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Sam Warain

Sam Warain

3 years ago

Sam Altman, CEO of Open AI, foresees the next trillion-dollar AI company

More on Science

Adam Frank

Adam Frank

3 years ago

Humanity is not even a Type 1 civilization. What might a Type 3 be capable of?

The Kardashev scale grades civilizations from Type 1 to Type 3 based on energy harvesting.

How do technologically proficient civilizations emerge across timescales measuring in the tens of thousands or even millions of years? This is a question that worries me as a researcher in the search for “technosignatures” from other civilizations on other worlds. Since it is already established that longer-lived civilizations are the ones we are most likely to detect, knowing something about their prospective evolutionary trajectories could be translated into improved search tactics. But even more than knowing what to seek for, what I really want to know is what happens to a society after so long time. What are they capable of? What do they become?

This was the question Russian SETI pioneer Nikolai Kardashev asked himself back in 1964. His answer was the now-famous “Kardashev Scale.” Kardashev was the first, although not the last, scientist to try and define the processes (or stages) of the evolution of civilizations. Today, I want to launch a series on this question. It is crucial to technosignature studies (of which our NASA team is hard at work), and it is also important for comprehending what might lay ahead for mankind if we manage to get through the bottlenecks we have now.

The Kardashev scale

Kardashev’s question can be expressed another way. What milestones in a civilization’s advancement up the ladder of technical complexity will be universal? The main notion here is that all (or at least most) civilizations will pass through some kind of definable stages as they progress, and some of these steps might be mirrored in how we could identify them. But, while Kardashev’s major focus was identifying signals from exo-civilizations, his scale gave us a clear way to think about their evolution.

The classification scheme Kardashev employed was not based on social systems of ethics because they are something that we can probably never predict about alien cultures. Instead, it was built on energy, which is something near and dear to the heart of everybody trained in physics. Energy use might offer the basis for universal stages of civilisation progression because you cannot do the work of establishing a civilization without consuming energy. So, Kardashev looked at what energy sources were accessible to civilizations as they evolved technologically and used those to build his scale.

From Kardashev’s perspective, there are three primary levels or “types” of advancement in terms of harvesting energy through which a civilization should progress.

Type 1: Civilizations that can capture all the energy resources of their native planet constitute the first stage. This would imply capturing all the light energy that falls on a world from its host star. This makes it reasonable, given solar energy will be the largest source available on most planets where life could form. For example, Earth absorbs hundreds of atomic bombs’ worth of energy from the Sun every second. That is a rather formidable energy source, and a Type 1 race would have all this power at their disposal for civilization construction.

Type 2: These civilizations can extract the whole energy resources of their home star. Nobel Prize-winning scientist Freeman Dyson famously anticipated Kardashev’s thinking on this when he imagined an advanced civilization erecting a large sphere around its star. This “Dyson Sphere” would be a machine the size of the complete solar system for gathering stellar photons and their energy.

Type 3: These super-civilizations could use all the energy produced by all the stars in their home galaxy. A normal galaxy has a few hundred billion stars, so that is a whole lot of energy. One way this may be done is if the civilization covered every star in their galaxy with Dyson spheres, but there could also be more inventive approaches.

Implications of the Kardashev scale

Climbing from Type 1 upward, we travel from the imaginable to the god-like. For example, it is not hard to envisage utilizing lots of big satellites in space to gather solar energy and then beaming that energy down to Earth via microwaves. That would get us to a Type 1 civilization. But creating a Dyson sphere would require chewing up whole planets. How long until we obtain that level of power? How would we have to change to get there? And once we get to Type 3 civilizations, we are virtually thinking about gods with the potential to engineer the entire cosmos.

For me, this is part of the point of the Kardashev scale. Its application for thinking about identifying technosignatures is crucial, but even more strong is its capacity to help us shape our imaginations. The mind might become blank staring across hundreds or thousands of millennia, and so we need tools and guides to focus our attention. That may be the only way to see what life might become — what we might become — once it arises to start out beyond the boundaries of space and time and potential.


This is a summary. Read the full article here.

Sara_Mednick

Sara_Mednick

3 years ago

Since I'm a scientist, I oppose biohacking

Understanding your own energy depletion and restoration is how to truly optimize

Photo: Towfiqu barbhuiya / Unsplash

Hack has meant many bad things for centuries. In the 1800s, a hack was a meager horse used to transport goods.

Modern usage describes a butcher or ax murderer's cleaver chop. The 1980s programming boom distinguished elegant code from "hacks". Both got you to your goal, but the latter made any programmer cringe and mutter about changing the code. From this emerged the hacker trope, the friendless anti-villain living in a murky hovel lit by the computer monitor, eating junk food and breaking into databases to highlight security system failures or steal hotdog money.

Remember the 1995 movie, Hackers, in which a bunch of super cool programmers (said no one ever) get caught up in a plot to destroy the world and only teenybopper Angelina Jolie and her punk rock gang of nerd-bots can use their lightening quick typing skills to save the world? Remember public phones?

Now, start-a-billion-dollar-business-from-your-garage types have shifted their sights from app development to DIY biology, coining the term "bio-hack". This is a required keyword and meta tag for every fitness-related podcast, book, conference, app, or device.

Bio-hacking involves bypassing your body and mind's security systems to achieve a goal. Many biohackers' initial goals were reasonable, like lowering blood pressure and weight. Encouraged by their own progress, self-determination, and seemingly exquisite control of their biology, they aimed to outsmart aging and death to live 180 to 1000 years (summarized well in this vox.com article).

With this grandiose north star, the hunt for novel supplements and genetic engineering began.

Companies selling do-it-yourself biological manipulations cite lab studies in mice as proof of their safety and success in reversing age-related diseases or promoting longevity in humans (the goal changes depending on whether a company is talking to the federal government or private donors).

The FDA is slower than science, they say. Why not alter your biochemistry by buying pills online, editing your DNA with a CRISPR kit, or using a sauna delivered to your home? How about a microchip or electrical stimulator?

What could go wrong?


I'm not the neo-police, making citizen's arrests every time someone introduces a new plumbing gadget or extrapolates from animal research on resveratrol or catechins that we should drink more red wine or eat more chocolate. As a scientist who's spent her career asking, "Can we get better?" I've come to view bio-hacking as misguided, profit-driven, and counterproductive to its followers' goals.

We're creatures of nature. Despite all the new gadgets and bio-hacks, we still use Roman plumbing technology, and the best way to stay fit, sharp, and happy is to follow a recipe passed down since the beginning of time. Bacteria, plants, and all natural beings are rhythmic, with alternating periods of high activity and dormancy, whether measured in seconds, hours, days, or seasons. Nature repeats successful patterns.

During the Upstate, every cell in your body is naturally primed and pumped full of glycogen and ATP (your cells' energy currencies), as well as cortisol, which supports your muscles, heart, metabolism, cognitive prowess, emotional regulation, and general "get 'er done" attitude. This big energy release depletes your batteries and requires the Downstate, when your subsystems recharge at the cellular level.

Downstates are when you give your heart a break from pumping nutrient-rich blood through your body; when you give your metabolism a break from inflammation, oxidative stress, and sympathetic arousal caused by eating fast food — or just eating too fast; or when you give your mind a chance to wander, think bigger thoughts, and come up with new creative solutions. When you're responding to notifications, emails, and fires, you can't relax.

Every biological plant and animal is regulated by rhythms of energy-depleting Upstate and energy-restoring Downstates.

Downstates aren't just for consistently recharging your battery. By spending time in the Downstate, your body and brain get extra energy and nutrients, allowing you to grow smarter, faster, stronger, and more self-regulated. This state supports half-marathon training, exam prep, and mediation. As we age, spending more time in the Downstate is key to mental and physical health, well-being, and longevity.

When you prioritize energy-demanding activities during Upstate periods and energy-replenishing activities during Downstate periods, all your subsystems, including cardiovascular, metabolic, muscular, cognitive, and emotional, hum along at their optimal settings. When you synchronize the Upstates and Downstates of these individual rhythms, their functioning improves. A hard workout causes autonomic stress, which triggers Downstate recovery.

This zig-zag trajectory of performance improvement illustrates that getting better at anything in life isn’t a straight shot. The close-up box shows how prioritizing Downstate recovery after an Upstate exertion (e.g., hard workout) leads to RECOVERYPLUS. Image from The Power of the Downstate by Sara C. Mednick PhD.

By choosing the right timing and type of exercise during the day, you can ensure a deeper recovery and greater readiness for the next workout by working with your natural rhythms and strengthening your autonomic and sleep Downstates.

Morning cardio workouts increase deep sleep compared to afternoon workouts. Timing and type of meals determine when your sleep hormone melatonin is released, ushering in sleep.

Rhythm isn't a hack. It's not a way to cheat the system or the boss. Nature has honed its optimization wisdom over trillions of days and nights. Stop looking for quick fixes. You're a whole system made of smaller subsystems that must work together to function well. No one pill or subsystem will make it all work. Understanding and coordinating your rhythms is free, easy, and only benefits you.

Dr. Sara C. Mednick is a cognitive neuroscientist at UC Irvine and author of The Power of the Downstate (HachetteGO)

Laura Sanders

Laura Sanders

3 years ago

Xenobots, tiny living machines, can duplicate themselves.

Strange and complex behavior of frog cell blobs


A xenobot “parent,” shaped like a hungry Pac-Man (shown in red false color), created an “offspring” xenobot (green sphere) by gathering loose frog cells in its opening.

Tiny “living machines” made of frog cells can make copies of themselves. This newly discovered renewal mechanism may help create self-renewing biological machines.

According to Kirstin Petersen, an electrical and computer engineer at Cornell University who studies groups of robots, “this is an extremely exciting breakthrough.” She says self-replicating robots are a big step toward human-free systems.

Researchers described the behavior of xenobots earlier this year (SN: 3/31/21). Small clumps of skin stem cells from frog embryos knitted themselves into small spheres and started moving. Cilia, or cellular extensions, powered the xenobots around their lab dishes.

The findings are published in the Proceedings of the National Academy of Sciences on Dec. 7. The xenobots can gather loose frog cells into spheres, which then form xenobots.
The researchers call this type of movement-induced reproduction kinematic self-replication. The study's coauthor, Douglas Blackiston of Tufts University in Medford, Massachusetts, and Harvard University, says this is typical. For example, sexual reproduction requires parental sperm and egg cells. Sometimes cells split or budded off from a parent.

“This is unique,” Blackiston says. These xenobots “find loose parts in the environment and cobble them together.” This second generation of xenobots can move like their parents, Blackiston says.
The researchers discovered that spheroid xenobots could only produce one more generation before dying out. The original xenobots' shape was predicted by an artificial intelligence program, allowing for four generations of replication.

A C shape, like an openmouthed Pac-Man, was predicted to be a more efficient progenitor. When improved xenobots were let loose in a dish, they began scooping up loose cells into their gaping “mouths,” forming more sphere-shaped bots (see image below). As many as 50 cells clumped together in the opening of a parent to form a mobile offspring. A xenobot is made up of 4,000–6,000 frog cells.

Petersen likes the Xenobots' small size. “The fact that they were able to do this at such a small scale just makes it even better,” she says. Miniature xenobots could sculpt tissues for implantation or deliver therapeutics inside the body.

Beyond the xenobots' potential jobs, the research advances an important science, says study coauthor and Tufts developmental biologist Michael Levin. The science of anticipating and controlling the outcomes of complex systems, he says.

“No one could have predicted this,” Levin says. “They regularly surprise us.” Researchers can use xenobots to test the unexpected. “This is about advancing the science of being less surprised,” Levin says.

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Alexander Nguyen

Alexander Nguyen

3 years ago

How can you bargain for $300,000 at Google?

Don’t give a number

Photo by Vitaly Taranov on Unsplash

Google pays its software engineers generously. While many of their employees are competent, they disregard a critical skill to maximize their pay.

Negotiation.

If Google employees have never negotiated, they're as helpless as anyone else.

In this piece, I'll reveal a compensation negotiation tip that will set you apart.

The Fallacy of Negotiating

How do you negotiate your salary? “Just give them a number twice the amount you really want”. - Someplace on the internet

Above is typical negotiation advice. If you ask for more than you want, the recruiter may meet you halfway.

It seems logical and great, but here's why you shouldn't follow that advice.

Haitian hostage rescue

In 1977, an official's aunt was kidnapped in Haiti. The kidnappers demanded $150,000 for the aunt's life. It seems reasonable until you realize why kidnappers want $150,000.

FBI detective and negotiator Chris Voss researched why they demanded so much.

“So they could party through the weekend”

When he realized their ransom was for partying, he offered $4,751 and a CD stereo. Criminals freed the aunt.

These thieves gave 31.57x their estimated amount and got a fraction. You shouldn't trust these thieves to negotiate your compensation.

What happened?

Negotiating your offer and Haiti

This narrative teaches you how to negotiate with a large number.

You can and will be talked down.

If a recruiter asks your wage expectation and you offer double, be ready to explain why.

If you can't justify your request, you may be offered less. The recruiter will notice and talk you down.

Reasonably,

  • a tiny bit more than the present amount you earn

  • a small premium over an alternative offer

  • a little less than the role's allotted amount

Real-World Illustration

Photo by Christina @ wocintechchat.com on Unsplash

Recruiter: What’s your expected salary? Candidate: (I know the role is usually $100,000) $200,000 Recruiter: How much are you compensated in your current role? Candidate: $90,000 Recruiter: We’d be excited to offer you $95,000 for your experiences for the role.

So Why Do They Even Ask?

Recruiters ask for a number to negotiate a lower one. Asking yourself limits you.

You'll rarely get more than you asked for, and your request can be lowered.

The takeaway from all of this is to never give an expected compensation.

Tell them you haven't thought about it when you applied.

Alexander Nguyen

Alexander Nguyen

3 years ago

A Comparison of Amazon, Microsoft, and Google's Compensation

Learn or earn

In 2020, I started software engineering. My base wage has progressed as follows:

Amazon (2020): $112,000

Microsoft (2021): $123,000

Google (2022): $169,000

I didn't major in math, but those jumps appear more than a 7% wage increase. Here's a deeper look at the three.

The Three Categories of Compensation

Most software engineering compensation packages at IT organizations follow this format.

Minimum Salary

Base salary is pre-tax income. Most organizations give a base pay. This is paid biweekly, twice monthly, or monthly.

Recruiting Bonus

Sign-On incentives are one-time rewards to new hires. Companies need an incentive to switch. If you leave early, you must pay back the whole cost or a pro-rated amount.

Equity

Equity is complex and requires its own post. A company will promise to give you a certain amount of company stock but when you get it depends on your offer. 25% per year for 4 years, then it's gone.

If a company gives you $100,000 and distributes 25% every year for 4 years, expect $25,000 worth of company stock in your stock brokerage on your 1 year work anniversary.

Performance Bonus

Tech offers may include yearly performance bonuses. Depends on performance and funding. I've only seen 0-20%.

Engineers' overall compensation usually includes:

Base Salary + Sign-On + (Total Equity)/4 + Average Performance Bonus

Amazon: (TC: 150k)

Photo by ANIRUDH on Unsplash

Base Pay System

Amazon pays Seattle employees monthly on the first work day. I'd rather have my money sooner than later, even if it saves processing and pay statements.

The company upped its base pay cap from $160,000 to $350,000 to compete with other tech companies.

Performance Bonus

Amazon has no performance bonus, so you can work as little or as much as you like and get paid the same. Amazon is savvy to avoid promising benefits it can't deliver.

Sign-On Bonus

Amazon gives two two-year sign-up bonuses. First-year workers could receive $20,000 and second-year workers $15,000. It's probably to make up for the company's strange equity structure.

If you leave during the first year, you'll owe the entire money and a prorated amount for the second year bonus.

Equity

Most organizations prefer a 25%, 25%, 25%, 25% equity structure. Amazon takes a different approach with end-heavy equity:

  • the first year, 5%

  • 15% after one year.

  • 20% then every six months

We thought it was constructed this way to keep staff longer.

Microsoft (TC: 185k)

Photo by Louis-Philippe Poitras on Unsplash

Base Pay System

Microsoft paid biweekly.

Gainful Performance

My offer letter suggested a 0%-20% performance bonus. Everyone will be satisfied with a 10% raise at year's end.

But misleading press where the budget for the bonus is doubled can upset some employees because they won't earn double their expected bonus. Still barely 10% for 2022 average.

Sign-On Bonus

Microsoft's sign-on bonus is a one-time payout. The contract can require 2-year employment. You must negotiate 1 year. It's pro-rated, so that's fair.

Equity

Microsoft is one of those companies that has standard 25% equity structure. Except if you’re a new graduate.

In that case it’ll be

  • 25% six months later

  • 25% each year following that

New grads will acquire equity in 3.5 years, not 4. I'm guessing it's to keep new grads around longer.

Google (TC: 300k)

Photo by Rubaitul Azad on Unsplash

Base Pay Structure

Google pays biweekly.

Performance Bonus

Google's offer letter specifies a 15% bonus. It's wonderful there's no cap, but I might still get 0%. A little more than Microsoft’s 10% and a lot more than Amazon’s 0%.

Sign-On Bonus

Google gave a 1-year sign-up incentive. If the contract is only 1 year, I can move without any extra obligations.

Not as fantastic as Amazon's sign-up bonuses, but the remainder of the package might compensate.

Equity

We covered Amazon's tail-heavy compensation structure, so Google's front-heavy equity structure may surprise you.

Annual structure breakdown

  • 33% Year 1

  • 33% Year 2

  • 22% Year 3

  • 12% Year 4

The goal is to get them to Google and keep them there.

Final Thoughts

This post hopefully helped you understand the 3 firms' compensation arrangements.

There's always more to discuss, such as refreshers, 401k benefits, and business discounts, but I hope this shows a distinction between these 3 firms.

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.