NASA's Artemis 1 mission will help return people to the Moon after a half-century break. The mission is a shakedown cruise for NASA's Space Launch System and Orion Crew Capsule.

The spaceship will visit the Moon, deploy satellites, and enter orbit. NASA wants to practice operating the spacecraft, test the conditions people will face on the Moon, and ensure a safe return to Earth.

We asked Jack Burns, a space scientist at the University of Colorado Boulder and former member of NASA's Presidential Transition Team, to describe the mission, explain what the Artemis program promises for space exploration, and reflect on how the space program has changed in the half-century since humans last set foot on the moon.

What distinguishes Artemis 1 from other rockets?

Artemis 1 is the Space Launch System's first launch. NASA calls this a "heavy-lift" vehicle. It will be more powerful than Apollo's Saturn V, which transported people to the Moon in the 1960s and 1970s.

It's a new sort of rocket system with two strap-on solid rocket boosters from the space shuttle. It's a mix of the shuttle and Saturn V.

The Orion Crew Capsule will be tested extensively. It'll spend a month in the high-radiation Moon environment. It will also test the heat shield, which protects the capsule and its occupants at 25,000 mph. The heat shield must work well because this is the fastest capsule descent since Apollo.

This mission will also carry miniature Moon-orbiting satellites. These will undertake vital precursor science, including as examining further into permanently shadowed craters where scientists suspect there is water and measuring the radiation environment to see long-term human consequences.

Artemis 1 will launch, fly to the Moon, place satellites, orbit it, return to Earth, and splash down in the ocean. NASA.

What's Artemis's goal? What launches are next?

The mission is a first step toward Artemis 3, which will lead to the first human Moon missions since 1972. Artemis 1 is unmanned.

Artemis 2 will have astronauts a few years later. Like Apollo 8, it will be an orbital mission that circles the Moon and returns. The astronauts will orbit the Moon longer and test everything with a crew.

Eventually, Artemis 3 will meet with the SpaceX Starship on the Moon's surface and transfer people. Orion will stay in orbit while the lunar Starship lands astronauts. They'll go to the Moon's south pole to investigate the water ice there.

Artemis is reminiscent of Apollo. What's changed in 50 years?

Kennedy wanted to beat the Soviets to the Moon with Apollo. The administration didn't care much about space flight or the Moon, but the goal would place America first in space and technology.

You live and die by the sword if you do that. When the U.S. reached the Moon, it was over. Russia lost. We planted flags and did science experiments. Richard Nixon canceled the program after Apollo 11 because the political goals were attained.

Large rocket with two boosters between two gates

NASA's new Space Launch System is brought to a launchpad. NASA

50 years later... It's quite different. We're not trying to beat the Russians, Chinese, or anyone else, but to begin sustainable space exploration.

Artemis has many goals. It includes harnessing in-situ resources like water ice and lunar soil to make food, fuel, and building materials.

SpaceX is part of this first journey to the Moon's surface, therefore the initiative is also helping to develop a lunar and space economy. NASA doesn't own the Starship but is buying seats for astronauts. SpaceX will employ Starship to transport cargo, private astronauts, and foreign astronauts.

Fifty years of technology advancement has made getting to the Moon cheaper and more practical, and computer technology allows for more advanced tests. 50 years of technological progress have changed everything. Anyone with enough money can send a spacecraft to the Moon, but not humans.

Commercial Lunar Payload Services engages commercial companies to develop uncrewed Moon landers. We're sending a radio telescope to the Moon in January. Even 10 years ago, that was impossible.

Since humans last visited the Moon 50 years ago, technology has improved greatly.

What other changes does Artemis have in store?

The government says Artemis 3 will have at least one woman and likely a person of color. 

I'm looking forward to seeing more diversity so young kids can say, "Hey, there's an astronaut that looks like me. I can do this. I can be part of the space program.”

The company seeking 24/7 ultra-powerful solar electricity.

We're rushing to adopt low-carbon energy to prevent a self-made doomsday. We're using solar, wind, and wave energy. These low-carbon sources aren't perfect. They consume large areas of land, causing habitat loss. They don't produce power reliably, necessitating large grid-level batteries, an environmental nightmare. We can and must do better than fossil fuels. Longi, one of the world's top solar panel producers, is creating a low-carbon energy source. Solar-powered spacecraft. But how does it work? Why is it so environmentally harmonious? And how can Longi unlock it?

Space-based solar makes sense. Satellites above Medium Earth Orbit (MEO) enjoy 24/7 daylight. Outer space has no atmosphere or ozone layer to block the Sun's high-energy UV radiation. Solar panels can create more energy in space than on Earth due to these two factors. Solar panels in orbit can create 40 times more power than those on Earth, according to estimates.

How can we utilize this immense power? Launch a geostationary satellite with solar panels, then beam power to Earth. Such a technology could be our most eco-friendly energy source. (Better than fusion power!) How?

Solar panels create more energy in space, as I've said. Solar panel manufacture and grid batteries emit the most carbon. This indicates that a space-solar farm's carbon footprint (which doesn't need a battery because it's a constant power source) might be over 40 times smaller than a terrestrial one. Combine that with carbon-neutral launch vehicles like Starship, and you have a low-carbon power source. Solar power has one of the lowest emissions per kWh at 6g/kWh, so space-based solar could approach net-zero emissions.

Space solar is versatile because it doesn't require enormous infrastructure. A space-solar farm could power New York and Dallas with the same efficiency, without cables. The satellite will transmit power to a nearby terminal. This allows an energy system to evolve and adapt as the society it powers changes. Building and maintaining infrastructure can be carbon-intensive, thus less infrastructure means less emissions.

Space-based solar doesn't destroy habitats, either. Solar and wind power can be engineered to reduce habitat loss, but they still harm ecosystems, which must be restored. Space solar requires almost no land, therefore it's easier on Mother Nature.

Space solar power could be the ultimate energy source. So why haven’t we done it yet?

Well, for two reasons: the cost of launch and the efficiency of wireless energy transmission.

Advances in rocket construction and reusable rocket technology have lowered orbital launch costs. In the early 2000s, the Space Shuttle cost $60,000 per kg launched into LEO, but a SpaceX Falcon 9 costs only $3,205. 95% drop! Even at these low prices, launching a space-based solar farm is commercially questionable.

Energy transmission efficiency is half of its commercial viability. Space-based solar farms must be in geostationary orbit to get 24/7 daylight, 22,300 miles above Earth's surface. It's a long way to wirelessly transmit energy. Most laser and microwave systems are below 20% efficient.

Space-based solar power is uneconomical due to low efficiency and high deployment costs.

Longi wants to create this ultimate power. But how?

They'll send solar panels into space to develop space-based solar power that can be beamed to Earth. This mission will help them design solar panels tough enough for space while remaining efficient.

Longi is a Chinese company, and China's space program and universities are developing space-based solar power and seeking commercial partners. Xidian University has built a 98%-efficient microwave-based wireless energy transmission system for space-based solar power. The Long March 5B is China's super-cheap (but not carbon-offset) launch vehicle.

Longi fills the gap. They have the commercial know-how and ability to build solar satellites and terrestrial terminals at scale. Universities and the Chinese government have transmission technology and low-cost launch vehicles to launch this technology.

It may take a decade to develop and refine this energy solution. This could spark a clean energy revolution. Once operational, Longi and the Chinese government could offer the world a flexible, environmentally friendly, rapidly deployable energy source.

Should the world adopt this technology and let China control its energy? I'm not very political, so you decide. This seems to be the beginning of tapping into this planet-saving energy source. Forget fusion reactors. Carbon-neutral energy is coming soon.

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.

OpenAI's ChatGPT is an amazing AI-powered chatbot. It can write poetry, stories, and marketing campaigns, and it's also adept at coding. ChatGPT's coding is so amazing that it replicated itself. What happened:

Me: Hi

Hello! Can I help? I'll answer any inquiries you have.

Me: Build a python and flask AI chatbot that responds to user messages on the frontend.

CGPT:

from flask import Flask, request, jsonify

import openai
openai.api_key = "YOUR_API_KEY"

@app.route('/chatbot', methods=['POST'])
def chatbot():
    user_message = request.get_json()['message']
    response = chatbot_response(user_message)
    return jsonify({'response': response})


def chatbot_response(user_message):
    response = openai.Completion.create(
        engine="text-davinci-002",
        prompt=user_message,
        max_tokens=1024,
        n = 1,
        temperature=0.5
    )
    return response['choices'][0]['text']

if __name__ == '__main__':
    app.run()

To integrate a chatbot with a frontend, use Flask to serve an HTML page with a form for user messages and the chatbot's answer. AJAX can submit the form to the /chatbot route, and JavaScript can show the chatbot's response.

I imported code snippets at the top of the file.

Let's add a frontend interface, I said.

CGPT:

<!DOCTYPE html>
<html>
<head>
    <title>AI Chatbot</title>
</head>
<body>
    <h1>AI Chatbot</h1>
    <form id="chatbot-form">
        <label for="message">Message:</label><br>
        <input type="text" id="message" name="message"><br>
        <input type="submit" value="Submit">
    </form> 
    <div id="chatbot-response"></div>

    <script src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
    <script>
        $(document).ready(function() {
            $("#chatbot-form").submit(function(e) {
                e.preventDefault();
                var userMessage = $("#message").val();
                $.ajax({
                    type: "POST",
                    url: "/chatbot",
                    data: JSON.stringify({message: userMessage}),
                    contentType: "application/json; charset=utf-8",
                    dataType: "json",
                    success: function(response) {
                        $("#chatbot-response").text(response.response);
                    }
                });
            });
        });
    </script>
</body>
</html>

To serve this HTML page using Flask, build a new route that returns the page as a GET response.

So far, so good.

Looked quite basic so I got chatGPT to add some tailwind to the project.

Me: Tailwind the chatbot.html page, please. Give it a futuristic style with purple and neon

After a few more prompts, Talk GPT aligned the form to the center, changed some colors, and added padding.

CGPT:

<!DOCTYPE html>
<html>
<head>
    <title>AI Chatbot</title>
    <link href="https://unpkg.com/tailwindcss@^1.0/dist/tailwind.min.css" rel="stylesheet">
</head>
<body class="bg-black flex flex-col justify-center items-center">
    <h1 class="sm:text-center text-purple-500">AI Chatbot</h1>
    <form id="chatbot-form" class="border-purple-500 bg-purple-800 rounded">
        <label for="message">Message:</label><br>
        <input type="text" id="message" name="message" class="min-w-30 rounded"><br>
        <input type="submit" value="Submit" class="bg-purple-500 border-red-500 transform hover:scale-110 rounded">
    </form> 
    <div class="flex justify-center">
        <div id="chatbot-response" class="text-white rounded"></div>
    </div>

    <script src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
    <script>
        var colors = ['red', 'orange', 'yellow', 'green', 'blue', 'indigo', 'violet'];
        var colorIndex = 0;
        
        $(document).ready(function() {
            setInterval(function() {
                $("#chatbot-form").css('border-color', colors[colorIndex]);
                colorIndex = (colorIndex + 1) % colors.length;
            }, 1000);

            $("#chatbot-form").submit(function(e) {
                e.preventDefault();
                var userMessage = $("#message").val();
                $.ajax({
                    type: "POST",
                    url: "/chatbot",
                    data: JSON.stringify({message: userMessage}),
                    contentType: "application/json; charset=utf-8",
                    dataType: "json",
                    success: function(response) {
                        $("#chatbot-response").text(response.response);
                    }
                });
            });
        });
    </script>
</body>
</html>

Improved:

A few more prompts like “Add more vertical and horizontal padding to the submit button and vertical margin, and vertically align this file's body.”

The result:

Is it effective? Now, I'll chat with ChatGPT's AI Chatbot. I intervened minimally throughout construction. Chat GPT created numerous files, connected and interacted with its own API, and presented the user request response on the front end by itself.

Me to AI Chatbot: Hey, can you give me 6 name suggestions for a black horse?

Me to AI Chatbot: Write a poem in the style of Jim Morrison. Make sure to mention cacti and black holes

ChatGPTs Chatbot:

In the desert night, I am confronted by cacti, 
Their arms reaching out, As if to grab me and take me away. 
The stars in the sky, Beckon me to come, 
To a world of black holes, Where I can be free. 
I am in a trance, My body and mind, 
In a state of limbo, As I wander the night. 
I hear a voice, Calling me to the unknown, 
I cannot resist, The lure of the black hole. 
The cacti watch, As I take my leave, 
To a place of mystery, Where I can find peace.

Of course, the next question I gave it was to build a chatbot!

Me: Build a python and flask AI chatbot that responds to user messages on the frontend.

ChatbotGPTs:

import os from flask 
import Flask, request, jsonify 
from chatterbot 
import ChatBot 
from chatterbot.trainers 
import ListTrainer 

# Create a new chatbot 
bot = ChatBot( 
  "My Bot", 
  storage_adapter="chatterbot.storage.SQLStorageAdapter", 
  logic_adapters=[ 
    "chatterbot.logic.BestMatch", 
    { "import_path": "chatterbot.logic.BestMatch", 
      "statement_comparison_function": "chatterbot.comparisons.levenshtein_distance", 
       "response_selection_method": "chatterbot.response_selection.get_first_response" } 
    ], 
    database_uri="sqlite:///database.sqlite3" ) 

# Train the chatbot with a few sample conversations 
conversation = [ "Hello", "Hi there!", "How are you doing?", "I'm doing great.", "That is good to hear", "Thank you.", "You're welcome." ] 
trainer = ListTrainer(bot) trainer.train(conversation) 

# Create a Flask app 
app = Flask(__name__) 

# Define a route for the default URL 
@app.route("/") def index(): return "<h1>Chatbot</h1>" 

# Define a route for the /get_response URL 
@app.route("/get_response", methods=["POST"]) 

def get_response(): 
# Get the user's message 
user_message = request.form["user_message"] 
# Get the bot's response 
bot_response = bot.get_response(user_message) 
# Return the bot's response 
return str(bot_response) 
# Run the Flask 
app if __name__ == "__main__": app.run()

No matter how many times I tried, the second generation always used chatterbot instead of the ChatGPT API. Even when I told it to use the ChatGPT API, it didn't.

ChatGTP's ability to reproduce or construct other machine learning algorithms is interesting and possibly terrifying. Nothing prevents ChatGPT from replicating itself ad infinitum throughout the Internet other than a lack of desire. This may be the first time a machine repeats itself, so I've preserved the project as a reference. Adding a requirements.txt file and python env for easier deployment is the only change to the code.

I hope you enjoyed this.

Elon's rides start rough, but then...

Elon Musk has never been so hated.

They don’t get Elon.

• He began using PayPal in this manner.

• He began with SpaceX in a similar manner.

• He began with Tesla in this manner.

Disruptive.

Elon had rocky starts. His creativity requires it. Just like writing a first draft.

His fastest way to find the way is to avoid it.

PayPal's pricey launch

PayPal was a 1999 business flop.

They were considered insane.

Elon and his co-founders had big plans for PayPal. They adopted the popular philosophy of the time, exchanging short-term profit for growth, and pulled off a miracle just before the bubble burst.

PayPal was created as a dollar alternative. Original PayPal software allowed PalmPilot money transfers. Unfortunately, there weren't enough PalmPilot users.

Since everyone had email, the company emailed payments. Costs rose faster than sales.

The startup wanted to get a million subscribers by paying $10 to sign up and $10 for each referral. Elon thought the price was fair because PayPal made money by charging transaction fees. They needed to make money quickly.

A Wall Street Journal article valuing PayPal at $500 million attracted investors. The dot-com bubble burst soon after they rushed to get financing.

Musk and his partners sold PayPal to eBay for $1.5 billion in 2002. Musk's most successful company was PayPal.

SpaceX's start-up error

Elon and his friends bought a reconditioned ICBM in Russia in 2002.

He planned to invest much of his wealth in a stunt to promote NASA and space travel.

Many called Elon crazy.

The goal was to buy a cheap Russian rocket to launch mice or plants to Mars and return them. He thought SpaceX would revive global space interest. After a bad meeting in Moscow, Elon decided to build his own rockets to undercut launch contracts.

Then SpaceX was founded.

Elon’s plan was harder than expected.

Explosions followed explosions.

• Millions lost on cargo.

• Millions lost on the rockets.

Investors thought Elon was crazy, but he wasn't.

NASA's biggest competitor became SpaceX. NASA hired SpaceX to handle many of its missions.

Tesla's shaky beginning

Tesla began shakily.

• Clients detested their roadster.

• They continued to miss deadlines.

Lotus would handle the car while Tesla focused on the EV component, easing Tesla's entry. The business experienced elegance creep. Modifying specific parts kept the car from getting worse.

Cost overruns, delays, and other factors changed the Elise-like car's appearance. Only 7% of the Tesla Roadster's parts matched its Lotus twin.

Tesla was about to die.

Elon saved the mess as CEO.

He fired 25% of the workforce to reduce costs.

Elon Musk transformed Tesla into the world's most valuable automaker by running it like a startup.

Tesla hasn't spent a dime on advertising. They let the media do the talking by investing in innovation.

Elon sheds. Elon tries. Elon learns. Elon refines.

Twitter doesn't worry me.

The media is shocked. I’m not.

This is just Elon being Elon.

• Elon makes lean.

• Elon tries new things.

• Elon listens to feedback.

• Elon refines.

Besides Twitter will always be Twitter.

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.