The Zero-knowledge Proof: A glimpse on why crypto is a 'crypto'

By Sorenized | Touch of Crypto | 26 Mar 2021

As a young student before in Mathematics, I studied for the sake of getting by and to be able to secure a job later on and have a living, period. It was so simple. I went on learning tricks which I would be able to use in the future. I remember that we had a subject which touched on cryptography and back then my mind was in a daze. I underappreciated its probable applications. I didn't really have a creative purpose studying during those times and so just like that I graduated with a degree in Mathematics.

We had a t-shirt before, printed in codes where if you decode will reveal the phrase, 'Numbers can kill.' A silly phrase that I shrug my shoulders every time I thought about it. But eventually I come to appreciate that memory as it finally gave some color into my life right now!

I immediately got employed as a Mathematics instructor at a university over a decade ago but I admit I still was very lacking in purpose back then. I simply taught what needed to be taught with respect to skills needed when attacking calculus problems. I leaned on books the traditional way. Years passed and I have forgotten about everything else except those that I actively teach to my students. And from being an instructor, I became a high school teacher which greatly diminished the chance that I would be leveling up my studies in Mathematics. Though of course I'm just thankful I'm employed even if it's not really my ultimate dream before.

But one morning, I opened my mobile chrome browser to read the article titled, "Can you solve it? The crazy maths of crypto." At first I felt I no longer was attracted to such topics but I still browsed thru the article. Then I went on till I encountered the zero-knowledge proof, which I will be discussing on the next part of this venture. Still not very interested until I finally arrived at a concrete problem which got me up and typing. I actually planned to sleep tonight because I felt very tired and mentally exhausted by the seemingly impossible writing career but this has fueled me. Let me now show you the problem.

The Stolen Paper Clip

The following is the exact problem in the article:

You work in an office of 100 people. One day your favourite paper clip is stolen. You have a pretty good idea of who did it. Your colleague Annabel tells you that she also has a pretty good idea.

You want to check with Annabel that you both suspect the same person, but neither of you are willing to identify your suspect just in case you are thinking of different people. (Because of office politics, no one wants to point fingers.)

Think of a method that allows you and Annabel to check whether your suspect and her suspect are the same person, without either of you revealing any information about your suspects.

Although I was already pumped I still was a little annoyed. How would I be able to solve without divulging anything? 'Crazy,' I thought. Upon reading on I found out that a possible solution is the following:

You and Annabel will assign numbers to everyone from 1 to 100. Then you will each pick a number which represents your suspect. Now, you shouldn't be showing each other the number that you have chosen. Let us say that you have a friend who we will just name as Dan (same name used in the article). What you will do is hand Dan the pieces of paper where you have written the number of suspect and ask him to tell the two of you if you two wrote the same number without divulging what the number really is. Dan is only allowed to tell whether you two have written the same number or not.

So there, you have at least solved the problem without actually divulging specific details. However, the solution is not perfect. Why? Because you both told Dan some information. It should be that you will not reveal anything to anyone. It means that you will not involve any other person.

My Solution to the Stolen Paper Clip

You will change the password of your laptop into the name of your suspect. Ask Annabel to log in into your laptop. If it's error, then you have a different suspect than hers. Job done. Teehee.

So how does this relate to my ongoing research on crypto?

I wanted to learn all that I can about crypto. Just because I feel the need to. I believe now that it is my desire and not because of any other reason. I try to be not in denial sometimes haha.

Anyway, it does relate to my ongoing research on crypto because of this: I often see the word 'confirmations' when I try to go to the block explorer. It was really an alien term to me with respect to the cryptosphere and it is only now that I was able to at least have a glimpse on why terms like this and that are being used here. And yes, on why crypto is 'crypto' after all! Just because you have to confirm while protecting the privacy of information. But I have to have a disclaimer on this, I am still very new hear and I have the tendency to commit error but I am still writing this in the hope of reflecting other peoples struggles in understanding cryptocurrencies.

So that's about it for this part. I wish to dive deeper into the zero-knowledge proof and I plan to give my personal touch on solving problems.