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For most people, the inner workings of Bitcoin are complex and cryptic. What you need to know is that at its core, the magic of Bitcoin boils down to one key innovation – the Elliptic Curve Digital Signature Algorithm (ECDSA). 
Simply put, this is a mathematical working of Bitcoin that allows Bitcoin wallets to transact with the network while remaining anonymous safely. 

So, what proves that you own the Bitcoin you are spending without revealing your identity is the wonders of ECDSA. 
Let’s ride together as we unlock the basics of this technology, its application, its security implications, and the future of ECDSA in Bitcoin. 

Basics Of Elliptic Curve Cryptography (ECC)

Elliptic Curve Cryptography (ECC) is a form of public-key cryptography, that leverages the algebraic structure of elliptic curves over finite fields. This means it uses mathematical equations based on curved graphs to secure data. The strength of ECC lies in the difficulty of solving these equations, making it a robust choice for digital security.

In practice, a Bitcoin wallet uses ECC to generate a pair of keys: a private key, which is a randomly generated number, and a public key, derived from this private key using elliptic curve multiplication. The public key is your wallet address, shareable without compromising security.

Here is a Quick Look at How it Works:

An elliptic curve equation is selected, and a curve is generated from it on a graph. This curve has unique mathematical properties that make it hard to crack.
So a starting point on the elliptic is chosen somewhere on the curve. This is the private key, which is used to encrypt messages. 
The public key is then generated from the private key and used to decrypt messages. These mathematical properties are what make elliptic curves secure.
Collins wants to receive 1 BTC from Grace. Grace then creates a Bitcoin wallet, which randomly generates a private key (point A) and the corresponding public address (point B).
So, when Collins shares his private address with Grace, Collin’s private key stays secret. However, when Grace BTC comes in, it is encrypted by Collin’s public key 
Only Collin’s private key can decrypt and approve the transaction. Nobody is able to decipher his private key from her public address because of the ECC math.
Now that you have a good idea of what elliptic curve cryptography is about, let us have a look at the algorithms and how they work.

Elliptic Curve Digital Signature Algorithms (ECDSA)

ECDSA is a specific digital signature algorithm used in Bitcoin, that utilizes these ECC-generated key pairs. The private key must remain confidential, as it is used to digitally sign transactions, proving ownership of the funds without revealing the signer’s identity.
The ECDSA relies on elliptic curve cryptography to generate key pairs- one private key and one public key. Although the owner of the private key must keep it safe from other parties.
ECDSA has recently received significant attention from developers as an alternative to existing standard security systems. It also has different applications and uses within digital currencies, blockchain technology, and securing communication. 

Application of ECDSA In Bitcoin 

ECDSA (Elliptic Curve Digital Signature Algorithm), as said earlier, is the cryptography behind private and public keys used in Bitcoin. Interesting right?
Each Bitcoin wallet contains a public and private ECDSA key pair. The public key is the wallet address that can be openly shared to receive Bitcoin payments. 
However, the private key must be kept secret, as it allows the owner to digitally sign and authorize transactions to spend bitcoins from that address.
When a user wants to transfer bitcoins to another party, their Bitcoin wallet will create a transaction message containing key details like the recipient’s address and amount to send. This transaction is digitally signed behind the scenes with the sender’s private key.
Once validated, the transaction is added to the blockchain ledger, and the transfer of the Bitcoin balance is completely secure. 
The receiver can then only unlock and spend those bitcoins by presenting the private key corresponding to their receiving address in future transactions.
For crypto wallet owners, these keys must also be accessible when needed in order to unlock the funds. It is important to store the private key in a secure location, such as a hardware wallet, to ensure that it is kept safe from unauthorized access.