Cryptocgraphy And The Mathematics Behind Cryptocurrencies

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, public keys, and the process of signing. And how long it 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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