9 months ago
Soon, a Starship Will Transform Humanity
Launched last week.
Four minutes in:
SpaceX will succeed. When it does, its massiveness will matter.
Its payload will revolutionize space economics.
Civilization will shift.
We don't yet understand how this will affect space and Earth culture. Grab it.
The Cost of Space Transportation Has Decreased Exponentially
Space launches have increased dramatically in recent years.
We mostly send items to LEO, the green area below:
SpaceX's reusable rockets can send these things to LEO. Each may launch dozens of payloads into space.
With all these launches, we're sending more than simply things to space. Volume and mass. Since the 1980s, launching a kilogram of payload to LEO has become cheaper:
One kilogram in a large rocket cost over $75,000 in the 1980s. Carrying one astronaut cost nearly $5M! Falcon Heavy's $1,500/kg price is 50 times lower. SpaceX's larger, reusable rockets are amazing.
SpaceX's Starship rocket will continue. It can carry over 100 tons to LEO, 50% more than the current Falcon heavy. Thousands of launches per year. Elon Musk predicts Falcon Heavy's $1,500/kg cost will plummet to $100 in 23 years.
People underestimate this.
2. The Benefits of Affordable Transportation
Compare Earth's transportation costs:
It's no surprise that the US and Northern Europe are the wealthiest and have the most navigable interior waterways.
So what? since sea transportation is cheaper than land. Inland waterways are even better than sea transportation since weather is less of an issue, currents can be controlled, and rivers serve two banks instead of one for coastal transportation.
In France, because population density follows river systems, rivers are valuable. Cheap transportation brought people and money to rivers, especially their confluences.
How come? Why were humans surrounding rivers?
Imagine selling meat for $10 per kilogram. Transporting one kg one kilometer costs $1. Your margin decreases $1 each kilometer. You can only ship 10 kilometers. For example, you can only trade with four cities:
If instead, your cost of transportation is half, what happens? It costs you $0.5 per km. You now have higher margins with each city you traded with. More importantly, you can reach 20-km markets.
However, 2x distance 4x surface! You can now trade with sixteen cities instead of four! Metcalfe's law states that a network's value increases with its nodes squared. Since now sixteen cities can connect to yours. Each city now has sixteen connections! They get affluent and can afford more meat.
Rivers lower travel costs, connecting many cities, which can trade more, get wealthy, and buy more.
The right network is worth at least an order of magnitude more than the left! The cheaper the transport, the more trade at a lower cost, the more income generated, the more that wealth can be reinvested in better canals, bridges, and roads, and the wealth grows even more.
Throughout history. Rome was established around cheap Mediterranean transit and preoccupied with cutting overland transportation costs with their famous roadways. Communications restricted their empire.
The Egyptians lived around the Nile, the Vikings around the North Sea, early Japan around the Seto Inland Sea, and China started canals in the 5th century BC.
Transportation costs shaped empires.Starship is lowering new-world transit expenses. What's possible?
3. Change Organizations, Change Companies, Change the World
Starship is a conveyor belt to LEO. A new world of opportunity opens up as transportation prices drop 100x in a decade.
Satellite engineers have spent decades shedding milligrams. Weight influenced every decision: pricing structure, volumes to be sent, material selections, power sources, thermal protection, guiding, navigation, and control software. Weight was everything in the mission. To pack as much science into every millimeter, NASA missions had to be miniaturized. Engineers were indoctrinated against mass.
Starship is not constrained by any space mission, robotic or crewed.
Starship obliterates the mass constraint and every last vestige of cultural baggage it has gouged into the minds of spacecraft designers. A dollar spent on mass optimization no longer buys a dollar saved on launch cost. It buys nothing. It is time to raise the scope of our ambition and think much bigger. — Casey Handmer, Starship is still not understood
A Tesla Roadster in space makes more sense.
It went beyond bad PR. It told the industry: Did you care about every microgram? No more. My rockets are big enough to send a Tesla without noticing. Industry watchers should have noticed.
Most didn’t. Artemis is a global mission to send astronauts to the Moon and build a base. Artemis uses disposable Space Launch System rockets. Instead of sending two or three dinky 10-ton crew habitats over the next decade, Starship might deliver 100x as much cargo and create a base for 1,000 astronauts in a year or two. Why not? Because Artemis remains in a pre-Starship paradigm where each kilogram costs a million dollars and we must aggressively descope our objective.
Space agencies can deliver 100x more payload to space for the same budget with 100x lower costs and 100x higher transportation volumes. How can space economy saturate this new supply?
Before Starship, NASA supplied heavy equipment for Moon base construction. After Starship, Caterpillar and Deere may space-qualify their products with little alterations. Instead than waiting decades for NASA engineers to catch up, we could send people to build a space outpost with John Deere equipment in a few years.
History is littered with the wreckage of former industrial titans that underestimated the impact of new technology and overestimated their ability to adapt: Blockbuster, Motorola, Kodak, Nokia, RIM, Xerox, Yahoo, IBM, Atari, Sears, Hitachi, Polaroid, Toshiba, HP, Palm, Sony, PanAm, Sega, Netscape, Compaq, GM… — Casey Handmer, Starship is still not understood
Everyone saw it coming, but senior management failed to realize that adaption would involve moving beyond their established business practice. Others will if they don't.
4. The Starship Possibilities
SpaceX invented affordable cargo space and grasped its implications first. How can we use all this inexpensive cargo nobody knows how to use?
Satellite communications seemed like the best way to capitalize on it. They tried. Starlink, designed by SpaceX, provides fast, dependable Internet worldwide. Beaming information down is often cheaper than cable. Already profitable.
Starlink is one use for all this cheap cargo space. Many more. The longer firms ignore the opportunity, the more SpaceX will acquire.
What are these chances?
Satellite imagery is outdated and lacks detail. We can improve greatly. Synthetic aperture radar can take beautiful shots like this:
Have you ever used Google Maps and thought, "I want to see this in more detail"? What if I could view Earth live? What if we could livestream an infrared image of Earth?
We could launch hundreds of satellites with such mind-blowing visual precision of the Earth that we would dramatically improve the accuracy of our meteorological models; our agriculture; where crime is happening; where poachers are operating in the savannah; climate change; and who is moving military personnel where. Is that useful?
What if we could see Earth in real time? That affects businesses? That changes society?
10 months ago
Because of this covert investment that Bezos made, Amazon became what it is today.
He kept it under wraps for years until he legally couldn’t.
His shirt is incomplete. I can’t stop thinking about this…
Actually, ignore the article. Look at it. JUST LOOK at it… It’s quite disturbing, isn’t it?
Me: “Hey, what up?” Friend: “All good, watching lord of the rings on amazon prime video.” Me: “Oh, do you know how Amazon grew and became famous?” Friend: “Geek alert…Can I just watch in peace?” Me: “But… Bezos?” Friend: “Let it go, just let it go…”
I can question you, the reader, and start answering instantly without his consent. This far.
Reader, how did Amazon succeed? You'll say, Of course, it was an internet bookstore, then it sold everything.
Mistaken. They moved from zero to one because of this. How did they get from one to thousand? AWS-some. Understand? It's geeky and lame. If not, I'll explain my geekiness.
Over an extended period of time, Amazon was not profitable.
Business basics. You want customers if you own a bakery, right?
Well, 100 clients per day order $5 cheesecakes (because cheesecakes are awesome.)
$5 x 100 consumers x 30 days Equals $15,000 monthly revenue. You proudly work here.
Now you have to pay the barista (unless ChatGPT is doing it haha? Nope..)
The barista is requesting $5000 a month.
Each cheesecake costs the cheesecake maker $2.5 ($2.5 × 100 x 30 = $7500).
The monthly cost of running your bakery, including power, is about $5000.
Assume no extra charges. Your operating costs are $17,500.
Just $15,000? You have income but no profit. You might make money selling coffee with your cheesecake next month.
Is losing money bad? You're broke. Losing money. It's bad for financial statements.
It's almost a business ultimatum. Most startups fail. Amazon took nine years.
I'm reading Amazon Unbound: Jeff Bezos and the Creation of a Global Empire to comprehend how a company has a $1 trillion market cap.
Many things made Amazon big. The book claims that Bezos and Amazon kept a specific product secret for a long period.
Clouds above the bald head.
In 2006, Bezos started a cloud computing initiative. They believed many firms like Snapchat would pay for reliable servers.
In 2006, cloud computing was not what it is today. I'll simplify. 2006 had no iPhone.
Bezos invested in Amazon Web Services (AWS) without disclosing its revenue. That's permitted till a certain degree.
Google and Microsoft would realize Amazon is heavily investing in this market and worry.
Bezos anticipated high demand for this product. Microsoft built its cloud in 2010, and Google in 2008.
If you managed Google or Microsoft, you wouldn't know how much Amazon makes from their cloud computing service. It's enough. Yet, Amazon is an internet store, so they'll focus on that.
All but Bezos were wrong.
Time to come clean now.
They revealed AWS revenue in 2015. Two things were apparent:
Bezos made the proper decision to bet on the cloud and keep it a secret.
In this race, Amazon is in the lead.
They continued. Let me list some AWS users today.
More. Amazon was unprofitable for nine years, remember? This article's main graph.
AWS accounted for 74% of Amazon's profit in 2021. This 74% might not exist if they hadn't invested in AWS.
Bring this with you home.
Amazon predated AWS. Yet, it helped the giant reach $1 trillion. Bezos' secrecy? Perhaps, until a time machine is invented (they might host the time machine software on AWS, though.)
Without AWS, Amazon would have been profitable but unimpressive. They may have invested in anything else that would have returned more (like crypto? No? Ok.)
Bezos has business flaws. His success. His failures include:
introducing the Fire Phone and suffering a $170 million loss.
Amazon's failure in China In 2011, Amazon had a about 15% market share in China. 2019 saw a decrease of about 1%.
not offering a higher price to persuade the creator of Netflix to sell the company to him. He offered a rather reasonable $15 million in his proposal. But what if he had offered $30 million instead (Amazon had over $100 million in revenue at the time)? He might have owned Netflix, which has a $156 billion market valuation (and saved billions rather than invest in Amazon Prime Video).
Some he could control. Some were uncontrollable. Nonetheless, every action he made in the foregoing circumstances led him to invest in AWS.
Sofien Kaabar, CFA
10 months ago
Innovative Trading Methods: The Catapult Indicator
Python Volatility-Based Catapult Indicator
As a catapult, this technical indicator uses three systems: Volatility (the fulcrum), Momentum (the propeller), and a Directional Filter (Acting as the support). The goal is to get a signal that predicts volatility acceleration and direction based on historical patterns. We want to know when the market will move. and where. This indicator outperforms standard indicators.
Knowledge must be accessible to everyone. This is why my new publications Contrarian Trading Strategies in Python and Trend Following Strategies in Python now include free PDF copies of my first three books (Therefore, purchasing one of the new books gets you 4 books in total). GitHub-hosted advanced indications and techniques are in the two new books above.
The Foundation: Volatility
The Catapult predicts significant changes with the 21-period Relative Volatility Index.
The Average True Range, Mean Absolute Deviation, and Standard Deviation all assess volatility. Standard Deviation will construct the Relative Volatility Index.
Standard Deviation is the most basic volatility. It underpins descriptive statistics and technical indicators like Bollinger Bands. Before calculating Standard Deviation, let's define Variance.
Variance is the squared deviations from the mean (a dispersion measure). We take the square deviations to compel the distance from the mean to be non-negative, then we take the square root to make the measure have the same units as the mean, comparing apples to apples (mean to standard deviation standard deviation). Variance formula:
As stated, standard deviation is:
# The function to add a number of columns inside an array
def adder(Data, times):
for i in range(1, times + 1):
new_col = np.zeros((len(Data), 1), dtype = float)
Data = np.append(Data, new_col, axis = 1)
# The function to delete a number of columns starting from an index
def deleter(Data, index, times):
for i in range(1, times + 1):
Data = np.delete(Data, index, axis = 1)
# The function to delete a number of rows from the beginning
def jump(Data, jump):
Data = Data[jump:, ]
# Example of adding 3 empty columns to an array
my_ohlc_array = adder(my_ohlc_array, 3)
# Example of deleting the 2 columns after the column indexed at 3
my_ohlc_array = deleter(my_ohlc_array, 3, 2)
# Example of deleting the first 20 rows
my_ohlc_array = jump(my_ohlc_array, 20)
# Remember, OHLC is an abbreviation of Open, High, Low, and Close and it refers to the standard historical data file
def volatility(Data, lookback, what, where):
for i in range(len(Data)):
Data[i, where] = (Data[i - lookback + 1:i + 1, what].std())
The RSI is the most popular momentum indicator, and for good reason—it excels in range markets. Its 0–100 range simplifies interpretation. Fame boosts its potential.
The more traders and portfolio managers look at the RSI, the more people will react to its signals, pushing market prices. Technical Analysis is self-fulfilling, therefore this theory is obvious yet unproven.
RSI is determined simply. Start with one-period pricing discrepancies. We must remove each closing price from the previous one. We then divide the smoothed average of positive differences by the smoothed average of negative differences. The RSI algorithm converts the Relative Strength from the last calculation into a value between 0 and 100.
def ma(Data, lookback, close, where):
Data = adder(Data, 1)
for i in range(len(Data)):
Data[i, where] = (Data[i - lookback + 1:i + 1, close].mean())
Data = jump(Data, lookback)
def ema(Data, alpha, lookback, what, where):
alpha = alpha / (lookback + 1.0)
beta = 1 - alpha
# First value is a simple SMA
Data = ma(Data, lookback, what, where)
# Calculating first EMA
Data[lookback + 1, where] = (Data[lookback + 1, what] * alpha) + (Data[lookback, where] * beta)
# Calculating the rest of EMA
for i in range(lookback + 2, len(Data)):
Data[i, where] = (Data[i, what] * alpha) + (Data[i - 1, where] * beta)
return Datadef rsi(Data, lookback, close, where, width = 1, genre = 'Smoothed'):
# Adding a few columns
Data = adder(Data, 7)
# Calculating Differences
for i in range(len(Data)):
Data[i, where] = Data[i, close] - Data[i - width, close]
# Calculating the Up and Down absolute values
for i in range(len(Data)):
if Data[i, where] > 0:
Data[i, where + 1] = Data[i, where]
elif Data[i, where] < 0:
Data[i, where + 2] = abs(Data[i, where])
# Calculating the Smoothed Moving Average on Up and Down
lookback = (lookback * 2) - 1 # From exponential to smoothed
Data = ema(Data, 2, lookback, where + 1, where + 3)
Data = ema(Data, 2, lookback, where + 2, where + 4)
# Calculating the Relative Strength
Data[:, where + 5] = Data[:, where + 3] / Data[:, where + 4]
# Calculate the Relative Strength Index
Data[:, where + 6] = (100 - (100 / (1 + Data[:, where + 5])))
Data = deleter(Data, where, 6)
Data = jump(Data, lookback)
def relative_volatility_index(Data, lookback, close, where):
# Calculating Volatility
Data = volatility(Data, lookback, close, where)
# Calculating the RSI on Volatility
Data = rsi(Data, lookback, where, where + 1)
Data = deleter(Data, where, 1)
The Arm Section: Speed
The Catapult predicts momentum direction using the 14-period Relative Strength Index.
As a reminder, the RSI ranges from 0 to 100. Two levels give contrarian signals:
A positive response is anticipated when the market is deemed to have gone too far down at the oversold level 30, which is 30.
When the market is deemed to have gone up too much, at overbought level 70, a bearish reaction is to be expected.
Comparing the RSI to 50 is another intriguing use. RSI above 50 indicates bullish momentum, while below 50 indicates negative momentum.
The direction-finding filter in the frame
The Catapult's directional filter uses the 200-period simple moving average to keep us trending. This keeps us sane and increases our odds.
Moving averages confirm and ride trends. Its simplicity and track record of delivering value to analysis make them the most popular technical indicator. They help us locate support and resistance, stops and targets, and the trend. Its versatility makes them essential trading tools.
This is the plain mean, employed in statistics and everywhere else in life. Simply divide the number of observations by their total values. Mathematically, it's:
We defined the moving average function above. Create the Catapult indication now.
Indicator of the Catapult
The indicator is a healthy mix of the three indicators:
The first trigger will be provided by the 21-period Relative Volatility Index, which indicates that there will now be above average volatility and, as a result, it is possible for a directional shift.
If the reading is above 50, the move is likely bullish, and if it is below 50, the move is likely bearish, according to the 14-period Relative Strength Index, which indicates the likelihood of the direction of the move.
The likelihood of the move's direction will be strengthened by the 200-period simple moving average. When the market is above the 200-period moving average, we can infer that bullish pressure is there and that the upward trend will likely continue. Similar to this, if the market falls below the 200-period moving average, we recognize that there is negative pressure and that the downside is quite likely to continue.
lookback_rvi = 21
lookback_rsi = 14
lookback_ma = 200
my_data = ma(my_data, lookback_ma, 3, 4)
my_data = rsi(my_data, lookback_rsi, 3, 5)
my_data = relative_volatility_index(my_data, lookback_rvi, 3, 6)
Two-handled overlay indicator Catapult. The first exhibits blue and green arrows for a buy signal, and the second shows blue and red for a sell signal.
The chart below shows recent EURUSD hourly values.
def signal(Data, rvi_col, signal):
Data = adder(Data, 10)
for i in range(len(Data)):
if Data[i, rvi_col] < 30 and \
Data[i - 1, rvi_col] > 30 and \
Data[i - 2, rvi_col] > 30 and \
Data[i - 3, rvi_col] > 30 and \
Data[i - 4, rvi_col] > 30 and \
Data[i - 5, rvi_col] > 30:
Data[i, signal] = 1
Signals are straightforward. The indicator can be utilized with other methods.
my_data = signal(my_data, 6, 7)
Lumiwealth shows how to develop all kinds of algorithms. I recommend their hands-on courses in algorithmic trading, blockchain, and machine learning.
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.
After you find a trading method or approach, follow these steps:
Put emotions aside and adopt an analytical perspective.
Test it in the past in conditions and simulations taken from real life.
Try improving it and performing a forward test if you notice any possibility.
Transaction charges and any slippage simulation should always be included in your tests.
Risk management and position sizing should always be included in your tests.
After checking the aforementioned, monitor the plan because market dynamics may change and render it unprofitable.
10 months ago
Mastering the Art of Rhetoric: A Guide to Rhetorical Devices in Successful Headlines and Titles
Unleash the power of persuasion and captivate your audience with compelling headlines.
As the old adage goes, "You never get a second chance to make a first impression."
In the world of content creation and social ads, headlines and titles play a critical role in making that first impression.
A well-crafted headline can make the difference between an article being read or ignored, a video being clicked on or bypassed, or a product being purchased or passed over.
To make an impact with your headlines, mastering the art of rhetoric is essential. In this post, we'll explore various rhetorical devices and techniques that can help you create headlines that captivate your audience and drive engagement.
tl;dr : Headline Magician will help you craft the ultimate headline titles powered by rhetoric devices
Example with a high-end luxury organic zero-waste skincare brand
✍️ The Power of Alliteration
Alliteration is the repetition of the same consonant sound at the beginning of words in close proximity. This rhetorical device lends itself well to headlines, as it creates a memorable, rhythmic quality that can catch a reader's attention.
By using alliteration, you can make your headlines more engaging and easier to remember.
"Crafting Compelling Content: A Comprehensive Course"
"Mastering the Art of Memorable Marketing"
🔁 The Appeal of Anaphora
Anaphora is the repetition of a word or phrase at the beginning of successive clauses. This rhetorical device emphasizes a particular idea or theme, making it more memorable and persuasive.
In headlines, anaphora can be used to create a sense of unity and coherence, which can draw readers in and pique their interest.
"Create, Curate, Captivate: Your Guide to Social Media Success"
"Innovation, Inspiration, and Insight: The Future of AI"
🔄 The Intrigue of Inversion
Inversion is a rhetorical device where the normal order of words is reversed, often to create an emphasis or achieve a specific effect.
In headlines, inversion can generate curiosity and surprise, compelling readers to explore further.
"Beneath the Surface: A Deep Dive into Ocean Conservation"
"Beyond the Stars: The Quest for Extraterrestrial Life"
⚖️ The Persuasive Power of Parallelism
Parallelism is a rhetorical device that involves using similar grammatical structures or patterns to create a sense of balance and symmetry.
In headlines, parallelism can make your message more memorable and impactful, as it creates a pleasing rhythm and flow that can resonate with readers.
"Eat Well, Live Well, Be Well: The Ultimate Guide to Wellness"
"Learn, Lead, and Launch: A Blueprint for Entrepreneurial Success"
⏭️ The Emphasis of Ellipsis
Ellipsis is the omission of words, typically indicated by three periods (...), which suggests that there is more to the story.
In headlines, ellipses can create a sense of mystery and intrigue, enticing readers to click and discover what lies behind the headline.
"The Secret to Success... Revealed"
"Unlocking the Power of Your Mind... A Step-by-Step Guide"
🎭 The Drama of Hyperbole
Hyperbole is a rhetorical device that involves exaggeration for emphasis or effect.
In headlines, hyperbole can grab the reader's attention by making bold, provocative claims that stand out from the competition. Be cautious with hyperbole, however, as overuse or excessive exaggeration can damage your credibility.
"The Ultimate Guide to Mastering Any Skill in Record Time"
"Discover the Revolutionary Technique That Will Transform Your Life"
❓The Curiosity of Questions
Posing questions in your headlines can be an effective way to pique the reader's curiosity and encourage engagement.
Questions compel the reader to seek answers, making them more likely to click on your content. Additionally, questions can create a sense of connection between the content creator and the audience, fostering a sense of dialogue and discussion.
"Are You Making These Common Mistakes in Your Marketing Strategy?"
"What's the Secret to Unlocking Your Creative Potential?"
💥 The Impact of Imperatives
Imperatives are commands or instructions that urge the reader to take action. By using imperatives in your headlines, you can create a sense of urgency and importance, making your content more compelling and actionable.
"Master Your Time Management Skills Today"
"Transform Your Business with These Innovative Strategies"
💢 The Emotion of Exclamations
Exclamations are powerful rhetorical devices that can evoke strong emotions and convey a sense of excitement or urgency.
Including exclamations in your headlines can make them more attention-grabbing and shareable, increasing the chances of your content being read and circulated.
"Unlock Your True Potential: Find Your Passion and Thrive!"
"Experience the Adventure of a Lifetime: Travel the World on a Budget!"
🎀 The Effectiveness of Euphemisms
Euphemisms are polite or indirect expressions used in place of harsher, more direct language.
In headlines, euphemisms can make your message more appealing and relatable, helping to soften potentially controversial or sensitive topics.
"Navigating the Challenges of Modern Parenting"
"Redefining Success in a Fast-Paced World"
⚡Antithesis: The Power of Opposites
Antithesis involves placing two opposite words side-by-side, emphasizing their contrasts. This device can create a sense of tension and intrigue in headlines.
"Once a day. Every day"
"Soft on skin. Kill germs"
"Mega power. Mini size."
To utilize antithesis, identify two opposing concepts related to your content and present them in a balanced manner.
🎨 Scesis Onomaton: The Art of Verbless Copy
Scesis onomaton is a rhetorical device that involves writing verbless copy, which quickens the pace and adds emphasis.
"7 days. 7 dollars. Full access."
To use scesis onomaton, remove verbs and focus on the essential elements of your headline.
🌟 Polyptoton: The Charm of Shared Roots
Polyptoton is the repeated use of words that share the same root, bewitching words into memorable phrases.
"Real bread isn't made in factories. It's baked in bakeries"
"Lose your knack for losing things."
To employ polyptoton, identify words with shared roots that are relevant to your content.
✨ Asyndeton: The Elegance of Omission
Asyndeton involves the intentional omission of conjunctions, adding crispness, conviction, and elegance to your headlines.
"You, Me, Sushi?"
"All the latte art, none of the environmental impact."
To use asyndeton, eliminate conjunctions and focus on the core message of your headline.
🔮 Tricolon: The Magic of Threes
Tricolon is a rhetorical device that uses the power of three, creating memorable and impactful headlines.
"Show it, say it, send it"
"Eat Well, Live Well, Be Well."
To use tricolon, craft a headline with three key elements that emphasize your content's main message.
🔔 Epistrophe: The Chime of Repetition
Epistrophe involves the repetition of words or phrases at the end of successive clauses, adding a chime to your headlines.
"Catch it. Bin it. Kill it."
"Joint friendly. Climate friendly. Family friendly."
To employ epistrophe, repeat a key phrase or word at the end of each clause.
Farhan Ali Khan
10 months ago
Introduction to Zero-Knowledge Proofs: The Art of Proving Without Revealing
Zero-Knowledge Proofs for Beginners
Published here originally.
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).
In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.
As Alex made his decision, Jack entered the cave and asked him to exit from the B path.
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:
Alex walks into the cave.
Alex follows a random route.
Jack walks into the cave.
Alex is asked to follow a random route by Jack.
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
Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.
Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.
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:
You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.
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.
You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.
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:
Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.
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.
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:
One of the two coins is chosen at random, and you secretly flip it more than once.
You show your pal the following series of coin flips without revealing which coin you actually flipped.
Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.
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.
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:
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.
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.
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:
You determine a new number s = r2 mod n by computing a random number r.
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.
A random number (either 0 or 1) is selected by your friend and sent to you.
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.
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:
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.
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.
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:
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.
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.
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.
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.
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:
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.
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.
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.
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.
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.
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:
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.
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.
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.
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.
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.