You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has two very powerful applications:

1. Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
2. Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.

But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.

Why ZK-SNARKs "should" be hard

Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.

A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.

One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?

Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.

But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.

It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.

If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? There is a clever solution.

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.

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.

4 Ways To Manage Remote Teams & Employees

The wheels hit the ground as I landed in Rochester.

Our six-person satellite office was now part of my team.

Their manager only reported to me the day before, but I had my ticket booked ahead of time.

I had managed remote employees before but this was different. Engineers dialed into headquarters for every meeting.

So when I learned about the org chart change, I knew a strong first impression would set the tone for everything else.

I was either their boss, or their boss's boss, and I needed them to know I was committed.

Managing a fleet of satellite freelancers or multiple offices requires treating others as more than just a face behind a screen.

The good news is that you can start using these techniques right now to better understand and elevate virtual team members.

1. Make Visits To Other Offices

If budgeted, visit and work from offices where teams and employees report to you. Only by living alongside them can one truly comprehend their problems with communication and other aspects of modern life.

2. Have Others Come to You

• Having remote, distributed, or satellite employees and teams visit headquarters every quarter or semi-quarterly allows the main office culture to rub off on them.

When remote team members visit, more people get to meet them, which builds empathy.

If you can't afford to fly everyone, at least bring remote managers or leaders. Hopefully they can resurrect some culture.

3. Weekly Work From Home

No home office policy?

Make one.

WFH is a team-building, problem-solving, and office-viewing opportunity.

For dial-in meetings, I started working from home on occasion.

It also taught me which teams “forget” or “skip” calls.

This isn't as accurate for understanding teams in other offices, but it can be done at any time.

4. Increase Contact Even If It’s Just To Chat

Don't underestimate office banter.

Sometimes it's about bonding and trust, other times it's about business.

If you get all this information in real-time, please forward it.

Even if nothing critical is happening, call remote team members to check in and chat.

I guarantee that building relationships and rapport will increase both their job satisfaction and yours.