I started smoking in 2002 at IIT BHU. Most of us thought it was enjoyable at first. I didn't realize the cost later.

In 2005, during my final semester, I lost my father. Suddenly, I felt more accountable for my mother and myself.

I quit before starting my first job in Bangalore. I didn't see any smoking friends in my hometown for 2 months before moving to Bangalore.

For the next 5-6 years, I had no regimen and smoked only when drinking.

Due to personal concerns, I started smoking again after my 2011 marriage. Now smoking was a constant guilty pleasure.

I smoked 3-4 cigarettes a day, but never in front of my family or on weekends. I used to excuse this with pride! First office ritual: smoking. Even with guilt, I couldn't stop this time because of personal concerns.

After 8-9 years, in mid 2019, a personal development program solved all my problems. I felt complete in myself. After this, I just needed one cigarette each day.

The hardest thing was leaving this final cigarette behind, even though I didn't want it.

James Clear's Atomic Habits was published last year. I'd only read 2-3 non-tech books before reading this one in August 2021. I knew everything but couldn't use it.

In April 2022, I realized the compounding effect of a bad habit thanks to my subconscious mind. 1 cigarette per day (excluding weekends) equals 240 = 24 packs per year, which is a lot. No matter how much I did, it felt negative.

Then I applied the 2nd principle of this book, identifying the trigger. I tried to identify all the major triggers of smoking. I found social drinking is one of them & If I am able to control it during that time, I can easily control it in other situations as well. Going further whenever I drank, I was pre-determined to ignore the craving at any cost. Believe me, it was very hard initially but gradually this craving started fading away even with drinks.

I've been smoke-free for 3 months. Now I know a bad habit's effects. After realizing the power of habits, I'm developing other good habits which I ignored all my life.

The human brain is amazing. As more scientists examine the brain, we learn how much it can store.

The human brain has 1 billion neurons, according to Scientific American. Each neuron creates 1,000 connections, totaling over a trillion. If each neuron could store one memory, we'd run out of room. [1]

What if you could store and access more info, freeing up brain space for problem-solving and creativity?

Build a second brain to keep up with rising knowledge (what I refer to as a Digital Brain). Effectively managing information entails realizing you can't recall everything.

Every action requires information. You need the correct information to learn a new skill, complete a project at work, or establish a business. You must manage information properly to advance your profession and improve your life.

How to construct a second brain to organize information and achieve goals.

What Is a Second Brain?

How often do you forget an article or book's key point? Have you ever wasted hours looking for a saved file?

If so, you're not alone. Information overload affects millions of individuals worldwide. Information overload drains mental resources and causes anxiety.

This is when the second brain comes in.

Building a second brain doesn't involve duplicating the human brain. Building a system that captures, organizes, retrieves, and archives ideas and thoughts. The second brain improves memory, organization, and recall.

Digital tools are preferable to analog for building a second brain.

Digital tools are portable and accessible. Due to these benefits, we'll focus on digital second-brain building.

Brainware

Digital Brains are external hard drives. It stores, organizes, and retrieves. This means improving your memory won't be difficult. 

Memory has three components in computing:

Recording — storing the information

Organization — archiving it in a logical manner

Recall — retrieving it again when you need it

For example:

Due to rigorous security settings, many websites need you to create complicated passwords with special characters.

You must now memorize (Record), organize (Organize), and input this new password the next time you check in (Recall).

Even in this simple example, there are many pieces to remember. We can't recognize this new password with our usual patterns. If we don't use the password every day, we'll forget it. You'll type the wrong password when you try to remember it.

It's common. Is it because the information is complicated? Nope. Passwords are basically letters, numbers, and symbols.

It happens because our brains aren't meant to memorize these. Digital Brains can do heavy lifting.

Why You Need a Digital Brain

Dual minds are best. Birth brain is limited.

The cerebral cortex has 125 trillion synapses, according to a Stanford Study. The human brain can hold 2.5 million terabytes of digital data. [2]

Building a second brain improves learning and memory.

Learn and store information effectively

Faster information recall

Organize information to see connections and patterns

Build a Digital Brain to learn more and reach your goals faster. Building a second brain requires time and work, but you'll have more time for vital undertakings. 

Why you need a Digital Brain:

1. Use Brainpower Effectively

Your brain has boundaries, like any organ. This is true while solving a complex question or activity. If you can't focus on a work project, you won't finish it on time.

Second brain reduces distractions. A robust structure helps you handle complicated challenges quickly and stay on track. Without distractions, it's easy to focus on vital activities.

2. Staying Organized

Professional and personal duties must be balanced. With so much to do, it's easy to neglect crucial duties. This is especially true for skill-building. Digital Brain will keep you organized and stress-free.

Life success requires action. Organized people get things done. Organizing your information will give you time for crucial tasks.

You'll finish projects faster with good materials and methods. As you succeed, you'll gain creative confidence. You can then tackle greater jobs.

3. Creativity Process

Creativity drives today's world. Creativity is mysterious and surprising for millions worldwide. Immersing yourself in others' associations, triggers, thoughts, and ideas can generate inspiration and creativity.

Building a second brain is crucial to establishing your creative process and building habits that will help you reach your goals. Creativity doesn't require perfection or overthinking.

4. Transforming Your Knowledge Into Opportunities

This is the age of entrepreneurship. Today, you can publish online, build an audience, and make money.

Whether it's a business or hobby, you'll have several job alternatives. Knowledge can boost your economy with ideas and insights.

5. Improving Thinking and Uncovering Connections

Modern career success depends on how you think. Instead of overthinking or perfecting, collect the best images, stories, metaphors, anecdotes, and observations.

This will increase your creativity and reveal connections. Increasing your imagination can help you achieve your goals, according to research. [3]

Your ability to recognize trends will help you stay ahead of the pack.

6. Credibility for a New Job or Business

Your main asset is experience-based expertise. Others won't be able to learn without your help. Technology makes knowledge tangible.

This lets you use your time as you choose while helping others. Changing professions or establishing a new business become learning opportunities when you have a Digital Brain.

7. Using Learning Resources

Millions of people use internet learning materials to improve their lives. Online resources abound. These include books, forums, podcasts, articles, and webinars.

These resources are mostly free or inexpensive. Organizing your knowledge can save you time and money. Building a Digital Brain helps you learn faster. You'll make rapid progress by enjoying learning.

How does a second brain feel?

Digital Brain has helped me arrange my job and family life for years.

No need to remember 1001 passwords. I never forget anything on my wife's grocery lists. Never miss a meeting. I can access essential information and papers anytime, anywhere.

Delegating memory to a second brain reduces tension and anxiety because you'll know what to do with every piece of information.

No information will be forgotten, boosting your confidence. Better manage your fears and concerns by writing them down and establishing a strategy. You'll understand the plethora of daily information and have a clear head.

How to Develop Your Digital Brain (Your Second Brain)

It's cheap but requires work.

Digital Brain development requires:

Recording — storing the information

Organization — archiving it in a logical manner

Recall — retrieving it again when you need it

1. Decide what information matters before recording.

To succeed in today's environment, you must manage massive amounts of data. Articles, books, webinars, podcasts, emails, and texts provide value. Remembering everything is impossible and overwhelming.

What information do you need to achieve your goals?

You must consolidate ideas and create a strategy to reach your aims. Your biological brain can imagine and create with a Digital Brain.

2. Use the Right Tool

We usually record information without any preparation - we brainstorm in a word processor, email ourselves a message, or take notes while reading.

This information isn't used. You must store information in a central location.

Different information needs different instruments.

Evernote is a top note-taking program. Audio clips, Slack chats, PDFs, text notes, photos, scanned handwritten pages, emails, and webpages can be added.

Pocket is a great software for saving and organizing content. Images, videos, and text can be sorted. Web-optimized design

Calendar apps help you manage your time and enhance your productivity by reminding you of your most important tasks. Calendar apps flourish. The best calendar apps are easy to use, have many features, and work across devices. These calendars include Google, Apple, and Outlook.

To-do list/checklist apps are useful for managing tasks. Easy-to-use, versatility, budget, and cross-platform compatibility are important when picking to-do list apps. Google Keep, Google Tasks, and Apple Notes are good to-do apps.

3. Organize data for easy retrieval

How should you organize collected data?

When you collect and organize data, you'll see connections. An article about networking can assist you comprehend web marketing. Saved business cards can help you find new clients.

Choosing the correct tools helps organize data. Here are some tools selection criteria:

• Can the tool sync across devices?

• Personal or team?

• Has a search function for easy information retrieval?

• Does it provide easy data categorization?

• Can users create lists or collections?

• Does it offer easy idea-information connections?

• Does it mind map and visually organize thoughts?

Conclusion

Building a Digital Brain (second brain) helps us save information, think creatively, and implement ideas. Your second brain is a biological extension. It prevents amnesia, allowing you to tackle bigger creative difficulties.

People who love learning often consume information without using it. Every day, they postpone life-improving experiences until they're forgotten. Useful information becomes strength. 

Reference

[1] ^ Scientific American: What Is the Memory Capacity of the Human Brain?

[2] ^ Clinical Neurology Specialists: What is the Memory Capacity of a Human Brain?

[3] ^ National Library of Medicine: Imagining Success: Multiple Achievement Goals and the Effectiveness of Imagery

These four, when combined, destroy procrastination.

You're not rushed. You waste it on busywork.

You'll accept this eventually.

• In 2022, the daily average usage of a user on social media is 2.5 hours.

• By 2020, 6 billion hours of video were watched each month by Netflix's customers, who used the service an average of 3.2 hours per day.

When we see these numbers, we think "Wow!" People squander so much time as though they don't contribute. True. These are yours. Likewise.

We don't lack time; we just waste it. Once you realize this, you can change your habits to save time. This article explains. If you adopt ALL 4 of these simple behaviors, you'll see amazing benefits.

Time-blocking

Cal Newport's time-blocking trick takes a minute but improves your day's clarity.

Divide the next day into 30-minute (or 5-minute, if you're Elon Musk) segments and assign responsibilities. As seen.

Here's why:

• The procrastination that results from attempting to determine when to begin working is eliminated. Procrastination is a given if you choose when to begin working in real-time. Even if you may assume you'll start working in five minutes, it won't take you long to realize that five minutes have turned into an hour. But if you've already determined to start working at 2:00 the next day, your odds of procrastinating are greatly decreased, if not eliminated altogether.

• You'll also see that you have a lot of time in a day when you plan your day out on paper and assign chores to each hour. Doing this daily will permanently eliminate the lack of time mindset.

5-4-3-2-1: Have breakfast with the frog!

“If it’s your job to eat a frog, it’s best to do it first thing in the morning. And If it’s your job to eat two frogs, it’s best to eat the biggest one first.”

Eating the frog means accomplishing the day's most difficult chore. It's better to schedule it first thing in the morning when time-blocking the night before. Why?

• The day's most difficult task is also the one that causes the most postponement. Because of the stress it causes, the later you schedule it, the more time you risk wasting by procrastinating.

• However, if you do it right away in the morning, you'll feel good all day. This is the reason it was set for the morning.

Mel Robbins' 5-second rule can help. Start counting backward 54321 and force yourself to start at 1. If you acquire the urge to work on a goal, you must act within 5 seconds or your brain will destroy it. If you're scheduled to eat your frog at 9, eat it at 8:59. Start working.

Micro-visualisation

You've heard of visualizing to enhance the future. Visualizing a bright future won't do much if you're not prepared to focus on the now and develop the necessary habits. Alexander said:

People don’t decide their futures. They decide their habits and their habits decide their future.

I visualize the next day's schedule every morning. My day looks like this

“I’ll start writing an article at 7:30 AM. Then, I’ll get dressed up and reach the medicine outpatient department by 9:30 AM. After my duty is over, I’ll have lunch at 2 PM, followed by a nap at 3 PM. Then, I’ll go to the gym at 4…”

etc.

This reinforces the day you planned the night before. This makes following your plan easy.

Set the timer.

It's the best iPhone productivity app. A timer is incredible for increasing productivity.

Set a timer for an hour or 40 minutes before starting work. Your call. I don't believe in techniques like the Pomodoro because I can focus for varied amounts of time depending on the time of day, how fatigued I am, and how cognitively demanding the activity is.

I work with a timer. A timer keeps you focused and prevents distractions. Your mind stays concentrated because of the timer. Timers generate accountability.

To pee, I'll pause my timer. When I sit down, I'll continue. Same goes for bottle refills. To use Twitter, I must pause the timer. This creates accountability and focuses work.

Connecting everything

If you do all 4, you won't be disappointed. Here's how:

• Plan out your day's schedule the night before.

• Next, envision in your mind's eye the same timetable in the morning.

• Speak aloud 54321 when it's time to work: Eat the frog! In the morning, devour the largest frog.

• Then set a timer to ensure that you remain focused on the task at hand.

The world's most prestigious vintage vehicle show included amazing autos and record-breaking sums.

This 1932 Duesenberg J Figoni Sports Torpedo earned Best of Show in 2022.

David Paul Morris (DPM)/Bloomberg

2022 Pebble Beach Concours d'Elegance winner was a pre-war roadster.

Lee Anderson's 1932 Duesenberg J Figoni Sports Torpedo won Best of Show at Pebble Beach Golf Links near Carmel, Calif., on Sunday. First American win since 2013.

Sandra Button, chairperson of the annual concours, said the car, whose chassis and body had been separated for years, "marries American force with European style." "Its resurrection story is passionate."

Pebble Beach Concours d'Elegance Auction

Since 1950, the Pebble Beach Concours d'Elegance has welcomed the world's most costly collectable vehicles for a week of parties, auctions, rallies, and high-roller meetings. The cold, dreary weather highlighted the automobiles' stunning lines and hues.

DPM/Bloomberg

A visitor photographs a 1948 Ferrari 166 MM Touring Barchetta. This is one of 25 Ferraris manufactured in the years after World War II. First shown at the 1948 Turin Salon. Others finished Mille Miglia and Le Mans, which set the tone for Ferrari racing for years.

DPM/Bloomberg

This year's frontrunners were ultra-rare pre-war and post-war automobiles with long and difficult titles, such a 1937 Talbot-Lago T150C-SS Figoni & Falaschi Teardrop Coupe and a 1951 Talbot-Lago T26 Grand Sport Stabilimenti Farina Cabriolet.

The hefty, enormous coaches inspire visions of golden pasts when mysterious saloons swept over the road with otherworldly style, speed, and grace. Only the richest and most powerful people, like Indian maharaja and Hollywood stars, owned such vehicles.

Antonio Chopitea, a Peruvian sugar tycoon, ordered a new Duesenberg in Paris. Hemmings says the two-tone blue beauty was moved to the US and dismantled in the 1960s. Body and chassis were sold separately and rejoined decades later in a three-year, prize-winning restoration.

The concours is the highlight of Monterey Car Week, a five-day Super Bowl for car enthusiasts. Early events included Porsche and Ferrari displays, antique automobile races, and new-vehicle debuts. Many auto executives call Monterey Car Week the "new auto show."

Many visitors were drawn to the record-breaking auctions.

A 1969 Porsche 908/02 auctioned for $4.185 million. Flat-eight air-cooled engine, 90.6-inch wheelbase, 1,320-pound weight. Vic Elford, Richard Attwood, Rudi Lins, Gérard Larrousse, Kurt Ahrens Jr., Masten Gregory, and Pedro Rodriguez drove it, according to Gooding.

DPM/Bloomberg

The 1931 Bentley Eight Liter Sports Tourer doesn't meet its reserve. Gooding & Co., the official auction house of the concours, made more than $105 million and had an 82% sell-through rate. This powerful open-top tourer is one of W.O. Bentley's 100 automobiles. Only 80 remain.

DPM/Bloomberg

The final auction on Aug. 21 brought in $456.1 million, breaking the previous high of $394.48 million established in 2015 in Monterey. “The week put an exclamation point on what has been an exceptional year for the collector automobile market,” Hagerty analyst John Wiley said.

Many cars that go unsold at public auction are sold privately in the days after. After-sales pushed the week's haul to $469 million on Aug. 22, up 18.9% from 2015's record.

In today's currencies, 2015's record sales amount to $490 million, Wiley noted. The dollar is degrading faster than old autos.

Still, 113 million-dollar automobiles sold. The average car sale price was $583,211, up from $446,042 last year, while multimillion-dollar hammer prices made up around 75% of total sales.

Industry insiders and market gurus expected that stock market volatility, the crisis in Ukraine, and the dollar-euro exchange rate wouldn't influence the world's biggest spenders.

Classic.com's CEO said there's no hint of a recession in an e-mail. Big sales and crowds.

Ticket-holders wore huge hats, flowery skirts, and other Kentucky Derby-esque attire. Coffee, beverages, and food are extra.

DPM/Bloomberg

Mercedes-Benz 300 SL Gullwing, 1955. Mercedes produced the two-seat gullwing coupe from 1954–1957 and the roadster from 1957–1963. It was once West Germany's fastest and most powerful automobile. You'd be hard-pressed to locate one for less $1 million.

DPM/Bloomberg

1955 Ferrari 410 Sport sold for $22 million at RM Sotheby's. It sold a 1937 Mercedes-Benz 540K Sindelfingen Roadster for $9.9 million and a 1924 Hispano-Suiza H6C Transformable Torpedo for $9.245 million. The family-run mansion sold $221.7 million with a 90% sell-through rate, up from $147 million in 2021. This year, RM Sotheby's cars averaged $1.3 million.

Not everyone saw such great benefits.

Gooding & Co., the official auction house of the concours, made more than $105 million and had an 82% sell-through rate. 1937 Bugatti Type 57SC Atalante, 1990 Ferrari F40, and 1994 Bugatti EB110 Super Sport were top sellers.

The 1969 Autobianchi A112 Bertone. This idea two-seater became a Hot Wheels toy but was never produced. It has a four-speed manual drive and an inline-four mid-engine arrangement like the Lamborghini Miura.

DPM/Bloomberg

1956 Porsche 356 A Speedster at Gooding & Co. The Porsche 356 is a lightweight, rear-engine, rear-wheel drive vehicle that lacks driving power but is loved for its rounded, Beetle-like hardtop coupé and open-top versions.

DPM/Bloomberg

Mecum sold $50.8 million with a 64% sell-through rate, down from $53.8 million and 77% in 2021. Its top lot, a 1958 Ferrari 250 GT 'Tour de France' Alloy Coupe, sold for $2.86 million, but its average price was $174,016.

Bonhams had $27.8 million in sales with an 88% sell-through rate. The same sell-through generated $35.9 million in 2021.

Gooding & Co. and RM Sotheby's posted all 10 top sales, leaving Bonhams, Mecum, and Hagerty-owned Broad Arrow fighting for leftovers. Six of the top 10 sellers were Ferraris, which remain the gold standard for collectable automobiles. Their prices have grown over decades.

Classic.com's Calle claimed RM Sotheby's "stole the show," but "BroadArrow will be a force to reckon with."

Although pre-war cars were hot, '80s and '90s cars showed the most appreciation and attention. Generational transition and new buyer profile."

2022 Pebble Beach Concours d'Elegance judges inspect 1953 Siata 208. The rounded coupe was introduced at the 1952 Turin Auto Show in Italy and is one of 18 ever produced. It sports a 120hp Fiat engine, five-speed manual transmission, and alloy drum brakes. Owners liked their style, but not their reliability.

DPM/Bloomberg

The Czinger 21 CV Max at Pebble Beach. Monterey Car Week concentrates on historic and classic automobiles, but modern versions like this Czinger hypercar also showed.

DPM/Bloomberg

The 1932 Duesenberg J Figoni Sports Torpedo won Best in Show in 2022. Lee and Penny Anderson of Naples, Fla., own the once-separate-chassis-from-body automobile.

DPM/Bloomberg

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.

Will Tesla be able to maintain its lead in the EV market for very long?

This is one of the most pressing issues in the American auto sector today. One positive aspect of Tesla is the company's devoted customer base and recognizable name recognition (similar to Apple). It also invests more in research and development per vehicle than its rivals and has a head start in EV production.

Conversely, established automakers like Volkswagen are actively plotting their strategy to surpass Tesla. As the current market leaders, they have decades of experience in the auto industry and are spending billions to catch up.

We've visualized data from the EPA's 2022 Automotive Trends Report to bring you up to speed on this developing story.

Info for the Model Year of 2021

The full production data used in this infographic is for the 2021 model year, but it comes from a report for 2022.

Combined EV and PHEV output is shown in the table below (plug-in hybrid electric vehicle).

It is important to note that Toyota and Stellantis, the two largest legacy automakers in this dataset, only produced PHEVs. Toyota's first electric vehicle, the bZ4X, won't hit the market until 2023.

Stellantis seems to be falling even further behind, despite having enormous unrealized potential in its Jeep and Ram brands. Stellantis CEO Carlos Tavares said in a recent interview that the firm has budgeted $36 billion for electrification and software.

Legacy Brands with the Most Momentum

In the race to develop electric vehicles, some long-standing manufacturers have gotten the jump on their rivals.

Volkswagen, one of these storied manufacturers, has made a significant investment in electric vehicles (EVs) in the wake of the Dieselgate scandal. The company plans to roll out multiple EV models, including the ID.3 hatchback, ID.4 SUV, and ID. Buzz, with the goal of producing 22 million EVs by 2028. (an electric revival of the classic Microbus).

Even Ford is keeping up, having just announced an EV investment of $22 billion between 2021 and 2025. In November of 2022, the company manufactured their 150,000th Mustang Mach-E, and by the end of 2023, they hoped to have 270,000 of them in circulation.

Additionally, over 200,000 F-150 Lightnings have been reserved since Ford announced the truck. The Lightning is scheduled to have a production run of 15,000 in 2022, 55,000 in 2023, and 80,000 in 2024. Ford's main competitor in the electric pickup truck segment, Rivian, is on track to sell 25,000 vehicles by 2022.