Bitcoin is a cryptocurrency created by “Satoshi Nakamoto”. The true identity of this person is not known yet. It can be a person or a group.

Bitcoin.org domain was registered 18 August 2008 and on 31 October he published the white paper titled “Bitcoin: A Peer-to-Peer Electronic Cash System” .The Bitcoin protocol is built on a blockchain. Satoshi cut off communication with the whole world and disappeared in 2011.
The system allows to online payments from one party to another party without any financial institution. Bitcoin uses digital signatures but additionally also uses peer to peer network in order to avoid double-spending problem.
This system needs cryptographic proof instead of trust. Two parties who want to send money to each other can pay without trust a third party. Traditionally, we trust the singular bank to manage financial services on our behalf.
Bitcoin creates an anonymous, trustless, decentralized currency. Instead of trusting any individual humans, we put trust into math, cryptography, and logic.

Satoshi defines electronic money as a digital signature chain. Each owner transfers the coin to the next by digitally signing a hash (encrypted text) of the previous transaction and the public key of the next owner and adding these to the end of the coin. A payee can verify the signatures to verify the chain of ownership.
The Bitcoin protocol and software are publicly published, and any developer in the world can review the code or publish their own modified version of the Bitcoin software.Bitcoin is controlled by all Bitcoin users around the world. Although the developers make additions to the software, they cannot forcefully change the Bitcoin protocol because all users are free to choose which software and version to use. To stay compatible with each other, all users must use software that follows the same rules. Bitcoin can only work if all users agree. That’s why all users and developers adhere to consensus. (bitcoin.org)
Transactions on the network create an unchangeable record with a timestamp and proof of work.The longest chain not only proves the recording order and time, but also that it comes from the pool with the largest CPU power.
The expense of the mediation service increases transaction costs and
prevents small payment transactions as it limits the small transaction amount.Since bitcoin eliminates this brokerage service, it allows money transfer at very low costs.It also allows much faster money transfer than swift transactions.
The system is secure as long as honest nodes collectively control more CPU powerthan any cooperating group of attacker nodes (CPU power- computers) .
The timestamp proves that the data must have existed at the
time, obviously, in order to get into the hash. Each timestamp includes the previous timestamp in its hash, forming a chain, with each additional timestamp reinforcing the ones before it.
The proof-of-work also solves the problem of determining representation in majority decisionmaking. If the majority were based on one-IP-address-one-vote, it could be subverted by anyone able to allocate many IPs. Proof-of-work is essentially one-CPU-one-vote.
The majority decision is represented by the longest chain, which has the greatest proof-of-work effort invested in it. If a majority of CPU power is controlled by honest nodes, the honest chain will grow the fastest and outpace any competing chains. To modify a past block, an attacker would have to redo the proof-of-work of the block and all blocks after it and then catch up with and surpass the work of the honest nodes.
NETWORK
The steps to run the network are as follows:
1) New transactions are broadcast to all nodes.
2) Each node collects new transactions into a block.
3) Each node works on finding a difficult proof-of-work for its block.
4) When a node finds a proof-of-work, it broadcasts the block to all nodes.
5) Nodes accept the block only if all transactions in it are valid and not already spent.
6) Nodes express their acceptance of the block by working on creating the next block in the chain, using the hash of the accepted block as the previous hash.
INCENTIVES
A reward must be given to the computer power that generates money and provides proof of work. This award is given for electricity and time provided to the system.The incentive can also be funded with transaction fees. The incentives makes the nodes stay honest. When gaining from the system is more attractive than defrauding the system, the possibility of an attack against the system is also reduced.Playing the game by its rules will earn more for the player.

PRIVACY
Every single purchase and sale transaction and time are published for everyone to see but the identities of the transactors are confidential.

CALCULATIONS

scenario 1 : an attacker trying to generate an alternate chain faster than the honest
chain. Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. Nodes are not going to accept an invalid transaction as payment, and honest nodes will never accept a block containing them. An attacker can only try to change one of his own transactions to take back.
scenario 2: How long the recipient of a new transaction needs to wait before being
sufficiently certain the sender can’t change the transaction. We assume the sender is an attacker who wants to make the recipient believe he paid him for a while, then switch it to pay back to himself after some time has passed. The receiver will be alerted when that happens, but the sender hopes it will be too late.
The receiver generates a new key pair and gives the public key to the sender shortly before signing. This prevents the sender from preparing a chain of blocks ahead of time by working on it continuously until he is lucky enough to get far enough ahead, then executing the transaction at that moment. Once the transaction is sent, the dishonest sender starts working in secret on a parallel chain containing an alternate version of his transaction.
Satoshi proposed a peer-to-peer network using proof-of-work to record a public history of transactions that quickly becomes computationally impractical for an attacker to change if honest nodes control a majority of CPU power. The network is robust in its unstructured simplicity. Nodes work all at once with little coordination. They do not need to be identified, since messages are not routed to any particular place and only need to be delivered on a best effort basis. Nodes can
leave and rejoin the network at will, accepting the proof-of-work chain as proof of what happened while they were gone. They vote with their CPU power, expressing their acceptance of valid blocks by working on extending them and rejecting invalid blocks by refusing to work on them. Any needed rules and incentives can be enforced with this consensus mechanism.