# The Math behind Cryptocurrency

## Those of you who did not want to click on this topic but still did when you saw the word Cryptocurrency; well don’t worry about the math it’s not going to be a article filled up with formulae; it’s just simple logic behind Crycptocurrency and Bitcoin. I am sure most of the readers are now aware of what Cryptocurrency is. So, let’s check out the Math behind it.

**The Math behind Cryptocurrency**

All of us must have hated Math at some point of our lives. But some people make a profession out of it. Those of you who did not want to click on this topic but still did when you saw the word Cryptocurrency; well don’t worry about the math it’s not going to be a article filled up with formulae; it’s just simple logic behind Crycptocurrency and Bitcoin. I am sure most of the readers are now aware of what Cryptocurrency is. So, let’s check out the Math behind it.

**The Blockchian**

The first cryptocurrency was Bitcoin created in 2009; it is independent of any bank, it is not physical and only exists as codes in a Blockchain. As nobody controls Bitcoins it is useful in online businesses. Cryptocurrency like Bitcoin maintains a public record of every transaction. In order to stop double spends all the Bitcoin transactions are displayed publicly. This allows anyone to verify that a new transaction isn’t spending assets that were spent in a previous transaction. This public record of every transaction is called the blockchain. All cryptocurrencies whether it is Bitcoin, Etherium, Moreno, etc; use blockchian technology.

Like the name suggests Cryptocurrency is based on cryptography- a branch of Math that deals with hiding secretive information. Let’s talk about Bitcoin here; Bitcoin can only function because of the clever mathematics which is in the background enabling it to exist.

**Cryptography- Public and Private Key**

Bitcoin ensures security by ‘elliptic curve cryptography' between owners of Bitcoins. Elliptic curve cryptography is a type of public key cryptography, relying on mathematics to ensure that a transaction can be secure. Bitcoin transactions are sent from or to electronic Bitcoin wallets, and are digitally signed for security. Everyone on the network knows about a transaction, and the history of a transaction can be traced back to the point where the Bitcoins were produced. Once you have installed a Bitcoin wallet on your computer or mobile phone, it will generate your first Bitcoin address and you can create more whenever you need one; this is your public key.

Bitcoin wallets keep a secret piece of data called a private key or seed, which is used to sign transactions, providing a mathematical proof that they have come from the owner of the wallet. The signature also prevents the transaction from being altered by anybody once it has been issued.

**The Mathematics**

Bitcoin uses Elliptic Curve Digital Signature Algorithm (ECDSE). It's a process that uses an elliptic curve and a finite field to "sign" data in such a way that third parties can verify the authenticity of the signature while the signer retains the exclusive ability to create the signature. With bitcoin, the data that is signed is the transaction that transfers ownership.ECDSA has separate procedures for signing and verification. Each procedure is an algorithm composed of a few arithmetic operations. The signing algorithm makes use of the private key, and the verification process makes use of the public key.

In ECDSA, the private key is an unpredictably chosen number between 1 and the order. The public key is derived from the private key by scalar multiplication of the base point a number of times equal to the value of the private key.

Expressed as an equation:
Public key = private key * base point.

There is math involved between private keys, pubic keys, and the process of signing. And how long does is takes, only ten minutes. If we see more mathematics behind the transactions, its complexity increases. But we need to keep in mind that major Math is behind Cryptocurrency.

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Sandeep Semwal

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