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The private key that gives a total control over bitcoins is simply a very big number generated at random.&nbsp;



Here the notion of randomness must be taken seriously: the “random” generation must be executed in the most secure way, so that no one could reproduce it. Once generated, the private key must be protected against a theft of a loss.



Insofar as the key generation method is reliable, the key security will depend on its size, generally expressed in bits: the size of 256 bits corresponding to 2256 possibilities of key creation. Bitcoin uses 256 bits private keys, the choice coming from the order of the elliptic curve used to run Bitcoin ECDSA signature&nbsp; algorithm: 2256– 4294968273. Every number between 1 and 2256 - 4294968272 (curve order -1) can become a private key, i.e. almost all numbers of 256 bits, which is an extremely big number - it can be compared to the number of atoms in an observable universe !



<h2>How to generate your private key</h2>



The first option is to create a private key yourself, by using a simple random number generator (RNG), which exists in almost all operating systems. Although being easy, this solution is not quite recommended, since all RNGs are not conceived for cryptographic use. When it comes to the method of randomness generation, it is preferable to use a CSPRNG (cryptographically secure pseudo-random number generator), a class within RNG which takes special measures in regards to the entropy. If you do not code, you can use websites that calculate private keys; some of them even interact with users in order to assure the entropy quality, for example by asking them to move the mouse while the key is being created.



Luckily for ordinary users, there is another option - to entrust private keys generation to a <a href="https://d.center/explore/bitcoin-wallets" class="ek-link">wallet</a>. They only have to make sure about the wallet’s RNG quality.

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In Bitcoin, the sender’s public key helps the network to verify a transaction they initiated, and the recipient’s public key helps identify to whom the bitcoins must be sent.&nbsp;



Public key is derived from the private key through a one-way function using an elliptic curve. This function is said to be one-way, because it is impossible to find a private key from a public one, unless by testing all the possibilities. Elliptic curve order (and thus the size of a private key) in the protocol was set in such a way to make this solution inoperable. 



<h2>Public key derivation and protection</h2>







The result of a private key derivation is a point (x,y) on an elliptic curve, every coordinate of which is stored on 32 bytes, thus making a public key’s size 64 bytes. In this form the public key is said to be “non-compressed”, however it is generally used in its “compressed” form, which is a number of 33 bytes (264 bits): 32 bytes for x and 1 byte to store the sign of y. In order to find y one only has to use the elliptic curve equation used by Bitcoin : y2 = x3 + 7. Knowing x, y2 can be found, leaving two possibilities for y positive and y negative, and the added byte allows to find the correct one.



Example of a compressed public key:



035792595892f86bbff330d9929ae31468b39cb48c4c9e1328a4f79e71c5b1540c



The sign of y is given in the beginning of the key as 02 or 03.



This public key, used together with the signature created with the private key, helps the network to validate a transaction initiated by the sender. Within the transaction propagated to the network this key is transferred as a hash, which is shorter and more secure (we do not communicate our public key to the person who will send us bitcoins). In order to create this hash two hash functions are applied one after another: SHA256, which gives a number on 32 bytes (256 bits), and then RIPEMD160, which produces a number on 20 bytes (160 bits).



The final result is the Public Key Hash (PKH). This acronym is regularly found in transaction scripts, notably in the most often used Pay-To-Public-Key-Hash (P2PKH).



Example of a PKH: 607a0e928e2bf3a96d70ea0adfb094b19f75385a 



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The PKH is used to send bitcoins while protecting the recipient’s public key, which is not communicated to the sender during transaction. However when the recipient is willing to send these bitcoins, he or she will have to disclose their public key, so that the network could verify the digital signature. That is why, while the private key is totally protected by the one-way derivation via an elliptic curve, it is recommended to use the public key only once, for safety and anonymity considerations. The wallets usually create a new pair of keys for every transaction.



PKH is a form in which the network uses the recipient's public key, however it is not PKH that a recipient communicates to other users, but the <a href="https://d.center/explore/bitcoin-address" class="ek-link">Bitcoin address</a>, a conversion of the PKH.

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Derived from the recipient’s public key, Bitcoin address is used to identify them in a transaction. 



The PKH (public key hash), which normally should identify a user in a transaction, is much shorter than a public key, however it is still a very long and hardy readable string of alphanumeric characters, which can lead to mistakes while transmitting it. If a mistake is not identified, bitcoins will be sent elsewhere and thus irrevocably lost. So in order to reduce such a risk it is not a PKH which is transmitted to a recipient, but an address Bitcoin. 



Bitcoin address is a PKH conversion to a more readable form, which also contains a typing error detecting system. Unlike one-way functions, this conversion is reversible: the network converts the address to PKH in order to execute transactions. This conversion is made using a special coding system called Base58check. 



<h2>Derivating an address from a PKH </h2>



The protocol deriving an address from a PKH follows the following stages:



PKH : 607a0e928e2bf3a96d70ea0adfb094b19f75385a&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;



<ul><li>1.       First a 00 is added before the PKH in order to signal that this address will be the mainnet address and not the testnet one</li></ul>







R1 = 00607a0e928e2bf3a96d70ea0adfb094b19f75385a 



<ul><li>2.    R1 is then double hashed with SHA256 and the first 4 bytes of the result (e4d1a1eaf6cbdf993e0afaa7960e35c12a8d87cd380625f9bb4f61e505e51260) added to the end of R1. These 4 bytes are called the Checksum and serve as a type error protection</li></ul>







R2 = 00607a0e928e2bf3a96d70ea0adfb094b19f75385ae4d1a1ea



<ul><li> 3.       Then the R2 is encoded with base58 and we get the address</li></ul>







R3 = Adresse = 19o865cJQ45wsjqUJRAJVJXNBVsKMgYKr1   



This encoding is reversible and one can easily switch from R2 to R3 and vice versa.&nbsp;&nbsp;&nbsp;&nbsp; 



<h2>Base58 coding </h2>



Private and public keys, as well as their hash, are coded in Hex (Hexadecimal), a coding system which uses 16 (24) characters (0123456789abcdef). However it is quite ineffective, since two characters are needed to code a byte (8 bits). 



A coding system with more characters would be more effective, hence the idea of employing the Base64 system, which contains 64 (26) characters (ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz 0123456789+/). In this system a character can code 6 bits. 



Base64 system would solve the addresses size problem, but not the readability. That is why the last conversion stage of Bitcoin address uses Base58 system, which contains 58 characters (123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz). It is much easier to read, because some characters that could be confused were cancelled: l and I (small L and a capital i), 0 and O (zero and the capital o), as well as the special characters + and /. 



It all would be great if 58 were a power of 2, as is 16 for Hexadecimal and 64 for Base64. However this is not the case, which means that there’s the last transformation to be done, the one that utilizes euclidien division of R2 (without 00 of the beginning and transformed into decimal base) by 58, in order to get the conversion table. The first 00 are converted into 1 and added to the end of the number obtained using the table, and this number is then written backwards in order to get to the address. That is why classic Bitcoin addresses start with 1, and with Segwit adoption this 1 can be replaced by a 3, if the address is Segwit-compatible. 



<h2>Checksum </h2>



Even though the address is now shorter and more readable than the PKH, there still exists a risk of misspelling. This is where the Checksum is used: during the inverse transformation to find the PKH from the address the Checksum is taken off the end of the R2 and R2 is double hashed with SHA256. The result must have the same first 4 bytes as the Checksum, otherwise there has been an error in writing the address and the network will not validate the transaction. The probability of getting the same Checksum after having misspelled the address is lower than 1 in 4 billions!

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What is Bitcoin and why it could be a valuable alternative to our usual currencies such as dollars and euros?



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<h2 class="wp-block-heading">Bitcoin and bitcoin</h2>



Bitcoin is both the blockchain and the cryptocurrency that exists on it. To distinguish the two, Bitcoin as the blockchain is usually written with a capital B. 



The basis of the technology were first outlined in Satoshi Nakamoto's (pseudonyme) <a href="https://d.center/en/explore/bitcoin-a-peer-to-peer-electronic-cash-system" class="ek-link">White Paper</a> published in 2008 and titled "A Peer-to-Peer Electronic Cash System". 



It was not the first try to create a digital currency, but it was the first to succeed in solving all the intricate problems that led to previous attempts’ failures. Satoshi Nakamoto exploited decades of research, in particular in the fields of cryptography and distributed systems, and brilliantly brought them together to create a fast, secure, independent, and borderless digital money.



<h3 class="wp-block-heading">Bitcoin consists of:</h3>



<ul>
<li>Bitcoin protocol - a set of rules and algorithms that enable bitcoin issuance and transactions validation via&nbsp;network consensus (a way to ensure that network participants are well-intentioned and will update transactions ledger fairly; Bitcoin consensus is called a <a href="https://d.center/explore/proof-of-work" class="ek-link">Proof-of-Work</a>)</li>



<li>decentralized <a href="https://d.center/explore/p2p-network" class="ek-link">peer-to-peer network</a><a href="https://d.center/explore/p2p-network" class="ek-link"> </a>to run the Bitcoin protocol. Without any central server, a P2P network is composed of computers with equal rights that verify transactions and, if they wish, participate in bitcoin issuance and transactions’ recording.</li>
</ul>



Running the Bitcoin protocol results in a public distributed ledger called the blockchain, where all the transactions are stored. Everyone can consult the blockchain and its transactions from the Genesis block up to now.



Bitcoins are issued according to the protocol as a reward for maintaining the network, and their transfer is carried out&nbsp; without intermediaries and centralized authorities. This means that, unlike [tooltip content=" fiduciary money with no intrinsic value backed by and dependent on the government (e.g. dollars or euros) "] fiat [/tooltip] currencies, Bitcoin does not depend on the government or banks to issue money or to settle and validate transactions. 



The only thing that gives control over bitcoins is the private key associated with every Bitcoin address and available exlusively to its owner.



<h2 class="wp-block-heading">Bitcoin alternative to fiat money</h2>



Store of value. No single entity could ever change Bitcoin code: it is stored and run on the network nodes - literally thousands of independent computers all over the world. This ensures that the code is law, and the rules embedded into code won’t change unless the majority of the network decides so. 



This stability is particularly important when it comes to the emission rules: bitcoin emission rate is predefined, with the supply divided by two every 4 years, meaning that there won’t ever be more than 21 million bitcoins. In the world where Central Banks can print as much fiat money as they wish, Bitcoin represents a remarkable store of value.



Free use. Bitcoin is also public and open source, allowing anyone to join, participate or use it. Anyone can open a Bitcoin wallet and send/receive bitcoins, without any approval from whatever organization. 



This is a significant improvement compared to the red tape of the banking system, not to mention a precious access to the world's finance for the unbanked. Furthermore, in the authoritarian countries where access to money is often used as a tool of repression, Bitcoin’s accessibility is vital. 



<h2 class="wp-block-heading">Bitcoin updates and developments</h2>



The rules that define Bitcoin protocol were first introduced by Satoshi Nakamoto, but as every computer program, they have to be regularly revised and updated, in order to reinforce the protocol security and introduce new functionalities. The way such updates are agreed upon is usually referred to as the <a href="https://d.center/explore/bitcoin-governance" class="ek-link">governance</a>, and in Bitcoin case its community plays a critical role.&nbsp;



Beyond the Bitcoin protocol itself, there have been numerous developments of the so-called layer 2, allowing&nbsp; to execute transactions off the mainchain. Such solutions usually aim to improve Bitcoin’s performance or introduce new functionalities.



Bitcoin's most popular layer-2 solution is Lightning Network, which increases dramatically its transaciton throughput and decreases network fees.

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Bitcoin is an assembly of&nbsp; technologies and principles that interact in a predefined manner, securing the whole system performance.&nbsp;So how does it work? 



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<a href="https://d.center/explore/keys-and-addresses" class="ek-link">Keys and addresses</a>. Bitcoin is a decentralized system without any trusted third party, which means that no one can dispose of coins except for their rightful owner. Such feature necessitates extensive security measures, and Bitcoin ensures them using a system of cryptographic keys and addresses. 



<a href="https://d.center/explore/bitcoin-wallets" class="ek-link">Wallets</a><a href="https://d.center/explore/bitcoin-wallets" class="ek-link"> </a>are programs capable of communicating with the Bitcoin network. They generate keys and addresses that allow sending and receiving bitcoins, and can reconstitute the bitcoin balance of a particular account by researching the blockchain. 



<a href="https://d.center/explore/bitcoin-transaction" class="ek-link">Transactions </a>are generated and sent by wallets. Bitcoin transactions have a simple structure called UTXO, and a limited coding language script, which ensure the system’s robustness. 



<a href="https://d.center/explore/bitcoin-network" class="ek-link">Bitcoin network</a> enjoys a Peer-to-Peer, or <a href="https://d.center/explore/p2p-network" class="ek-link">P2P</a>, architecture - its nodes communicate with each other without any central server. Network nodes run Bitcoin protocol to verify if a transaction is valid (the sender has enough coins on their account and their signatures are correct) and if a candidate block (set of confirmed transactions) sent by a miner is OK, then propagate them to the network. 



<a href="https://d.center/explore/bitcoin-consensus-and-mining" class="ek-link">Consensus </a>is needed in order to determine which node will add the next block to the blockchain and to guarantee that this block is not fraudulent. Bitcoin utilizes <a href="https://d.center/explore/proof-of-work" class="ek-link">Proof-of-Work</a> consensus, where nodes need to find a solution to a cryptographic problem, which necessitates a big amount of electricity and specific equipment. As a reward for such work a node gets to add a block and receives newly created bitcoins. Such “bitcoin extraction” activity is called mining and the nodes engaging in it - miners. Mining is the only way to create new bitcoins.



 The node who finds a PoW solution first broadcasts a new block to the network, where, if the block is validated by the network, other nodes start working on the following blocks. Each block having a cryptographic reference to the previous one, a <a href="https://d.center/explore/bitcoin-blockchain" class="ek-link">blockchain </a>is being formed.

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The only one who can dispose of their bitcoins is the one holding the corresponding keys - cryptographic tools that secure transactions. #notyourkeysnotyourmoney



Bitcoin protocol largely rests on cryptography, but contrary to what one might think, in most cases it’s not about encrypting messages, but about creating digital signatures and footprints.&nbsp;



Digital signatures allow to safely transfer bitcoins from one person to another by exploiting the properties of asymmetric cryptography, which uses a pair of keys: private and public.



<a href="https://d.center/explore/bitcoin-private-key" class="ek-link">Bitcoin private key</a> is a very big randomly generated number, which must be kept secret and whose generation must be carefully chosen for security reasons. This key gives its owner an entire possession of bitcoins and therefore must be carefully kept, for when stolen, it will allow the thief to spend bitcoins, and when lost, bitcoins will become forever inaccessible.



<a href="https://d.center/explore/bitcoin-public-key" class="ek-link">Bitcoin public key</a> is derived from the private key via one-way cryptographic function, meaning that it is impossible to find a private key from the public key. 



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Private key allows the sender to sign a <a href="https://d.center/explore/bitcoin-transaction" class="ek-link">transaction</a>. Transaction’s content, the signature and the sender’s public key are used by the network to verify the sender’s authenticity and the integrity of data within the transaction. 



The receiver’s public key is used to identify him or her as a receiver within a transaction. For the sake of security and ease, the users do not transfer the public key as it is, but rather utilize its footprint called <a href="https://d.center/explore/bitcoin-address" class="ek-link">Bitcoin address</a>. The address is what users usually see, and it can be assimilated to an account number in a classical financial transaction. 



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In the case of Bitcoin a method called ECDSA (Elliptic Curve Digital Signature Algorithm) is used to derive public keys and sign transactions. 



The keys are generally created and managed by a <a href="https://d.center/explore/bitcoin-wallets" class="ek-link">wallet </a>- an application that connects the user to the <a href="https://d.center/explore/bitcoin-network" class="ek-link">Bitcoin network</a>.&nbsp;Private keys, public keys, addresses and wallets allow users to send and to receive bitcoins easily and safely, enjoying a total control over them in a decentralized environment.&nbsp;