recognizing the coins by flipping one of them in front of you and validating your answer, thus the proof is sound in that regard. Because of this, your acquaintance can be sure that you are not just speculating or picking a coin at random.

  3. Zero-knowledge: The argument is that your friend has no idea which coin is biased and which is fair beyond your ability to distinguish between them. Your friend is not made aware of the coin you used to make your decision or the order in which you flipped the coins. Consequently, except from letting you know which coin is biased and which is fair, the proof does not give any additional information about the coins themselves.

Figure out the prime number in Example #3.

You want to prove to a friend that you know their product n=pq without revealing p and q. Zero-knowledge proof?

Use a variant of the RSA algorithm. Method:

  1. You determine a new number s = r2 mod n by computing a random number r.

  2. You email your friend s and a declaration that you are aware of the values of p and q necessary for n to equal pq.

  3. A random number (either 0 or 1) is selected by your friend and sent to you.

  4. You send your friend r as evidence that you are aware of the values of p and q if e=0. You calculate and communicate your friend's s/r if e=1.

  5. Without knowing the values of p and q, your friend can confirm that you know p and q (in the case where e=0) or that s/r is a legitimate square root of s mod n (in the situation where e=1).

This is a zero-knowledge proof since your friend learns nothing about p and q other than their product is n and your ability to verify it without exposing any other information. You can prove that you know p and q by sending r or by computing s/r and sending that instead (if e=1), and your friend can verify that you know p and q or that s/r is a valid square root of s mod n without learning anything else about their values. This meets the conditions of completeness, soundness, and zero-knowledge.

Zero-knowledge proofs satisfy the following:

  1. Completeness: The prover can demonstrate this to the verifier by computing q = n/p and sending both p and q to the verifier. The prover also knows a prime number p and a factorization of n as p*q.

  2. Soundness: Since it is impossible to identify any pair of numbers that correctly factorize n without being aware of its prime factors, the prover is unable to demonstrate knowledge of any p and q that do not do so.

  3. Zero knowledge: The prover only admits that they are aware of a prime number p and its associated factor q, which is already known to the verifier. This is the extent of their knowledge of the prime factors of n. As a result, the prover does not provide any new details regarding n's prime factors.

Types of Proofs of Zero Knowledge

Each zero-knowledge proof has pros and cons. Most zero-knowledge proofs are:

  1. Interactive Zero Knowledge Proofs: The prover and the verifier work together to establish the proof in this sort of zero-knowledge proof. The verifier disputes the prover's assertions after receiving a sequence of messages from the prover. When the evidence has been established, the prover will employ these new problems to generate additional responses.

  2. Non-Interactive Zero Knowledge Proofs: For this kind of zero-knowledge proof, the prover and verifier just need to exchange a single message. Without further interaction between the two parties, the proof is established.

  3. A statistical zero-knowledge proof is one in which the conclusion is reached with a high degree of probability but not with certainty. This indicates that there is a remote possibility that the proof is false, but that this possibility is so remote as to be unimportant.

  4. Succinct Non-Interactive Argument of Knowledge (SNARKs): SNARKs are an extremely effective and scalable form of zero-knowledge proof. They are utilized in many different applications, such as machine learning, blockchain technology, and more. Similar to other zero-knowledge proof techniques, SNARKs enable one party—the prover—to demonstrate to another—the verifier—that they are aware of a specific piece of information without disclosing any more information about that information.

  5. The main characteristic of SNARKs is their succinctness, which refers to the fact that the size of the proof is substantially smaller than the amount of the original data being proved. Because to its high efficiency and scalability, SNARKs can be used in a wide range of applications, such as machine learning, blockchain technology, and more.

Uses for Zero Knowledge Proofs

ZKP applications include:

  1. Verifying Identity ZKPs can be used to verify your identity without disclosing any personal information. This has uses in access control, digital signatures, and online authentication.

  2. Proof of Ownership ZKPs can be used to demonstrate ownership of a certain asset without divulging any details about the asset itself. This has uses for protecting intellectual property, managing supply chains, and owning digital assets.

  3. Financial Exchanges Without disclosing any details about the transaction itself, ZKPs can be used to validate financial transactions. Cryptocurrency, internet payments, and other digital financial transactions can all use this.

  4. By enabling parties to make calculations on the data without disclosing the data itself, Data Privacy ZKPs can be used to preserve the privacy of sensitive data. Applications for this can be found in the financial, healthcare, and other sectors that handle sensitive data.

  5. By enabling voters to confirm that their vote was counted without disclosing how they voted, elections ZKPs can be used to ensure the integrity of elections. This is applicable to electronic voting, including internet voting.

  6. Cryptography Modern cryptography's ZKPs are a potent instrument that enable secure communication and authentication. This can be used for encrypted messaging and other purposes in the business sector as well as for military and intelligence operations.

Proofs of Zero Knowledge and Compliance

Kubernetes and regulatory compliance use ZKPs in many ways. Examples:

  1. Security for Kubernetes ZKPs offer a mechanism to authenticate nodes without disclosing any sensitive information, enhancing the security of Kubernetes clusters. ZKPs, for instance, can be used to verify, without disclosing the specifics of the program, that the nodes in a Kubernetes cluster are running permitted software.

  2. Compliance Inspection Without disclosing any sensitive information, ZKPs can be used to demonstrate compliance with rules like the GDPR, HIPAA, and PCI DSS. ZKPs, for instance, can be used to demonstrate that data has been encrypted and stored securely without divulging the specifics of the mechanism employed for either encryption or storage.

  3. Access Management Without disclosing any private data, ZKPs can be used to offer safe access control to Kubernetes resources. ZKPs can be used, for instance, to demonstrate that a user has the necessary permissions to access a particular Kubernetes resource without disclosing the details of those permissions.

  4. Safe Data Exchange Without disclosing any sensitive information, ZKPs can be used to securely transmit data between Kubernetes clusters or between several businesses. ZKPs, for instance, can be used to demonstrate the sharing of a specific piece of data between two parties without disclosing the details of the data itself.

  5. Kubernetes deployments audited Without disclosing the specifics of the deployment or the data being processed, ZKPs can be used to demonstrate that Kubernetes deployments are working as planned. This can be helpful for auditing purposes and for ensuring that Kubernetes deployments are operating as planned.

ZKPs preserve data and maintain regulatory compliance by letting parties prove things without revealing sensitive information. ZKPs will be used more in Kubernetes as it grows.

Evgenii Nelepko

Evgenii Nelepko

3 years ago

My 3 biggest errors as a co-founder and CEO

Reflections on the closed company Hola! Dating app

My pitch to investors

I'll discuss my fuckups as an entrepreneur and CEO. All of them refer to the dating app Hola!, which I co-founded and starred in.

Spring 2021 was when we started. Two techies and two non-techies created a dating app. Pokemon Go and Tinder were combined.

Online dating is a business, and it takes two weeks from a like to a date. We questioned online dating app users if they met anyone offline last year.

75% replied yes, 50% sometimes, 25% usually.

Offline dating is popular, yet people have concerns.

  • Men are reluctant to make mistakes in front of others.

  • Women are curious about the background of everyone who approaches them.

We designed unique mechanics that let people date after a match. No endless chitchat. Women would be safe while men felt like cowboys.

I wish to emphasize three faults that lead to founders' estrangement.

This detachment ultimately led to us shutting down the company.

The wrong technology stack

Situation

Instead of generating a faster MVP and designing an app in a universal stack for iOS and Android, I argued we should pilot the app separately for iOS and Android. Technical founders' expertise made this possible.

Self-reflection

Mistaken strategy. We lost time and resources developing two apps at once. We chose iOS since it's more profitable. Apple took us out after the release, citing Guideline 4.3 Spam. After 4 months, we had nothing. We had a long way to go to get the app on Android and the Store.

I suggested creating a uniform platform for the company's growth. This makes parallel product development easier. The strategist's lack of experience and knowledge made it a piece of crap.

What would I have changed if I could?

We should have designed an Android universal stack. I expected Apple to have issues with a dating app.

Our approach should have been to launch something and subsequently improve it, but prejudice won.

The lesson

Discuss the IT stack with your CTO. It saves time and money. Choose the easiest MVP method.

UX description

2. A tardy search for investments

Situation

Though the universe and other founders encouraged me to locate investors first, I started pitching when we almost had an app.

When angels arrived, it was time to close. The app was banned, war broke out, I left the country, and the other co-founders stayed. We had no savings.

Self-reflection

I loved interviewing users. I'm proud of having done 1,000 interviews. I wanted to understand people's pain points and improve the product.

Interview results no longer affected the product. I was terrified to start pitching. I filled out accelerator applications and redid my presentation. You must go through that so you won't be terrified later.

What would I have changed if I could?

Get an external or internal mentor to help me with my first pitch as soon as possible. I'd be supported if criticized. He'd cheer with me if there was enthusiasm.

In 99% of cases, I'm comfortable jumping into the unknown, but there are exceptions. The mentor's encouragement would have prompted me to act sooner.

The lesson

Begin fundraising immediately. Months may pass. Show investors your pre-MVP project. Draw inferences from feedback.

3. Role ambiguity

Situation

My technical co-founders were also part-time lead developers, which produced communication issues. As co-founders, we communicated well and recognized the problems. Stakes, vesting, target markets, and approach were agreed upon.

We were behind schedule. Technical debt and strategic gap grew.

Bi-daily and weekly reviews didn't help. Each time, there were explanations. Inside, I was freaking out.

Our team

Self-reflection

I am a fairly easy person to talk to. I always try to stick to agreements; otherwise, my head gets stuffed with unnecessary information, interpretations, and emotions.

Sit down -> talk -> decide -> do -> evaluate the results. Repeat it.

If I don't get detailed comments, I start ruining everyone's mood. If there's a systematic violation of agreements without a good justification, I won't join the project or I'll end the collaboration.

What would I have done otherwise?

This is where it’s scariest to draw conclusions. Probably the most logical thing would have been not to start the project as we started it. But that was already a completely different project. So I would not have done anything differently and would have failed again.

But I drew conclusions for the future.

The lesson

First-time founders should find an adviser or team coach for a strategic session. It helps split the roles and responsibilities.

Simon Egersand

Simon Egersand

3 years ago

Working from home for more than two years has taught me a lot.

Since the pandemic, I've worked from home. It’s been +2 years (wow, time flies!) now, and during this time I’ve learned a lot. My 4 remote work lessons.

I work in a remote distributed team. This team setting shaped my experience and teachings.

Isolation ("I miss my coworkers")

The most obvious point. I miss going out with my coworkers for coffee, weekend chats, or just company while I work. I miss being able to go to someone's desk and ask for help. On a remote world, I must organize a meeting, share my screen, and avoid talking over each other in Zoom - sigh!

Social interaction is more vital for my health than I believed.

Online socializing stinks

My company used to come together every Friday to play Exploding Kittens, have food and beer, and bond over non-work things.

Different today. Every Friday afternoon is for fun, but it's not the same. People with screen weariness miss meetings, which makes sense. Sometimes you're too busy on Slack to enjoy yourself.

We laugh in meetings, but it's not the same as face-to-face.

Digital social activities can't replace real-world ones

Improved Work-Life Balance, if You Let It

At the outset of the pandemic, I recognized I needed to take better care of myself to survive. After not leaving my apartment for a few days and feeling miserable, I decided to walk before work every day. This turned into a passion for exercise, and today I run or go to the gym before work. I use my commute time for healthful activities.

Working from home makes it easier to keep working after hours. I sometimes forget the time and find myself writing coding at dinnertime. I said, "One more test." This is a disadvantage, therefore I keep my office schedule.

Spend your commute time properly and keep to your office schedule.

Remote Pair Programming Is Hard

As a software developer, I regularly write code. My team sometimes uses pair programming to write code collaboratively. One person writes code while another watches, comments, and asks questions. I won't list them all here.

Internet pairing is difficult. My team struggles with this. Even with Tuple, it's challenging. I lose attention when I get a notification or check my computer.

I miss a pen and paper to rapidly sketch down my thoughts for a colleague or a whiteboard for spirited talks with others. Best answers are found through experience.

Real-life pair programming beats the best remote pair programming tools.

Lessons Learned

Here are 4 lessons I've learned working remotely for 2 years.

  • Socializing is more vital to my health than I anticipated.

  • Digital social activities can't replace in-person ones.

  • Spend your commute time properly and keep your office schedule.

  • Real-life pair programming beats the best remote tools.

Conclusion

Our era is fascinating. Remote labor has existed for years, but software companies have just recently had to adapt. Companies who don't offer remote work will lose talent, in my opinion.

We're still figuring out the finest software development approaches, programming language features, and communication methods since the 1960s. I can't wait to see what advancements assist us go into remote work.

I'll certainly work remotely in the next years, so I'm interested to see what I've learnt from this post then.


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