As the world watches the Russia-Ukraine border situation, This bill would bar aid to Ukraine until the Mexican border is secured.
Although Mexico and Ukraine are thousands of miles apart, this legislation would link their responses.
Context
Ukraine was a Soviet republic until 1991. A significant proportion of the population, particularly in the east, is ethnically Russian. In February, the Russian military invaded Ukraine, intent on overthrowing its democratically elected government.
This could be the biggest European land invasion since WWII. In response, President Joe Biden sent 3,000 troops to NATO countries bordering Ukraine to help with Ukrainian refugees, with more troops possible if the situation worsened.
In July 2021, the US Border Patrol reported its highest monthly encounter total since March 2000. Some Republicans compare Biden's response to the Mexican border situation to his response to the Ukrainian border situation, though the correlation is unclear.
What the bills do
Two new Republican bills seek to link the US response to Ukraine to the situation in Mexico.
The Secure America's Borders First Act would prohibit federal funding for Ukraine until the US-Mexico border is “operationally controlled,” including a wall as promised by former President Donald Trump. (The bill even mandates a 30-foot-high wall.)
The USB (Ukraine and Southern Border) Act, introduced on February 8 by Rep. Matt Rosendale (R-MT0), would allow the US to support Ukraine, but only if the number of Armed Forces deployed there is less than the number deployed to the Mexican border. Madison Cawthorne introduced H.R. 6665 on February 9th (R-NC11).
What backers say
Supporters argue that even if the US should militarily assist Ukraine, our own domestic border situation should take precedence.
After failing to secure our own border and protect our own territorial integrity, ‘America Last' politicians on both sides of the aisle now tell us that we must do so for Ukraine. “Before rushing America into another foreign conflict over an Eastern European nation's border thousands of miles from our shores, they should first secure our southern border.”
“If Joe Biden truly cared about Americans, he would prioritize national security over international affairs,” Rep. Cawthorn said in a separate press release. The least we can do to secure our own country is send the same number of troops to the US-Mexico border to assist our border patrol agents working diligently to secure America.
What opponents say
The president has defended his Ukraine and Mexico policies, stating that both seek peace and diplomacy.
Our nations [the US and Mexico] have a long and complicated history, and we haven't always been perfect neighbors, but we have seen the power and purpose of cooperation,” Biden said in 2021. “We're safer when we work together, whether it's to manage our shared border or stop the pandemic. [In both the Obama and Biden administration], we made a commitment that we look at Mexico as an equal, not as somebody who is south of our border.”
No mistake: If Russia goes ahead with its plans, it will be responsible for a catastrophic and unnecessary war of choice. To protect our collective security, the United States and our allies are ready to defend every inch of NATO territory. We won't send troops into Ukraine, but we will continue to support the Ukrainian people... But, I repeat, Russia can choose diplomacy. It is not too late to de-escalate and return to the negotiating table.”
Odds of passage
The Secure America's Borders First Act has nine Republican sponsors. Either the House Armed Services or Foreign Affairs Committees may vote on it.
Rep. Paul Gosar, a Republican, co-sponsored the USB Act (R-AZ4). The House Armed Services Committee may vote on it.
With Republicans in control, passage is unlikely.
More on Current Events
Claire Berehova
3 years ago
There’s no manual for that
| Kyiv oblast in springtime. Photo by author. |
We’ve been receiving since the war began text messages from the State Emergency Service of Ukraine every few days. They’ve contained information on how to comfort a child and what to do in case of a water outage.
But a question that I struggle to suppress irks within me: How would we know if there really was a threat coming our away? So how can I happily disregard an air raid siren and continue singing to my three-month-old son when I feel like a World War II film became reality? There’s no manual for that.
Along with the anxiety, there’s the guilt that always seems to appear alongside dinner we’re fortunate to still have each evening while brave Ukrainian soldiers are facing serious food insecurity. There’s no manual for how to deal with this guilt.
When it comes to the enemy, there is no manual for how to react to the news of Russian casualties. Every dead Russian soldier weakens Putin, but I also know that many of these men had wives and girlfriends who are now living a nightmare.
So, I felt like I had to start writing my own manual.
The anxiety around the air raid siren? Only with time does it get easier to ignore it, but never completely.
The guilt? All we can do is pray.
That inner conflict? As Russia continues to stun the world with its war crimes, my emotions get less gray — I have to get used to accommodating absurd levels of hatred.
Sadness? It feels a bit more manageable when we laugh, and a little alcohol helps (as it usually does).
Cabin fever? Step outside in the yard when possible. At least the sunshine is becoming more fervent with spring approaching.
Slava Ukraini. Heroyam slava. (Glory to Ukraine. Glory to the heroes.)
Gill Pratt
3 years ago
War's Human Cost
War's Human Cost
I didn't start crying until I was outside a McDonald's in an Olempin, Poland rest area on highway S17.
Children pick toys at a refugee center, Olempin, Poland, March 4, 2022.
Refugee children, mostly alone with their mothers, but occasionally with a gray-haired grandfather or non-Ukrainian father, were coaxed into picking a toy from boxes provided by a kind-hearted company and volunteers.
I went to Warsaw to continue my research on my family's history during the Holocaust. In light of the ongoing Ukrainian conflict, I asked former colleagues in the US Department of Defense and Intelligence Community if it was safe to travel there. They said yes, as Poland was a NATO member.
I stayed in a hotel in the Warsaw Ghetto, where 90% of my mother's family was murdered in the Holocaust. Across the street was the first Warsaw Judenrat. It was two blocks away from the apartment building my mother's family had owned and lived in, now dilapidated and empty.
Building of my great-grandfather, December 2021.
A mass grave of thousands of rocks for those killed in the Warsaw Ghetto, I didn't cry when I touched its cold walls.
Warsaw Jewish Cemetery, 200,000–300,000 graves.
Mass grave, Warsaw Jewish Cemetery.
My mother's family had two homes, one in Warszawa and the rural one was a forest and sawmill complex in Western Ukraine. For the past half-year, a local Ukrainian historian had been helping me discover faint traces of her family’s life there — in fact, he had found some people still alive who remembered the sawmill and that it belonged to my mother’s grandfather. The historian was good at his job, and we had become close.
My historian friend, December 2021, talking to a Ukrainian.
With war raging, my second trip to Warsaw took on a different mission. To see his daughter and one-year-old grandson, I drove east instead of to Ukraine. They had crossed the border shortly after the war began, leaving men behind, and were now staying with a friend on Poland's eastern border.
I entered after walking up to the house and settling with the dog. The grandson greeted me with a huge smile and the Ukrainian word for “daddy,” “Tato!” But it was clear he was awaiting his real father's arrival, and any man he met would be so tentatively named.
After a few moments, the boy realized I was only a stranger. He had musical talent, like his mother and grandfather, both piano teachers, as he danced to YouTube videos of American children's songs dubbed in Ukrainian, picking the ones he liked and crying when he didn't.
Songs chosen by my historian friend's grandson, March 4, 2022
He had enough music and began crying regardless of the song. His mother picked him up and started nursing him, saying she was worried about him. She had no idea where she would live or how she would survive outside Ukraine. She showed me her father's family history of losses in the Holocaust, which matched my own research.
After an hour of drinking tea and trying to speak of hope, I left for the 3.5-hour drive west to Warsaw.
It was unlike my drive east. It was reminiscent of the household goods-filled carts pulled by horses and people fleeing war 80 years ago.
Jewish refugees relocating, USHMM Holocaust Encyclopaedia, 1939.
The carefully chosen trinkets by children to distract them from awareness of what is really happening and the anxiety of what lies ahead, made me cry despite all my research on the Holocaust. There is no way for them to communicate with their mothers, who are worried, absent, and without their fathers.
It's easy to see war as a contest of nations' armies, weapons, and land. The most costly aspect of war is its psychological toll. My father screamed in his sleep from nightmares of his own adolescent trauma in Warsaw 80 years ago.
Survivor father studying engineering, 1961.
In the airport, I waited to return home while Ukrainian public address systems announced refugee assistance. Like at McDonald's, many mothers were alone with their children, waiting for a flight to distant relatives.
That's when I had my worst trip experience.
A woman near me, clearly a refugee, answered her phone, cried out, and began wailing.
The human cost of war descended like a hammer, and I realized that while I was going home, she never would
Will Lockett
3 years ago
Russia's nukes may be useless
Russia's nuclear threat may be nullified by physics.
Putin seems nostalgic and wants to relive the Cold War. He's started a deadly war to reclaim the old Soviet state of Ukraine and is threatening the West with nuclear war. NATO can't risk starting a global nuclear war that could wipe out humanity to support Ukraine's independence as much as they want to. Fortunately, nuclear physics may have rendered Putin's nuclear weapons useless. However? How will Ukraine and NATO react?
To understand why Russia's nuclear weapons may be ineffective, we must first know what kind they are.
Russia has the world's largest nuclear arsenal, with 4,447 strategic and 1,912 tactical weapons (all of which are ready to be rolled out quickly). The difference between these two weapons is small, but it affects their use and logistics. Strategic nuclear weapons are ICBMs designed to destroy a city across the globe. Russia's ICBMs have many designs and a yield of 300–800 kilotonnes. 300 kilotonnes can destroy Washington. Tactical nuclear weapons are smaller and can be fired from artillery guns or small truck-mounted missile launchers, giving them a 1,500 km range. Instead of destroying a distant city, they are designed to eliminate specific positions, bases, or military infrastructure. They produce 1–50 kilotonnes.
These two nuclear weapons use different nuclear reactions. Pure fission bombs are compact enough to fit in a shell or small missile. All early nuclear weapons used this design for their fission bombs. This technology is inefficient for bombs over 50 kilotonnes. Larger bombs are thermonuclear. Thermonuclear weapons use a small fission bomb to compress and heat a hydrogen capsule, which undergoes fusion and releases far more energy than ignition fission reactions, allowing for effective giant bombs.
Here's Russia's issue.
A thermonuclear bomb needs deuterium (hydrogen with one neutron) and tritium (hydrogen with two neutrons). Because these two isotopes fuse at lower energies than others, the bomb works. One problem. Tritium is highly radioactive, with a half-life of only 12.5 years, and must be artificially made.
Tritium is made by irradiating lithium in nuclear reactors and extracting the gas. Tritium is one of the most expensive materials ever made, at $30,000 per gram.
Why does this affect Putin's nukes?
Thermonuclear weapons need tritium. Tritium decays quickly, so they must be regularly refilled at great cost, which Russia may struggle to do.
Russia has a smaller economy than New York, yet they are running an invasion, fending off international sanctions, and refining tritium for 4,447 thermonuclear weapons.
The Russian military is underfunded. Because the state can't afford it, Russian troops must buy their own body armor. Arguably, Putin cares more about the Ukraine conflict than maintaining his nuclear deterrent. Putin will likely lose power if he loses the Ukraine war.
It's possible that Putin halted tritium production and refueling to save money for Ukraine. His threats of nuclear attacks and escalating nuclear war may be a bluff.
This doesn't help Ukraine, sadly. Russia's tactical nuclear weapons don't need expensive refueling and will help with the invasion. So Ukraine still risks a nuclear attack. The bomb that destroyed Hiroshima was 15 kilotonnes, and Russia's tactical Iskander-K nuclear missile has a 50-kiloton yield. Even "little" bombs are deadly.
We can't guarantee it's happening in Russia. Putin may prioritize tritium. He knows the power of nuclear deterrence. Russia may have enough tritium for this conflict. Stockpiling a material with a short shelf life is unlikely, though.
This means that Russia's most powerful weapons may be nearly useless, but they may still be deadly. If true, this could allow NATO to offer full support to Ukraine and push the Russian tyrant back where he belongs. If Putin withholds funds from his crumbling military to maintain his nuclear deterrent, he may be willing to sink the ship with him. Let's hope the former.
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Duane Michael
2 years ago
Don't Fall Behind: 7 Subjects You Must Understand to Keep Up with Technology
As technology develops, you should stay up to date
You don't want to fall behind, do you? This post covers 7 tech-related things you should know.
You'll learn how to operate your computer (and other electronic devices) like an expert and how to leverage the Internet and social media to create your brand and business. Read on to stay relevant in today's tech-driven environment.
You must learn how to code.
Future-language is coding. It's how we and computers talk. Learn coding to keep ahead.
Try Codecademy or Code School. There are also numerous free courses like Coursera or Udacity, but they take a long time and aren't necessarily self-paced, so it can be challenging to find the time.
Artificial intelligence (AI) will transform all jobs.
Our skillsets must adapt with technology. AI is a must-know topic. AI will revolutionize every employment due to advances in machine learning.
Here are seven AI subjects you must know.
What is artificial intelligence?
How does artificial intelligence work?
What are some examples of AI applications?
How can I use artificial intelligence in my day-to-day life?
What jobs have a high chance of being replaced by artificial intelligence and how can I prepare for this?
Can machines replace humans? What would happen if they did?
How can we manage the social impact of artificial intelligence and automation on human society and individual people?
Blockchain Is Changing the Future
Few of us know how Bitcoin and blockchain technology function or what impact they will have on our lives. Blockchain offers safe, transparent, tamper-proof transactions.
It may alter everything from business to voting. Seven must-know blockchain topics:
Describe blockchain.
How does the blockchain function?
What advantages does blockchain offer?
What possible uses for blockchain are there?
What are the dangers of blockchain technology?
What are my options for using blockchain technology?
What does blockchain technology's future hold?
Cryptocurrencies are here to stay
Cryptocurrencies employ cryptography to safeguard transactions and manage unit creation. Decentralized cryptocurrencies aren't controlled by governments or financial institutions.
Bitcoin, the first cryptocurrency, was launched in 2009. Cryptocurrencies can be bought and sold on decentralized exchanges.
Bitcoin is here to stay.
Bitcoin isn't a fad, despite what some say. Since 2009, Bitcoin's popularity has grown. Bitcoin is worth learning about now. Since 2009, Bitcoin has developed steadily.
With other cryptocurrencies emerging, many people are wondering if Bitcoin still has a bright future. Curiosity is natural. Millions of individuals hope their Bitcoin investments will pay off since they're popular now.
Thankfully, they will. Bitcoin is still running strong a decade after its birth. Here's why.
The Internet of Things (IoT) is no longer just a trendy term.
IoT consists of internet-connected physical items. These items can share data. IoT is young but developing fast.
20 billion IoT-connected devices are expected by 2023. So much data! All IT teams must keep up with quickly expanding technologies. Four must-know IoT topics:
Recognize the fundamentals: Priorities first! Before diving into more technical lingo, you should have a fundamental understanding of what an IoT system is. Before exploring how something works, it's crucial to understand what you're working with.
Recognize Security: Security does not stand still, even as technology advances at a dizzying pace. As IT professionals, it is our duty to be aware of the ways in which our systems are susceptible to intrusion and to ensure that the necessary precautions are taken to protect them.
Be able to discuss cloud computing: The cloud has seen various modifications over the past several years once again. The use of cloud computing is also continually changing. Knowing what kind of cloud computing your firm or clients utilize will enable you to make the appropriate recommendations.
Bring Your Own Device (BYOD)/Mobile Device Management (MDM) is a topic worth discussing (MDM). The ability of BYOD and MDM rules to lower expenses while boosting productivity among employees who use these services responsibly is a major factor in their continued growth in popularity.
IoT Security is key
As more gadgets connect, they must be secure. IoT security includes securing devices and encrypting data. Seven IoT security must-knows:
fundamental security ideas
Authorization and identification
Cryptography
electronic certificates
electronic signatures
Private key encryption
Public key encryption
Final Thoughts
With so much going on in the globe, it can be hard to stay up with technology. We've produced a list of seven tech must-knows.
Charlie Brown
2 years ago
What Happens When You Sell Your House, Never Buying It Again, Reverse the American Dream
Homeownership isn't the only life pattern.
Want to irritate people?
My party trick is to say I used to own a house but no longer do.
I no longer wish to own a home, not because I lost it or because I'm moving.
It was a long-term plan. It was more deliberate than buying a home. Many people are committed for this reason.
Poppycock.
Anyone who told me that owning a house (or striving to do so) is a must is wrong.
Because, URGH.
One pattern for life is to own a home, but there are millions of others.
You can afford to buy a home? Go, buddy.
You think you need 1,000 square feet (or more)? You think it's non-negotiable in life?
Nope.
It's insane that society forces everyone to own real estate, regardless of income, wants, requirements, or situation. As if this trade brings happiness, stability, and contentment.
Take it from someone who thought this for years: drywall isn't happy. Living your way brings contentment.
That's in real estate. It may also be renting a small apartment in a city that makes your soul sing, but you can't afford the downpayment or mortgage payments.
Living or traveling abroad is difficult when your life savings are connected to something that eats your money the moment you sign.
#vanlife, which seems like torment to me, makes some people feel alive.
I've seen co-living, vacation rental after holiday rental, living with family, and more work.
Insisting that home ownership is the only path in life is foolish and reduces alternative options.
How little we question homeownership is a disgrace.
No one challenges a homebuyer's motives. We congratulate them, then that's it.
When you offload one, you must answer every question, even if you have a loose screw.
Why do you want to sell?
Do you have any concerns about leaving the market?
Why would you want to renounce what everyone strives for?
Why would you want to abandon a beautiful place like that?
Why would you mismanage your cash in such a way?
But surely it's only temporary? RIGHT??
Incorrect questions. Buying a property requires several inquiries.
The typical American has $4500 saved up. When something goes wrong with the house (not if, it’s never if), can you actually afford the repairs?
Are you certain that you can examine a home in less than 15 minutes before committing to buying it outright and promising to pay more than twice the asking price on a 30-year 7% mortgage?
Are you certain you're ready to leave behind friends, family, and the services you depend on in order to acquire something?
Have you thought about the connotation that moving to a suburb, which more than half of Americans do, means you will be dependent on a car for the rest of your life?
Plus:
Are you sure you want to prioritize home ownership over debt, employment, travel, raising kids, and daily routines?
Homeownership entails that. This ex-homeowner says it will rule your life from the time you put the key in the door.
This isn't questioned. We don't question enough. The holy home-ownership grail was set long ago, and we don't challenge it.
Many people question after signing the deeds. 70% of homeowners had at least one regret about buying a property, including the expense.
Exactly. Tragic.
Homes are different from houses
We've been fooled into thinking home ownership will make us happy.
Some may agree. No one.
Bricks and brick hindered me from living the version of my life that made me most comfortable, happy, and steady.
I'm spending the next month in a modest apartment in southern Spain. Even though it's late November, today will be 68 degrees. My spouse and I will soon meet his visiting parents. We'll visit a Sherry store. We'll eat, nap, walk, and drink Sherry. Writing. Jerez means flamenco.
That's my home. This is such a privilege. Living a fulfilling life brings me the contentment that buying a home never did.
I'm happy and comfortable knowing I can make almost all of my days good. Rejecting home ownership is partly to blame.
I'm broke like most folks. I had to choose between home ownership and comfort. I said, I didn't find them together.
Feeling at home trumps owning brick-and-mortar every day.
The following is the reality of what it's like to turn the American Dream around.
Leaving the housing market.
Sometimes I wish I owned a home.
I miss having my own yard and bed. My kitchen, cookbooks, and pizza oven are missed.
But I rarely do.
Someone else's life plan pushed home ownership on me. I'm grateful I figured it out at 35. Many take much longer, and some never understand homeownership stinks (for them).
It's confusing. People will think you're dumb or suicidal.
If you read what I write, you'll know. You'll realize that all you've done is choose to live intentionally. Find a home beyond four walls and a picket fence.
Miss? As I said, they're not home. If it were, a pizza oven, a good mattress, and a well-stocked kitchen would bring happiness.
No.
If you can afford a house and desire one, more power to you.
There are other ways to discover home. Find calm and happiness. For fun.
For it, look deeper than your home's foundation.
Farhan Ali Khan
2 years ago
Introduction to Zero-Knowledge Proofs: The Art of Proving Without Revealing
Zero-Knowledge Proofs for Beginners
Published here originally.
Introduction
I Spy—did you play as a kid? One person chose a room object, and the other had to guess it by answering yes or no questions. I Spy was entertaining, but did you know it could teach you cryptography?
Zero Knowledge Proofs let you show your pal you know what they picked without exposing how. Math replaces electronics in this secret spy mission. Zero-knowledge proofs (ZKPs) are sophisticated cryptographic tools that allow one party to prove they have particular knowledge without revealing it. This proves identification and ownership, secures financial transactions, and more. This article explains zero-knowledge proofs and provides examples to help you comprehend this powerful technology.
What is a Proof of Zero Knowledge?
Zero-knowledge proofs prove a proposition is true without revealing any other information. This lets the prover show the verifier that they know a fact without revealing it. So, a zero-knowledge proof is like a magician's trick: the prover proves they know something without revealing how or what. Complex mathematical procedures create a proof the verifier can verify.
Want to find an easy way to test it out? Try out with tis awesome example! ZK Crush
Describe it as if I'm 5
Alex and Jack found a cave with a center entrance that only opens when someone knows the secret. Alex knows how to open the cave door and wants to show Jack without telling him.
Alex and Jack name both pathways (let’s call them paths A and B).
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.