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Hello, welcome, my dear student friend, my dear internet friend, and you too, my dear female student and internet user. You who are enthusiasts, you who are curious, who are trying to learn more about Bitcoin and other cryptocurrencies, welcome to the Bitcoin course: Understanding to Trust. In this series of videos that I will record, I intend to explain to you from scratch, from the most basic possible knowledge, how Bitcoin works, how cryptocurrencies work.
You must have heard in the media, read on the internet, or seen on some news program: Bitcoin is a digital currency, it's internet money. We will try to demonstrate here how Bitcoin works. No prior knowledge is necessary beyond the knowledge of using a computer itself because we will really present all the concepts from the most basic possible to the most profound possible, so that you understand the workings of this digital revolution, this financial revolution called Bitcoin, called cryptocurrencies in general.
I want you to understand so you can trust because Bitcoin today belongs to a kind of ghetto. Those who use Bitcoin are mainly computer enthusiasts, especially in Brazil. And not all of them are people with a libertarian political bias. A political, anti-state, anti-government bias, since Bitcoin is an example of a decentralized currency without the intervention of any government or country.
We're going to understand Bitcoin from scratch. We're going to start now. You might understand what's happening here, what will happen here, in a repetitive way. I've already seen these concepts; just wait for the next videos, but I'm going to start here completely from scratch. Okay, so follow me here regarding how we're going to work with Bitcoin.
Okay, so first of all, what is Bitcoin? Bitcoin is a digital currency, a currency made to function within the cyber world, within the digital world. It's even possible to make it function outside the digital world; we'll see that in the future. But it was created, Bitcoin was created to function on its own network around the entire internet, spread across the entire internet.
Bitcoin is classified as a cryptocurrency; it's not the only cryptocurrency. There are several types, several models manufactured by other entities, by various different entities, and most of them were born as improvements or enhancements of Bitcoin. Each with its own characteristics, but Bitcoin is the most famous and is the one we're going to analyze, broadly speaking, in this video.
This course, this specific cryptocurrency... What is a cryptocurrency? Well, a currency is an entity that serves as a medium of exchange, a means to make exchanges. I want to exchange my mouse for your keyboard. If you want my mouse and I want your keyboard, the exchange is done. I exchanged one product for another, one good for another.
When this combination doesn't exist, I want to exchange my mouse for a keyboard, you want to exchange your keyboard but not for a mouse. So when this happens, what do we need to do? We need an intermediary, and that's what money does. So I sell my mouse. Actually, I exchange my mouse for a sum of money, and then I take that sum of money and exchange it for your keyboard.
So you sold the keyboard to me, actually you made the exchange for a sum of money. Bitcoin is a cryptocurrency, it's a currency because it serves as a medium of exchange. One of the strong characteristics of Bitcoin, which our government currencies don't have today, is a basic principle of economics, which is scarcity.
We're going to talk about this: programmed scarcity, a scarcity that gives value to the good, value to the currency. The crypto part of the word comes from cryptography. Cryptography means mathematical guarantees. Guarantees made or offered by very powerful mathematical processes, right? Cryptography.
So let's go up to continue on this point. Cryptography, in a few words, is mathematics for information, mathematics being used to protect information. Cryptography, writing in riddles, writing hidden, that's what this word means. Two basic cryptographic resources are used in Bitcoin and other cryptocurrencies.
These two resources are the hash, which is the summary of messages. We're going to see the numerical summary of messages, and the digital signature. The digital signature serves to authenticate messages, to give authenticity to transactions made in cryptocurrencies. Two procedures, two resources that are based on cryptography, that are based on mathematics, and that are widely used within Bitcoin and other cryptocurrencies.
Let's start by understanding the hash. What is a hash? Let's do a practical test. Let's imagine a CPF (Brazilian taxpayer identification number). A CPF is the number you have with the Federal Revenue Service as a taxpayer. You make contributions to the Federal Revenue Service of the country, and you have a number.
This number is formed by nine digits. You might criticize, saying there aren't 11, but there are nine. The Federal Revenue Service generates a new CPF on its computer for a new citizen, a new taxpayer. And so, nine numbers are generated. The computer generated these nine numbers. It performs a mathematical calculation with these nine numbers, and from this mathematical calculation, the last two numbers result, which we call the check digits (R).
This is the hash. The hash is a mathematical summary of an original message. An original numerical message results in a hash if the correct mathematical calculation is done. What is it for? Let's imagine our real CPF (Brazilian tax identification number) that we just created and a forged CPF. A certain internet user decided to enter a website.
And upon entering the website, he typed in a random CPF that wasn't his; he guessed the numbers and wrote this. Now, when he clicks OK to enter his information on the website, the website will take those nine numbers, perform the same mathematical calculation that the Federal Revenue Service did when it generated the CPF, and realize that the result should be 43 and not 30.
Automatically, what does the website do? Invalid CPF. It warns you that you cannot use this CPF because it is wrong. The hash serves this purpose. The 'r' serves to guarantee the integrity of the message content. If the 'r' is wrong, the message cannot be validated. Let's see... Where does this lead us?
If we have an original message, performing the calculation that results in the hash is a very easy and straightforward procedure; it's just a matter of repeating the same mathematical and arithmetic operations on the original message, and I will have the same hash in the end. Starting from the hash, we cannot find the original message.
The original message cannot be obtained from R; it's a calculation that is, strictly speaking, impossible to perform. The word "impossible" is a bit strong. Many people don't trust the degree of impossibility of something, so let's use the more appropriate word: it's improbable to find the original message starting from the hash.
The hash is a unidirectional mathematical function; it can only be performed in one direction. You might question this, saying, "But wait, if I have a number that was multiplied by 2 and resulted in 10, I just take the answer number and reverse the mathematical procedure, divide by two, and find the original BCC.
I find it if I do the inverse arithmetic procedure. I find the original input number." No, not in all cases. Let's look at a very simple example to prove this unidirectional issue. Let's imagine that the hash of a certain number n is... The remainder of the division of n by 14, so to calculate the hash I have to divide the original number by 14 and know what the remainder is.
Therefore, let's imagine the number 298 as our number, n as our original number. Divide 298 by 14, and you have 298 x 14 = 294. 294 divided by 298 = 4. There you go, I had the original message, I found r. 298 is the original message, and then I ask the question: what is the remainder of the division of this number 298 by 14?
The remainder is 4. Well, this 4 here was easy to obtain because I had 298. Now, if I only have the number 4, the question is: What is the number that, when divided by 14, gives a remainder of four? The answer is infinitely many numbers; it's improbable to find. In this case, what was the number that gave rise to the remainder of four?
So, going from the message to the hash is easy, possible, straightforward. Going from the remainder to the original message is impossible. Continuing... Here we're going to take a large message, a very large text message, and we're going to analyze this message to determine one of the strongest characteristics it has, and one of the characteristics that makes it so brilliant, so interesting.
I have a very large message here, and I calculated its remainder, but John... This is a text message, a text message. It can't go through a mathematical process because the remainder, as seen during this video, is a mathematical process. Yes, I know it's a mathematical process. But look, everything on your computer is mathematics, everything is number, everything—this message, a photo, this video you're watching now—all of this is electrical energy, small electrical pulses that can take two forms: zero or one, and which we affectionately call bits, hence the name Bitcoin, right?
So bits are electrical pulses, zeros and ones. They are all the information that our computer knows how to manipulate. This is the format of information that our computer knows how to manipulate. When I gather 8 bits, when I gather several bits, eight to be more precise, I have what we call bytes. So when you use a computer, you're dealing with bits and bytes.
When you buy a... A 16 GB pen drive is 16 GB, that's the capacity of that pen drive. When you subscribe to a 30 MB internet service, that's 30 Mbits per second. So bits and bytes are units of measurement; each zero and each one, each electrical pulse, each little bit is information in itself, an electrical pulse.
Okay, so we treat this as numbers. All texts, all photos, all videos, all music are numbers for the computer; they can go through HR processes. Okay, so let's look at this characteristic. Now I want you to notice this characteristic. Now take a look at this word, Psalms, which is here. I'm going to remove the final 's' from it.
There was a change in the message. There was a change in the message. John, a change of one little letter. John, neither here nor there; on the contrary, this change results in a completely different hash. Any minimal change in a message, no matter its size, results in a completely different hash. So if your source hash is equal to the destination hash, it's because the message wasn't altered.
You'll see how sensitive the 'r' is. One letter, John, one letter was enough to change the rest like this, my friend. Less than one letter is needed to make a big change, less than that. Let's imagine a song. In an MP3 of Bob Marley's "Redemption Song," which is 8.3 MB, here we have the hash below. The hash of this song is 8.3 MB.
8.3 MB results in 8 * 73.18 by, which is equivalent to 6962 * 5446 bits. Out of these 69 million bits, let's choose eight. I went into those 69 million and randomly selected eight. Okay, so I'm going to make a change to one of them. I changed one bit. The result is a completely different hash. I'm talking about making a change to one individual bit within a group of 70 million bits.
One individual bit is 69 MB, 70 MB is a lot, but if I had 10 GB, 20 GB, a much larger amount of information, changing one bit, a simple bit, would result in a completely different hash. To prove to you how sensitive a hash is, what else can we remember to say about the hash? What is its function? Let's imagine that an email is being written, and the person who wrote it, the program used by the sender, calculated the rest of this message.
The message is sent by... The internet reaching the destination, which I suspect, will calculate its own version of R. If the R version calculated now is equal to the original R version brought by the internet, then it's fine; the message hasn't been altered. Two distinct messages don't give the same R.
If a small alteration happens to the point of changing the hash, if I know that the rest hasn't changed, if I know that it was calculated and that the rest is exactly the same as the original rest, I can categorically state with certainty that the message hasn't been altered in any bit, not even a tiny bit has been altered.
Okay, let's get to the conclusions regarding rest, our first topic. We are reaching the end of this first video. It's necessary that you understand this so that you can understand the entire functioning of Bitcoin that follows. R summarizes digital information with the objective of guaranteeing its content.
The function of R is to guarantee the integrity of the message's content. Rest is a unidirectional mathematical function, meaning it's not possible to reverse the hashing process. To discover the original message based on the hash is impossible, but precisely speaking, it's improbable. The hash is extremely sensitive to alterations; any minimal alteration of a bit in the message results in a complete alteration of the hash.
And finally, confirm the hash or... To validate a hash, to say that the hash is valid, is the same as confirming the message itself. If you have a message with a hash, and you say "I trust this hash, this hash is reliable," then it's the same as saying "this message is reliable." Just like when you sign at the end of a contract, you're validating all its pages.
Similarly, when you initial the bottom page of a contract to validate the entire page, all the characters written on that page, then validating the hash is validating the message itself. Okay, well, this is our first meeting, our first meeting about Bitcoin and cryptocurrencies. It's necessary that you understand the hash well.
Watch this lesson again if necessary to understand how sensitive, how secure, and how mathematically guaranteed the hash is. It's one of the fundamental principles, one of the basic resources for any cryptocurrency, especially Bitcoin. In our next video, which may happen this week or next week, we will continue and move on to understanding the digital signature process.
Okay, a hug to all of you. Our course, "From Zero: Understanding to Trusting Bitcoin," until next time.
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