How cryptography formed the basis of bitcoin

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Now only babies do not know about cryptocurrencies.  And almost everyone knows that Bitcoin is based on cryptography.  But can you te...

Now only babies do not know about cryptocurrencies. And almost everyone knows that Bitcoin is based on cryptography. But can you tell us how encryption works in cryptocurrencies and how a science that has been in linguistics for centuries led to the digital revolution?
Cryptocurrencies could not exist without public key encryption.
Public key cryptography (or asymmetric cryptography) provides privacy and proves ownership. It was born relatively recently - in the mid-1970s - and coincided with the personal computer revolution.
The advantage of this encryption method is that the message can only be read by the person to whom it was addressed. In other words, public key cryptography ensures the secrecy of communications between parties.
The key is used to encode and decode messages. In asymmetric cryptography, the key used to encrypt a message is different from the key used to decode it.
Symmetric encryption uses only one key. The result is a transport problem: the sender not only sends the message, but must find a reliable way to transmit the key. If a third party intercepts the message and key, it can decode the data.

Diffie-Hellman Key Exchange Method

For most of history, cryptography has dealt with linguistic analysis and puzzle solving, but since the second half of the 20th century, mathematical methods have come to the fore.
In the 1970s, Stanford University staff Whitfield Diffie, Martin Hellman, and Ralph Merkle found a formal mathematical solution to the key exchange problem. In it, they used modular arithmetic and one-way functions (Ralph Merkle made a huge contribution to the development of cryptocurrencies as the inventor of the trees of the same name).
Modular arithmetic compares numbers modulo and deals with periodic functions whose values ​​are repeated at intervals. For example, the remainder of dividing 7 by 3 ("modulo 3") is 1. The idea of ​​periodic functions helps to understand the 12-hour time format. For example, if it is 8:00 am now, then 6 hours later it will not be 14:00 (as in the 24-hour format), but 2:00 pm. The bottom line is that modular arithmetic behaves unintuitively and leads to unexpected results.
One-way functions have a remarkable feature: they are easy to evaluate for any argument, but it is almost impossible to find the argument itself from a given final value. Imagine a bowl of soup in a restaurant. The chef prepared it without much difficulty following the recipe. You can taste it and even reveal some of the ingredients, but without an exact recipe and a set of ingredients, you can't cook the soup yourself.
In the Diffie-Hellman algorithm, participants disclose some information about a key, but keep the data secret to reproduce the key. The scientists presented their idea in June 1976 at the National Computer Conference.

The birth of asymmetric cryptography

The Diffie-Hellman algorithm solves a key key exchange problem but still uses symmetric encryption.
After reviewing Diffie-Hellman's solution, Ron Rivest, Adi Shamir, and Leonard Adelman of MIT set out to find an asymmetric encryption solution. In April 1977 they succeeded. The algorithm they created received the abbreviation RSA after the names of the authors.
In asymmetric encryption, each party publishes a public public key. The other party uses it to encrypt messages that only the owner of the private key can decode. In simple terms, a public key is a number obtained by multiplying two numbers in a private key. If the numbers are large enough, it will be very difficult to establish them from the resulting product.

Encryption for everyone

Drawing from a patent for an electrical encryption machine, 1923
In the past, due to the high demands on computer power, RSA encryption was available only to a select few - the government, the military, large corporations. Phil Zimmerman decided to open it to everyone. He developed Pretty Good Privacy (PGP) and released it for free in June 1991.
Zimmermann bypassed the high computing power requirements of asymmetric encryption by implementing a hybrid algorithm. The message was encrypted with a symmetric key, then it was encrypted using asymmetric methods and sent with the message.

Hi Hal Finney!

The first employee to be hired by Phil Zimmerman was Hal Finney. Finney was the first to show interest in the concept of bitcoin, proposed in 2008 by a certain Satoshi Sakamoto.
In the 1990s, a number of attempts to create private digital money protected by asymmetric encryption ended in failure. David Chaum developed DigiCash, but all transactions in his project were verified centrally. The project failed, and the company filed for bankruptcy in 1998.
In 1997, British researcher Adam Beck came up with HashCash. In this project, the Proof-of-Work method was used to create new coins. HashCash failed because coins could only be used once: when a user wanted to buy something, he had to mine new coins.
Hal Finney solved the HashCash problem with the first Reusable Proof-of-Work (RPOW) system. He tried to create his own digital money called CRASH (CRypto cASH), however, the project failed.

The emergence of bitcoin

Hal Finney became the first person after Nakamoto to launch a Bitcoin network node, and the first recipient of a payment in Bitcoin. Finney strongly  supported the  creator of bitcoin:
“Imagine Bitcoin becoming the dominant means of payment in the world. Then the total cryptocurrency capitalization should equal the value of all the wealth in the world ... Even if the probability of this is small, it still exists. There is something to think about here. "
In August 2009, Finney was diagnosed with amyotrophic lateral sclerosis. On March 19, 2013, he addressed the community with a  farewell message , in which he described his early experience with Bitcoin:
“After a few days, the network was pretty stable, so I left it alone. At that time, the complexity was equal to one, and blocks could be mined using a conventional central processor. Over the next days, I created several blocks. Then I turned off the computer, because it was getting very hot and bothering me with the noise of the fans ... The next time I remembered about Bitcoin at the end of 2010, when I was surprised to find that the project is not only alive, but the cryptocurrency even has a certain price. I loaded up my old wallet and was relieved to find that my bitcoins are safe and sound. As the price went up, I transferred the coins to an offline wallet and I hope they will benefit my heirs. ”

Conclusion

The development of cryptography didn't stop at bitcoin. It is based on modern mathematics, which opens up perspectives that could not have been imagined in the middle of the last century. Research continues, and with the advent of quantum computers, new, unique opportunities arise.
Besides mathematics, an important part of modern cryptography is decentralization. Everyone has a right to confidentiality. When Rivest, Shamir, and Adelman created a public-key encryption method, only powerful and centralized organizations had access to it. Phil Zimmerman's PGP program greatly expanded the range of possible uses and allowed anyone with a personal computer to encrypt their messages. Then bitcoin appeared, of which public key cryptography became an integral part.
Many books describe in detail the history of cryptography and the specifics of its application in cryptocurrencies. The Book of Ciphers by Simon Singh tells the story of encryption that spans over 20 centuries.
You can also recommend Nathaniel Popper's book Digital Gold: The Incredible History of Bitcoin, or How Idealists and Businessmen Reinvent Money.

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