Bitcoin has been somewhat difficult to grasp for a lot of people due to the fact that they consider its phenomenon complex. The origin and formula behind the currency seems out of the norm for quite a number of people, and most people who somewhat understand how it works will rather just want to use the cryptocurrency than bother much about its origins or the mathematical and algorithmic formulae that brought it into existence.
This write-up will be majorly centred on the simplified version of the maths that helped to create the modern day digital currency revolution – Bitcoin. This article will try to make it as interesting as it can be (even though there isn’t anything much interesting about digital currency maths… maybe the maths that converts it to $$$ is 😊). This article will however not seek to delve into the deeper realms of Bitcoin maths, it will only barely scratch the surface just to make readers appreciate the work and dedication that gave rise to digital currencies as we have them today.
The Elliptic curve is the cornerstone for Bitcoin’s maths, it is the heart of the Bitcoin protocol – the Bitcoin protocol more or less makes use of Elliptic Curve Cryptography (ECC) to create and execute transactions. The ECC can be regarded as a public key crypto-system. Bitcoin transactions are carried out within a system that combines the ECC and digital signatures which are public and accessible to all. This way, a trustless system of approval and consensus is built since transactions are carried out within the premise of a distributed ledger (Blockchain) which is verifiable by all parties and even observers. These public digital signatures/wallet addresses also go to proof without contention that the owner has the stated funds in his or her possession.
The Elliptic Curve
Bitcoin uses the secp256k1 curve which is mathematically represented in the algebraic equation y2 = (x3 + 7). The elliptic curve acts as a mathematical trap door which only allows you to calculate from private keys to public keys but not the other way around. This ensures that users are able to share their public keys with other people, especially for purposes of accepting payment without risking having their funds getting stolen – this process brings the importance of the elliptic curve in Bitcoin transactions to the fore. It is imperative to note that all Bitcoin wallets/accounts are linked to both private and public keys.
As stated above, the elliptic curve acts as a one-way trap door such that your private key is practically not accessible to the public unless you make them known – and people can only have access to your funds when they get access to your password and/or private keys, and it is almost impossible for anyone to guess your private keys because there are 2256 key combinations for anyone who attempts to guess a wallet’s private keys – possibly over 4 billion guesses to be made!
The explanations above show that Bitcoin is kept safe cryptographically, hence the term cryptocurrency. Bitcoin stays secure because of its private keys which are almost impossible to access unless you are the owner of the coins as such private keys can be regarded as mathematical guarantees which help to confirm payments and notifies all who have access to the blockchain about both the origin and destination of a transaction – this makes it almost impossible to alter, duplicate or delete.
The Elliptic Curve Digital Signature Algorithm (ECDSA) does not only ensure the protection of funds and veracity of transactions, it also helps to mitigate against double-spend such that users do not try to outsmart the system by trying to use same Bitcoins to purchase two or more different items simultaneously. The Bitcoin network and users’ wallet automatically check previous transactions to ensure that funds are enough in the first place before a transaction is allowed – all these are done without the need for third parties (banks), just cryptography based on the ECDSA sorts these.
This write-up does not cover every aspect of the mathematical make-up that Bitcoin is, it only tries to an extent explain and interpret the maths behind Bitcoin and make it relatable… hopefully :/