Most online activity is now public. Businesses collect, store, and use our personal data to improve sales and services.

In 2014, Uber executives and employees were accused of spying on customers using tools like maps. Another incident raised concerns about the use of ‘FaceApp'. The app was created by a small Russian company, and the photos can be used in unexpected ways. The Cambridge Analytica scandal exposed serious privacy issues. The whole incident raised questions about how governments and businesses should handle data. Modern technologies and practices also make it easier to link data to people.

As a result, governments and regulators have taken steps to protect user data. The General Data Protection Regulation (GDPR) was introduced by the EU to address data privacy issues. The law governs how businesses collect and process user data. The Data Protection Bill in India and the General Data Protection Law in Brazil are similar.
Despite the impact these regulations have made on data practices, a lot of distance is yet to cover.

Blockchain's solution

Blockchain may be able to address growing data privacy concerns. The technology protects our personal data by providing security and anonymity. The blockchain uses random strings of numbers called public and private keys to maintain privacy. These keys allow a person to be identified without revealing their identity. Blockchain may be able to ensure data privacy and security in this way. Let's dig deeper.

Financial transactions

Online payments require third-party services like PayPal or Google Pay. Using blockchain can eliminate the need to trust third parties. Users can send payments between peers using their public and private keys without providing personal information to a third-party application. Blockchain will also secure financial data.

Healthcare data

Blockchain technology can give patients more control over their data. There are benefits to doing so. Once the data is recorded on the ledger, patients can keep it secure and only allow authorized access. They can also only give the healthcare provider part of the information needed.

The major challenge

We tried to figure out how blockchain could help solve the growing data privacy issues. However, using blockchain to address privacy concerns has significant drawbacks. Blockchain is not designed for data privacy. A ‘distributed' ledger will be used to store the data. Another issue is the immutability of blockchain. Data entered into the ledger cannot be changed or deleted. It will be impossible to remove personal data from the ledger even if desired.

MIT's Enigma Project aims to solve this. Enigma's ‘Secret Network' allows nodes to process data without seeing it. Decentralized applications can use Secret Network to use encrypted data without revealing it.

Another startup, Oasis Labs, uses blockchain to address data privacy issues. They are working on a system that will allow businesses to protect their customers' data. 

Conclusion

Blockchain technology is already being used. Several governments use blockchain to eliminate centralized servers and improve data security. In this information age, it is vital to safeguard our data. How blockchain can help us in this matter is still unknown as the world explores the technology.

If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.

Polynomials

Polynomials are a special class of algebraic expressions of the form:

• x+5
• x^4
• x^3+3x^2+3x+1
• 628x^{271}+318x^{270}+530x^{269}+…+69x+381

i.e. they are a sum of any (finite!) number of terms of the form cx^k

There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.

Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:

• A(0)+B(0)=C(0)
• A(1)+B(1)=C(1)
• A(2)+B(2)=C(2)
• A(3)+B(3)=C(3)

And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:

• 12+1=13
• 10+8=18
• 15+8=23
• 15+13=28

You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:

• A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
• B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
• C(x)=5x+13

Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.

Comparing a polynomial to itself

You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)

As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.

Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).

Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!

Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.

What can't Google do?
Seriously, nothing! Google rocks.
Google is a major player in online tools and services. We use it for everything, from research to entertainment.
Did I say entertain yourself?
Yes, with so many features and options, it can be difficult to fully utilize Google.

#1. Drive Google Mad

You can make Google's homepage dance if you want to be silly.
Just type “Google Gravity” into Google.com. Then select I'm lucky.
See the page unstick before your eyes!

#2 Play With Google Image

Google isn't just for work.
Then have fun with it!
You can play games right in your search results. When you need a break, google “Solitaire” or “Tic Tac Toe”. 

#3. Do a Barrel Roll

Need a little more excitement in your life? Want to see Google dance?
Type “Do a barrel roll” into the Google search bar.
Then relax and watch your screen do a 360. 

#4  No Internet?  No issue!

This is a fun trick to use when you have no internet.
If your browser shows a “No Internet” page, simply press Space.
Boom!
We have dinosaurs! Now use arrow keys to save your pixelated T-Rex from extinction.

#5 Google Can Help

Play this Google coin flip game to see if you're lucky.
Enter “Flip a coin” into the search engine.
You'll see a coin flipping animation. If you get heads or tails, click it. 

#6. Think with Google

My favorite Google find so far is the “Think with Google” website.
Think with Google is a website that offers marketing insights, research, and case studies.
I highly recommend it to entrepreneurs, small business owners, and anyone interested in online marketing. 

#7. Google Can Read Images!

This is a cool Google trick that few know about.
You can search for images by keyword or upload your own by clicking the camera icon on Google Images.
Google will then show you all of its similar images.

#8. Modify the Google Logo!

Clicking on the “I'm Feeling Lucky” button on Google.com takes you to a random Google Doodle.
Each year, Google creates a Doodle to commemorate holidays, anniversaries, and other occasions.

#9. What is my IP?

Simply type “What is my IP” into Google to find out.
Your IP address will appear on the results page.

#10. Send a Self-Destructing Email With Gmail, 

Create a new message in Gmail. Find an icon that resembles a lock and a clock near the SEND button. That's where the Confidential Mode is.
By clicking it, you can set an expiration date for your email. Expiring emails are automatically deleted from both your and the recipient's inbox.

#11. Blink, Google Blink!

This is a unique Google trick.
Type “blink HTML” into Google. The words “blink HTML” will appear and then disappear.
The text is displayed for a split second before being deleted.
To make this work, Google reads the HTML code and executes the “blink” command. 

#12. The Answer To Everything

This is for all Douglas Adams fans.
The answer to life, the universe, and everything is 42, according to Google.
An allusion to Douglas Adams' Hitchhiker's Guide to the Galaxy, in which Ford Prefect seeks to understand life, the universe, and everything.

#13. Google in 1998

It's a blast!
Type “Google in 1998” into Google. "I'm feeling lucky"
You'll be taken to an old-school Google homepage.
It's a nostalgic trip for long-time Google users. 

#14. Scholarships and Internships

Google can help you find college funding!
Type “scholarships” or “internships” into Google.
The number of results will surprise you. 

#15. OK, Google. Dice!

To roll a die, simply type “Roll a die” into Google.
On the results page is a virtual dice that you can click to roll. 

#16. Google has secret codes!

Hit the nine squares on the right side of your Google homepage to go to My Account. Then Personal Info.
You can add your favorite language to the “General preferences for the web” tab. 

#17. Google Terminal 

You can feel like a true hacker.
Just type “Google Terminal” into Google.com. "I'm feeling lucky"
Voila~!
You'll be taken to an old-school computer terminal-style page.
You can then type commands to see what happens.

Have you tried any of these activities? Tell me in the comments.

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