Yes, client meetings are difficult. Especially when I'm alone.

Clients must tell us their problems so we can help.

In-meeting challenges contribute nothing to our work. Consider this:

• Clients are unprepared.

• Clients are distracted.

• Clients are confused.

Introducing Jack Dorsey's Google Doc approach

I endorse his approach to meetings.

Not Google Doc-related. Jack uses it for meetings.

This is what his meetings look like.

• Prior to the meeting, the Chair creates the agenda, structure, and information using Google Doc.

• Participants in the meeting would have 5-10 minutes to read the Google Doc.

• They have 5-10 minutes to type their comments on the document.

• In-depth discussion begins

There is elegance in simplicity. Here's how Jack's approach is fantastic.

Unprepared clients are given time to read.

During the meeting, they think and work on it.

They can see real-time remarks from others.

Discussion ensues.

Three months ago, I fell for this strategy. After trying it with a client, I got good results.

I conducted social control experiments in a few client workshops.

Context matters.

I am sure Jack Dorsey’s method works well in meetings. What about client workshops?

So, I tested Enterprise of the Future with a consulting client.

I sent multiple emails to client stakeholders describing the new approach.

No PowerPoints that day. I spent the night setting up the Google Doc with conversation topics, critical thinking questions, and a Before and After section.

The client was shocked. First, a Google Doc was projected. Second surprise was a verbal feedback.

“No pre-meeting materials?”

“Don’t worry. I know you are not reading it before our meeting, anyway.”

We laughed. The experiment started.

Observations throughout a 90-minute engagement workshop from beginning to end

For 10 minutes, the workshop was silent.

People read the Google Doc. For some, the silence was unnerving.

“Are you not going to present anything to us?”

I said everything's in Google Doc. I asked them to read, remark, and add relevant paragraphs.

As they unlocked their laptops, they were annoyed.

Ten client stakeholders are typing on the Google Doc. My laptop displays comment bubbles, red lines, new paragraphs, and strikethroughs.

The first 10 minutes were productive. Everyone has seen and contributed to the document.

I was silent.

The move to a classical workshop was smooth. I didn't stimulate dialogue. They did.

Stephanie asked Joe why a blended workforce hinders company productivity. She questioned his comments and additional paragraphs.

That is when a light bulb hit my head. Yes, you want to speak to the right person to resolve issues!

Not only that was discussed. Others discussed their remark bubbles with neighbors. Debate circles sprung up one after the other.

The best part? I asked everyone to add their post-discussion thoughts on a Google Doc.

After the workshop, I have:

• An agreement-based working document

• A post-discussion minutes that are prepared for publication

• A record of the discussion points that were brought up, argued, and evaluated critically

It showed me how stakeholders viewed their Enterprise of the Future. It allowed me to align with them.

Finale Keynotes

Client meetings are a hit-or-miss. I know that.

Jack Dorsey's meeting strategy works for consulting. It promotes session alignment.

It relieves clients of preparation.

I get the necessary information to advance this consulting engagement.

It is brilliant.

Many can't concentrate. The first 20% of the day isn't optimized.

Elon Musk, Tony Robbins, and Bill Gates share something:

Morning Routines.

A repeatable morning ritual saves time.

The result?

Time for hobbies.

I'll discuss 5 easy morning routines you can use.

1. Stop pressing snooze

Waking up starts the day. You disrupt your routine by hitting snooze.

One sleep becomes three. Your morning routine gets derailed.

Fix it:

Hide your phone. This disables snooze and wakes you up.

Once awake, staying awake is 10x easier. Simple trick, big results.

2. Drink water

Chronic dehydration is common. Mostly urban, air-conditioned workers/residents.

2% cerebral dehydration causes short-term memory loss.

Dehydration shrinks brain cells.

Drink 3-4 liters of water daily to avoid this.

3. Improve your focus

How to focus better?

Meditation.

• Improve your mood

• Enhance your memory

• increase mental clarity

• Reduce blood pressure and stress

Headspace helps with the habit.

Here's a meditation guide.

1. Sit comfortably

2. Shut your eyes.

3. Concentrate on your breathing

4. Breathe in through your nose

5. Breathe out your mouth.

5 in, 5 out.

Repeat for 1 to 20 minutes.

Here's a beginner's video:

4. Workout

Exercise raises:

• Mental Health

• Effort levels

• focus and memory

15-60 minutes of fun:

• Exercise Lifting

• Running

• Walking

• Stretching and yoga

This helps you now and later.

5. Keep a journal

You have countless thoughts daily. Many quietly steal your focus.

Here’s how to clear these:

Write for 5-10 minutes.

You'll gain 2x more mental clarity.

Recap

5 morning practices for 5x more productivity:

1. Say no to snoozing

2. Hydrate

3. Improve your focus

4. Exercise

5. Journaling

Conclusion

One step starts a thousand-mile journey. Try these easy yet effective behaviors if you have trouble concentrating or have too many thoughts.

Start with one of these behaviors, then add the others. Its astonishing results are instant.

The holy grail of plain text task management is finally within reach

Plain text task management? Are you serious?? Dedicated task managers exist for a reason, you know. Sheesh.

—Oh, I know. Believe me, I know! But hear me out.

I've managed projects and tasks in plain text for more than four years. Since reorganizing my to-do list, plain text task management is within reach.

Data completely yours? One billion percent. Beef it up with coding? Be my guest.

Enter: The List

The answer? A list. That’s it!

Write down tasks. Obsidian, Notenik, Drafts, or iA Writer are good plain text note-taking apps.

List too long? Of course, it is! A large list tells you what to do. Feel the itch and friction. Then fix it.

• But I want to be able to distinguish between work and personal life! List two things.

• However, I need to know what should be completed first. Put those items at the top.

• However, some things keep coming up, and I need to be reminded of them! Put those in your calendar and make an alarm for them.

• But since individual X hasn't completed task Y, I can't proceed with this. Create a Waiting section on your list by dividing it.

• But I must know what I'm supposed to be doing right now! Read your list(s). Check your calendar. Think critically.

Before I begin a new one, I remind myself that "Listory Never Repeats."

There’s no such thing as too many lists if all are needed. There is such a thing as too many lists if you make them before they’re needed. Before they complain that their previous room was small or too crowded or needed a new light.

A list that feels too long has a voice; it’s telling you what to do next.

I use one Master List. It's a control panel that tells me what to focus on short-term. If something doesn't need semi-immediate attention, it goes on my Backlog list.

Todd Lewandowski's DWTS (Done, Waiting, Top 3, Soon) performance deserves praise. His DWTS to-do list structure has transformed my plain-text task management. I didn't realize it was upside down.

This is my take on it:

D = Done

Move finished items here. If they pile up, clear them out every week or month. I have a Done Archive folder.

W = Waiting

Things seething in the background, awaiting action. Stir them occasionally so they don't burn.

T = Top 3

Three priorities. Personal comes first, then work. There will always be a top 3 (no more than 5) in every category. Projects, not chores, usually.

S = Soon

This part is action-oriented. It's for anything you can accomplish to finish one of the Top 3. This collection includes thoughts and project lists. The sole requirement is that they should be short-term goals.

Some of you have probably concluded this isn't for you. Please read Todd's piece before throwing out the baby. Often. You shouldn't miss a newborn.

As much as Dancing With The Stars helps me recall this method, I may try switching their order. TSWD; Drilling Tunnel Seismic? Serenity After Task?

Master List Showcase

My Master List lives alone in its own file, but sometimes appears in other places.  It's included in my Weekly List template. Here's a (soon-to-be-updated) demo vault of my Obsidian planning setup to download for free.

Here's the code behind my weekly screenshot:

## [[Master List - 2022|✓]]  TO DO

![[Master List - 2022]]

FYI, I use the Minimal Theme in Obsidian, with a few tweaks.

You may note I'm utilizing a checkmark as a link. For me, that's easier than locating the proper spot to click on the embed.

Blue headings for Done and Waiting are links. Done links to the Done Archive page and Waiting to a general waiting page.

Read my full article here.

Python Heatmap Technical Indicator

Heatmaps provide an instant overview. They can be used with correlations or to predict reactions or confirm the trend in trading. This article covers RSI heatmap creation.

The Market System

Market regime:

• Bullish trend: The market tends to make higher highs, which indicates that the overall trend is upward.

• Sideways: The market tends to fluctuate while staying within predetermined zones.

• Bearish trend: The market has the propensity to make lower lows, indicating that the overall trend is downward.

Most tools detect the trend, but we cannot predict the next state. The best way to solve this problem is to assume the current state will continue and trade any reactions, preferably in the trend.

If the EURUSD is above its moving average and making higher highs, a trend-following strategy would be to wait for dips before buying and assuming the bullish trend will continue.

Indicator of Relative Strength

J. Welles Wilder Jr. introduced the RSI, a popular and versatile technical indicator. Used as a contrarian indicator to exploit extreme reactions. Calculating the default RSI usually involves these steps:

• Determine the difference between the closing prices from the prior ones.

• Distinguish between the positive and negative net changes.

• Create a smoothed moving average for both the absolute values of the positive net changes and the negative net changes.

• Take the difference between the smoothed positive and negative changes. The Relative Strength RS will be the name we use to describe this calculation.

• To obtain the RSI, use the normalization formula shown below for each time step.

The 13-period RSI and black GBPUSD hourly values are shown above. RSI bounces near 25 and pauses around 75. Python requires a four-column OHLC array for RSI coding.

import numpy as np
def add_column(data, times):
    
    for i in range(1, times + 1):
    
        new = np.zeros((len(data), 1), dtype = float)
        
        data = np.append(data, new, axis = 1)
    return data
def delete_column(data, index, times):
    
    for i in range(1, times + 1):
    
        data = np.delete(data, index, axis = 1)
    return data
def delete_row(data, number):
    
    data = data[number:, ]
    
    return data
def ma(data, lookback, close, position): 
    
    data = add_column(data, 1)
    
    for i in range(len(data)):
           
            try:
                
                data[i, position] = (data[i - lookback + 1:i + 1, close].mean())
            
            except IndexError:
                
                pass
            
    data = delete_row(data, lookback)
    
    return data
def smoothed_ma(data, alpha, lookback, close, position):
    
    lookback = (2 * lookback) - 1
    
    alpha = alpha / (lookback + 1.0)
    
    beta  = 1 - alpha
    
    data = ma(data, lookback, close, position)
    data[lookback + 1, position] = (data[lookback + 1, close] * alpha) + (data[lookback, position] * beta)
    for i in range(lookback + 2, len(data)):
        
            try:
                
                data[i, position] = (data[i, close] * alpha) + (data[i - 1, position] * beta)
        
            except IndexError:
                
                pass
            
    return data
def rsi(data, lookback, close, position):
    
    data = add_column(data, 5)
    
    for i in range(len(data)):
        
        data[i, position] = data[i, close] - data[i - 1, close]
     
    for i in range(len(data)):
        
        if data[i, position] > 0:
            
            data[i, position + 1] = data[i, position]
            
        elif data[i, position] < 0:
            
            data[i, position + 2] = abs(data[i, position])
            
    data = smoothed_ma(data, 2, lookback, position + 1, position + 3)
    data = smoothed_ma(data, 2, lookback, position + 2, position + 4)
    data[:, position + 5] = data[:, position + 3] / data[:, position + 4]
    
    data[:, position + 6] = (100 - (100 / (1 + data[:, position + 5])))
    data = delete_column(data, position, 6)
    data = delete_row(data, lookback)
    return data

Make sure to focus on the concepts and not the code. You can find the codes of most of my strategies in my books. The most important thing is to comprehend the techniques and strategies.

My weekly market sentiment report uses complex and simple models to understand the current positioning and predict the future direction of several major markets. Check out the report here:

Using the Heatmap to Find the Trend

RSI trend detection is easy but useless. Bullish and bearish regimes are in effect when the RSI is above or below 50, respectively. Tracing a vertical colored line creates the conditions below. How:

• When the RSI is higher than 50, a green vertical line is drawn.

• When the RSI is lower than 50, a red vertical line is drawn.

Zooming out yields a basic heatmap, as shown below.

Plot code:

def indicator_plot(data, second_panel, window = 250):
    fig, ax = plt.subplots(2, figsize = (10, 5))
    sample = data[-window:, ]
    for i in range(len(sample)):
        ax[0].vlines(x = i, ymin = sample[i, 2], ymax = sample[i, 1], color = 'black', linewidth = 1)  
        if sample[i, 3] > sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 0], ymax = sample[i, 3], color = 'black', linewidth = 1.5)  
        if sample[i, 3] < sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
        if sample[i, 3] == sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
    ax[0].grid() 
    for i in range(len(sample)):
        if sample[i, second_panel] > 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'green', linewidth = 1.5)  
        if sample[i, second_panel] < 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'red', linewidth = 1.5)  
    ax[1].grid()
indicator_plot(my_data, 4, window = 500)

Call RSI on your OHLC array's fifth column. 4. Adjusting lookback parameters reduces lag and false signals. Other indicators and conditions are possible.

Another suggestion is to develop an RSI Heatmap for Extreme Conditions.

Contrarian indicator RSI. The following rules apply:

• Whenever the RSI is approaching the upper values, the color approaches red.

• The color tends toward green whenever the RSI is getting close to the lower values.

Zooming out yields a basic heatmap, as shown below.

Plot code:

import matplotlib.pyplot as plt
def indicator_plot(data, second_panel, window = 250):
    fig, ax = plt.subplots(2, figsize = (10, 5))
    sample = data[-window:, ]
    for i in range(len(sample)):
        ax[0].vlines(x = i, ymin = sample[i, 2], ymax = sample[i, 1], color = 'black', linewidth = 1)  
        if sample[i, 3] > sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 0], ymax = sample[i, 3], color = 'black', linewidth = 1.5)  
        if sample[i, 3] < sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
        if sample[i, 3] == sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
    ax[0].grid() 
    for i in range(len(sample)):
        if sample[i, second_panel] > 90:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'red', linewidth = 1.5)  
        if sample[i, second_panel] > 80 and sample[i, second_panel] < 90:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'darkred', linewidth = 1.5)  
        if sample[i, second_panel] > 70 and sample[i, second_panel] < 80:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'maroon', linewidth = 1.5)  
        if sample[i, second_panel] > 60 and sample[i, second_panel] < 70:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'firebrick', linewidth = 1.5) 
        if sample[i, second_panel] > 50 and sample[i, second_panel] < 60:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'grey', linewidth = 1.5) 
        if sample[i, second_panel] > 40 and sample[i, second_panel] < 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'grey', linewidth = 1.5) 
        if sample[i, second_panel] > 30 and sample[i, second_panel] < 40:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'lightgreen', linewidth = 1.5)
        if sample[i, second_panel] > 20 and sample[i, second_panel] < 30:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'limegreen', linewidth = 1.5) 
        if sample[i, second_panel] > 10 and sample[i, second_panel] < 20:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'seagreen', linewidth = 1.5)  
        if sample[i, second_panel] > 0 and sample[i, second_panel] < 10:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'green', linewidth = 1.5)
    ax[1].grid()
indicator_plot(my_data, 4, window = 500)

Dark green and red areas indicate imminent bullish and bearish reactions, respectively. RSI around 50 is grey.

Summary

To conclude, my goal is to contribute to objective technical analysis, which promotes more transparent methods and strategies that must be back-tested before implementation.

Technical analysis will lose its reputation as subjective and unscientific.

When you find a trading strategy or technique, follow these steps:

• Put emotions aside and adopt a critical mindset.

• Test it in the past under conditions and simulations taken from real life.

• Try optimizing it and performing a forward test if you find any potential.

• Transaction costs and any slippage simulation should always be included in your tests.

• Risk management and position sizing should always be considered in your tests.

After checking the above, monitor the strategy because market dynamics may change and make it unprofitable.

Inspired by someone I never met

Inspiration is good and bad.

Paul Jarvis inspires me. He's a web person and writer who created his own category by being himself.

Paul said no thank you when everyone else was developing, building, and assuming greater responsibilities. This isn't success. He rewrote the rules. Working for himself, expanding at his own speed, and doing what he loves were his definitions of success.

Play with a problem that you have

The biggest problem can be not recognizing a problem.

Acceptance without question is deception. When you don't push limits, you forget how. You start thinking everything must be as it is.

For example: working. Paul worked a 9-5 agency work with little autonomy. He questioned whether the 9-5 was a way to live, not the way.

Another option existed. So he chipped away at how to live in this new environment.

Don't simply jump

Internet writers tell people considering quitting 9-5 to just quit. To throw in the towel. To do what you like.

The advice is harmful, despite the good intentions. People think quitting is hard. Like courage is the issue. Like handing your boss a resignation letter.

Nope. The tough part comes after. It’s easy to jump. Landing is difficult.

The landing

Paul didn't quit. Intelligent individuals don't. Smart folks focus on landing. They imagine life after 9-5.

Paul had been a web developer for a long time, had solid clients, and was respected. Hence if he pushed the limits and discovered another route, he had the potential to execute.

Working on the side

Society loves polarization. It’s left or right. Either way. Or chaos. It's 9-5 or entrepreneurship.

But like Paul, you can stretch polarization's limits. In-between exists.

You can work a 9-5 and side jobs (as I do). A mix of your favorites. The 9-5's stability and creativity. Fire and routine.

Remember you can't have everything but anything. You can create and work part-time.

My hybrid lifestyle

Not selling books doesn't destroy my world. My globe keeps spinning if my new business fails or if people don't like my Tweets. Unhappy algorithm? Cool. I'm not bothered (okay maybe a little).

The mix gives me the best of both worlds. To create, hone my skill, and grasp big-business basics. I like routine, but I also appreciate spending 4 hours on Saturdays writing.

Some days I adore leaving work at 5 pm and disconnecting. Other days, I adore having a place to write if inspiration strikes during a run or a discussion.

I’m a part-time creator

I’m a part-time creator. No, I'm not trying to quit. I don't work 5 pm - 2 am on the side. No, I'm not at $10,000 MRR.

I work part-time but enjoy my 9-5. My 9-5 has goodies. My side job as well.

It combines both to meet my lifestyle. I'm satisfied.

Join the Part-time Creators Club for free here. I’ll send you tips to enhance your creative game.

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.