This Month Will See The Release Of Travis Scott x Nike Footwear
Following the catastrophes at Astroworld, Travis Scott was swiftly vilified by both media outlets and fans alike, and the names who had previously supported him were quickly abandoned. Nike, on the other hand, remained silent, only delaying the release of La Flame's planned collaborations, such as the Air Max 1 and Air Trainer 1, indefinitely. While some may believe it is too soon for the artist to return to the spotlight, the Swoosh has other ideas, as Nice Kicks reveals that these exact sneakers will be released in May.
Both the Travis Scott x Nike Air Max 1 and the Travis Scott x Nike Air Trainer 1 are set to come in two colorways this month. Tinker Hatfield's renowned runner will meet La Flame's "Baroque Brown" and "Saturn Gold" make-ups, which have been altered with backwards Swooshes and outdoors-themed webbing. The high-top trainer is being customized with Hatfield's "Wheat" and "Grey Haze" palettes, both of which include zippers across the heel, co-branded patches, and other details.
See below for a closer look at the four footwear. TravisScott.com is expected to release the shoes on May 20th, according to Nice Kicks. Following that, on May 27th, Nike SNKRS will release the shoe.
Travis Scott x Nike Air Max 1 "Baroque Brown"
Release Date: 2022
Color: Baroque Brown/Lemon Drop/Wheat/Chile Red
Mens: $160
Style Code: DO9392-200
Pre-School: $85
Style Code: DN4169-200
Infant & Toddler: $70
Style Code: DN4170-200
Travis Scott x Nike Air Max 1 "Saturn Gold"
Release Date: 2022
Color: N/A
Mens: $160
Style Code: DO9392-700
Travis Scott x Nike Air Trainer 1 "Wheat"
Restock Date: May 27th, 2022 (Friday)
Original Release Date: May 20th, 2022 (Friday)
Color: N/A
Mens: $140
Style Code: DR7515-200
Travis Scott x Nike Air Trainer 1 "Grey Haze"
Restock Date: May 27th, 2022 (Friday)
Original Release Date: May 20th, 2022 (Friday)
Color: N/A
Mens: $140
Style Code: DR7515-001
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Peter Steven Ho
3 years ago
Thank You for 21 Fantastic Years, iPod
Apple's latest revelation may shock iPod fans and former owners.
Apple discontinued the iPod touch on May 11, 2022. After 21 years, Apple killed the last surviving iPod, a device Steve Jobs believed would revolutionize the music industry.
Jobs was used to making bold predictions, but few expected Apple's digital music player to change the music industry. It did.
This chaos created new business opportunities. Spotify, YouTube, and Amazon are products of that chaotic era.
As the digital landscape changes, so do consumers, and the iPod has lost favor. I'm sure Apple realizes the importance of removing an icon. The iPod was Apple like the Mac and iPhone. I think it's bold to retire such a key Apple cornerstone. What would Jobs do?
iPod evolution across the ages
Here's an iPod family tree for all you enthusiasts.
iPod vintage (Oct 2001 to Sep 2014, 6 generations)
The original iPod had six significant upgrades since 2001. Apple announced an 80 GB ($249) and 160 GB ($349) iPod classic in 2007.
Apple updated the 80 GB model with a 120 GB device in September 2008. Apple upgraded the 120 GB model with a 160 GB variant a year later (2009). This was the last iteration, and Apple discontinued the classic in September 2014.
iPod nano (Jan 2004 to Sep 2005, 2 generations)
Apple debuted a smaller, brightly-colored iPod in 2004. The first model featured 4 GB, enough for 1,000 songs.
Apple produced a new 4 GB or 6 GB iPod mini in February 2005 and discontinued it in September when they released a better-looking iPod nano.
iTouch nano (Sep 2005 to July 2017, 7 generations)
I loved the iPod nano. It was tiny and elegant with enough tech to please most music aficionados, unless you carry around your complete music collection.
Apple owed much of the iPod nano's small form and success to solid-state flash memory. Flash memory doesn't need power because it has no moving parts. This makes the iPod nano more durable than the iPod classic and mini, which employ hard drives.
Apple manufactured seven generations of the iPod nano, improving its design, display screen, memory, battery, and software, but abandoned it in July 2017 due to dwindling demand.
Shuffle iPod (Jan 2005 to Jul 2017, 4 generations)
The iPod shuffle was entry-level. It was a simple, lightweight, tiny music player. The iPod shuffle was perfect for lengthy bike trips, runs, and hikes.
Apple sold 10 million iPod shuffles in the first year and kept making them for 12 years, through four significant modifications.
iOS device (Sep 2007 to May 2022, 7 generations)
The iPod touch's bigger touchscreen interface made it a curious addition to the iPod family. The iPod touch resembled an iPhone more than the other iPods, making them hard to tell apart.
Many were dissatisfied that Apple removed functionality from the iPod touch to avoid making it too similar to the iPhone. Seven design improvements over 15 years brought the iPod touch closer to the iPhone, but not completely.
The iPod touch uses the same iOS operating system as the iPhone, giving it access to many apps, including handheld games.
The iPod touch's long production run is due to the next generation of music-loving gamers.
What made the iPod cool
iPod revolutionized music listening. It was the first device to store and play MP3 music, allowing you to carry over 1,000 songs anywhere.
The iPod changed consumer electronics with its scroll wheel and touchscreen. Jobs valued form and function equally. He showed people that a product must look good to inspire an emotional response and ignite passion.
The elegant, tiny iPod was a tremendous sensation when it arrived for $399 in October 2001. Even at this price, it became a must-have for teens to CEOs.
It's hard to identify any technology that changed how music was downloaded and played like the iPod. Apple iPod and iTunes had 63% of the paid music download market in the fourth quarter of 2012.
The demise of the iPod was inevitable
Apple discontinuing the iPod touch after 21 years is sad. This ends a 00s music icon.
Jobs was a genius at anticipating market needs and opportunities, and Apple launched the iPod at the correct time.
Few consumer electronics items have had such a lasting impact on music lovers and the music industry as the iPod.
Smartphones and social media have contributed to the iPod's decline. Instead of moving to the music, the new generation of consumers is focused on social media. They're no longer passive content consumers; they're active content creators seeking likes and followers. Here, the smartphone has replaced the iPod.
It's hard not to feel a feeling of loss, another part of my adolescence now forgotten by the following generation.
So, if you’re lucky enough to have a working iPod, hang on to that relic and enjoy the music and the nostalgia.

Tech With Dom
3 years ago
6 Awesome Desk Accessories You Must Have!
I'm gadget-obsessed. So I shared my top 6 desk gadgets.
These gadgets improve my workflow and are handy for working from home.
Without further ado...
Computer light bar Xiaomi Mi
I've previously recommended the Xiaomi Mi Light Bar, and I still do. It's stylish and convenient.
The Mi bar is a monitor-mounted desk lamp. The lamp's hue and brightness can be changed with a stylish wireless remote.
Changeable hue and brightness make it ideal for late-night work.
Desk Mat 2.
I wasn't planning to include a desk surface in this article, but I find it improves computer use.
The mouse feels smoother and is a better palm rest than wood or glass.
I'm currently using the overkill Razer Goliathus Extended Chroma RGB Gaming Surface, but I like RGB.
Using a desk surface or mat makes computer use more comfortable, and it's not expensive.
Third, the Logitech MX Master 3 Mouse
The Logitech MX Master 3 or any from the MX Master series is my favorite mouse.
The side scroll wheel on these mice is a feature I've never seen on another mouse.
Side scroll wheels are great for spreadsheets and video editing. It would be hard for me to switch from my Logitech MX Master 3 to another mouse. Only gaming is off-limits.
Google Nest 4.
Without a smart assistant, my desk is useless. I'm currently using the second-generation Google Nest Hub, but I've also used the Amazon Echo Dot, Echo Spot, and Apple HomePod Mini.
As a Pixel 6 Pro user, the Nest Hub works best with my phone.
My Nest Hub plays news, music, and calendar events. It also lets me control lights and switches with my smartphone. It plays YouTube videos.
Google Pixel Stand, No. 5
A wireless charger on my desk is convenient for charging my phone and other devices while I work. My desk has two wireless chargers. I have a Satechi aluminum fast charger and a second-generation Google Pixel Stand.
If I need to charge my phone and earbuds simultaneously, I use two wireless chargers. Satechi chargers are well-made and fast. Micro-USB is my only complaint.
The Pixel Stand converts compatible devices into a smart display for adjusting charging speeds and controlling other smart devices. My Pixel 6 Pro charges quickly. Here's my video review.
6. Anker Power Bank
Anker's 65W charger is my final recommendation. This online find was a must-have. This can charge my laptop and several non-wireless devices, perfect for any techie!
The charger has two USB-A ports and two USB-C ports, one with 45W and the other with 20W, so it can charge my iPad Pro and Pixel 6 Pro simultaneously.
Summary
These are some of my favorite office gadgets. My kit page has an updated list.
Links to the products mentioned in this article are in the appropriate sections. These are affiliate links.
You're up! Share the one desk gadget you can't live without and why.

Michael Le
3 years ago
Union LA x Air Jordan 2 “Future Is Now” PREVIEW
With the help of Virgil Abloh and Union LA‘s Chris Gibbs, it's now clear that Jordan Brand intended to bring the Air Jordan 2 back in 2022.
The “Future Is Now” collection includes two colorways of MJ's second signature as well as an extensive range of apparel and accessories.
“We wanted to juxtapose what some futuristic gear might look like after being worn and patina'd,”
Union stated on the collaboration's landing page.
“You often see people's future visions that are crisp and sterile. We thought it would be cool to wear it in and make it organic...”
The classic co-branding appears on short-sleeve tees, hoodies, and sweat shorts/sweat pants, all lightly distressed at the hems and seams.
Also, a filtered black-and-white photo of MJ graces the adjacent long sleeves, labels stitch into the socks, and the Jumpman logo adorns the four caps.
Liner jackets and flight pants will also be available, adding reimagined militaria to a civilian ensemble.
The Union LA x Air Jordan 2 (Grey Fog and Rattan) shares many of the same beats. Vintage suedes show age, while perforations and detailing reimagine Bruce Kilgore's design for the future.
The “UN/LA” tag across the modified eye stays, the leather patch across the tongue, and the label that wraps over the lateral side of the collar complete the look.
The footwear will also include a Crater Slide in the “Grey Fog” color scheme.
BUYING
On 4/9 and 4/10 from 9am-3pm, Union LA will be giving away a pair of Air Jordan 2s at their La Brea storefront (110 S. LA BREA AVE. LA, CA 90036). The raffle is only open to LA County residents with a valid CA ID. You must enter by 11:59pm on 4/10 to win. Winners will be notified via email.
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Tim Soulo
3 years ago
Here is why 90.63% of Pages Get No Traffic From Google.
The web adds millions or billions of pages per day.
How much Google traffic does this content get?
In 2017, we studied 2 million randomly-published pages to answer this question. Only 5.7% of them ranked in Google's top 10 search results within a year of being published.
94.3 percent of roughly two million pages got no Google traffic.
Two million pages is a small sample compared to the entire web. We did another study.
We analyzed over a billion pages to see how many get organic search traffic and why.
How many pages get search traffic?
90% of pages in our index get no Google traffic, and 5.2% get ten visits or less.
90% of google pages get no organic traffic
How can you join the minority that gets Google organic search traffic?
There are hundreds of SEO problems that can hurt your Google rankings. If we only consider common scenarios, there are only four.
Reason #1: No backlinks
I hate to repeat what most SEO articles say, but it's true:
Backlinks boost Google rankings.
Google's "top 3 ranking factors" include them.
Why don't we divide our studied pages by the number of referring domains?
66.31 percent of pages have no backlinks, and 26.29 percent have three or fewer.
Did you notice the trend already?
Most pages lack search traffic and backlinks.
But are these the same pages?
Let's compare monthly organic search traffic to backlinks from unique websites (referring domains):
More backlinks equals more Google organic traffic.
Referring domains and keyword rankings are correlated.
It's important to note that correlation does not imply causation, and none of these graphs prove backlinks boost Google rankings. Most SEO professionals agree that it's nearly impossible to rank on the first page without backlinks.
You'll need high-quality backlinks to rank in Google and get search traffic.
Is organic traffic possible without links?
Here are the numbers:
Four million pages get organic search traffic without backlinks. Only one in 20 pages without backlinks has traffic, which is 5% of our sample.
Most get 300 or fewer organic visits per month.
What happens if we exclude high-Domain-Rating pages?
The numbers worsen. Less than 4% of our sample (1.4 million pages) receive organic traffic. Only 320,000 get over 300 monthly organic visits, or 0.1% of our sample.
This suggests high-authority pages without backlinks are more likely to get organic traffic than low-authority pages.
Internal links likely pass PageRank to new pages.
Two other reasons:
Our crawler's blocked. Most shady SEOs block backlinks from us. This prevents competitors from seeing (and reporting) PBNs.
They choose low-competition subjects. Low-volume queries are less competitive, requiring fewer backlinks to rank.
If the idea of getting search traffic without building backlinks excites you, learn about Keyword Difficulty and how to find keywords/topics with decent traffic potential and low competition.
Reason #2: The page has no long-term traffic potential.
Some pages with many backlinks get no Google traffic.
Why? I filtered Content Explorer for pages with no organic search traffic and divided them into four buckets by linking domains.
Almost 70k pages have backlinks from over 200 domains, but no search traffic.
By manually reviewing these (and other) pages, I noticed two general trends that explain why they get no traffic:
They overdid "shady link building" and got penalized by Google;
They're not targeting a Google-searched topic.
I won't elaborate on point one because I hope you don't engage in "shady link building"
#2 is self-explanatory:
If nobody searches for what you write, you won't get search traffic.
Consider one of our blog posts' metrics:
No organic traffic despite 337 backlinks from 132 sites.
The page is about "organic traffic research," which nobody searches for.
News articles often have this. They get many links from around the web but little Google traffic.
People can't search for things they don't know about, and most don't care about old events and don't search for them.
Note:
Some news articles rank in the "Top stories" block for relevant, high-volume search queries, generating short-term organic search traffic.
The Guardian's top "Donald Trump" story:
Ahrefs caught on quickly:
"Donald Trump" gets 5.6M monthly searches, so this page got a lot of "Top stories" traffic.
I bet traffic has dropped if you check now.
One of the quickest and most effective SEO wins is:
Find your website's pages with the most referring domains;
Do keyword research to re-optimize them for relevant topics with good search traffic potential.
Bryan Harris shared this "quick SEO win" during a course interview:
He suggested using Ahrefs' Site Explorer's "Best by links" report to find your site's most-linked pages and analyzing their search traffic. This finds pages with lots of links but little organic search traffic.
We see:
The guide has 67 backlinks but no organic traffic.
We could fix this by re-optimizing the page for "SERP"
A similar guide with 26 backlinks gets 3,400 monthly organic visits, so we should easily increase our traffic.
Don't do this with all low-traffic pages with backlinks. Choose your battles wisely; some pages shouldn't be ranked.
Reason #3: Search intent isn't met
Google returns the most relevant search results.
That's why blog posts with recommendations rank highest for "best yoga mat."
Google knows that most searchers aren't buying.
It's also why this yoga mats page doesn't rank, despite having seven times more backlinks than the top 10 pages:
The page ranks for thousands of other keywords and gets tens of thousands of monthly organic visits. Not being the "best yoga mat" isn't a big deal.
If you have pages with lots of backlinks but no organic traffic, re-optimizing them for search intent can be a quick SEO win.
It was originally a boring landing page describing our product's benefits and offering a 7-day trial.
We realized the problem after analyzing search intent.
People wanted a free tool, not a landing page.
In September 2018, we published a free tool at the same URL. Organic traffic and rankings skyrocketed.
Reason #4: Unindexed page
Google can’t rank pages that aren’t indexed.
If you think this is the case, search Google for site:[url]. You should see at least one result; otherwise, it’s not indexed.
A rogue noindex meta tag is usually to blame. This tells search engines not to index a URL.
Rogue canonicals, redirects, and robots.txt blocks prevent indexing.
Check the "Excluded" tab in Google Search Console's "Coverage" report to see excluded pages.
Google doesn't index broken pages, even with backlinks.
Surprisingly common.
In Ahrefs' Site Explorer, the Best by Links report for a popular content marketing blog shows many broken pages.
One dead page has 131 backlinks:
According to the URL, the page defined content marketing. —a keyword with a monthly search volume of 5,900 in the US.
Luckily, another page ranks for this keyword. Not a huge loss.
At least redirect the dead page's backlinks to a working page on the same topic. This may increase long-tail keyword traffic.
This post is a summary. See the original post here
Ash Parrish
3 years ago
Sonic Prime and indie games on Netflix
Netflix will stream Spiritfarer, Raji: An Ancient Epic, and Lucky Luna.
Netflix's Geeked Week brought a slew of announcements. The flurry of reveals for The Sandman, The Umbrella Academy season 3, One Piece, and more also included game and game-adjacent announcements.
Netflix released a teaser for Cuphead season 2 ahead of its August premiere, featuring more of Grey DeLisle's Ms. Chalice. DOTA: Dragon's Blood season 3 hits Netflix in August. Tekken, the fighting game that throws kids off cliffs, gets an anime, Tekken: Bloodline.
Netflix debuted a clip of Sonic Prime before Sonic Origins in June and Sonic Frontiers in 2022.
Castlevania: Nocturne will follow Richter Belmont.
Netflix is reviving licensed games with titles based on its shows. There's a Queen's Gambit chess game, a Shadow and Bone RPG, a La Casa de Papel heist adventure, and a Too Hot to Handle game where a pregnant woman must choose between stabbing her cheating ex or forgiving him.
Riot's rhythm platformer Hextech Mayhem debuted on Netflix last year, and now Netflix is adding games from Devolver Digital. Reigns: Three Kingdoms is a card game that lets players choose the fate of Three Kingdoms-era China by swiping left or right on cards. Spiritfarer, the "cozy game about death" from 2020, and Raji: An Ancient Epic are coming to Netflix. Poinpy, a vertical climber from the creator of Downwell, is now on Netflix.
Desta: The Memories Between is a turn-based strategy game set in dreams and memories.
Snowman's Lucky Luna will also be added soon.
With these games, Netflix is expanding beyond dinky mobile games — it plans to have 50 by the end of the year — and could be a serious platform for indies that want to expand into mobile. It takes gaming seriously.

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.