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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.

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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