More than 14 years ago, Satoshi Nakamoto introduced the Bitcoin network to the world by creating the very first triple-entry accounting system. This technological marvel combines encryption and mathematical formulas to enhance security. At the core of Bitcoin's complex architecture are several mathematical approaches that determine block rewards, transaction inputs and outputs, and mining difficulty adjustments, and regulate the rate at which new blocks are discovered. The Bitcoin system works based on Satoshi's mathematics.

Integers in Action: A Look at Using Integers

Bitcoin was created using various encryption processes and mathematical formulas, each with a specific purpose. One of the design elements included in Bitcoin is the use of integers, or integers, and their negative counterparts.

The Bitcoin network uses integer mathematics to prevent potential disagreements that could arise when using decimal or fractional numbers. The use of integers and their negative counterparts ensures that all computing devices are more efficiently synchronized and specific network changes are accommodated.

The use of integers to support Bitcoin's ruleset includes block rewards and halvings that occur at a certain block height, a multiple of 210,000.

Bitcoin mining difficulty also uses integers to adjust the difficulty every 2016 blocks. Integers, a type of numeric data often used in computing software, are also used for input and output of Bitcoin transactions.

In addition, integer calculations are generally faster and less error-prone than floating point numbers. If Bitcoin used floating point numbers, it could lead to rounding errors, leading to inconsistencies and disagreements between different nodes on the network.

Since Bitcoin uses integers, the block reward from a future halving will eventually be truncated or rounded to the nearest integer using bit shift or bitwise operators. Since the smallest unit of Bitcoin is a satoshi, it is impossible to halve it. As a result, the much-discussed limited supply of Bitcoins will actually be less than 21 million.

Block time regulation using Poisson distribution and the Bitcoin system

In addition to integers, Bitcoin uses a mathematical formula similar to the Poisson distribution to regulate block time consistency. The Poisson distribution model was developed in 1837 by the French mathematician Simeon Denis Poisson. Using this model, Bitcoin's design ensures that blocks are discovered every 10 minutes or so.

The actual time required to mine a block may vary due to the probabilistic nature of the mining process, but blocks typically range from 8 to 12 minutes. Satoshi enabled a difficulty setting every 2,016 blocks, using a formula to maintain a rough average of 10-minute intervals between blocks.

Both integer mathematics and Poisson distribution are important mathematical tools in Bitcoin, providing a consistent framework for performing calculations and modeling various aspects of the system.

Bitcoin uses many other mathematical mechanisms and encryption schemes to ensure the accuracy, consistency, and efficiency of the system as a whole. These include concepts and formulas such as:

  • proof of work (PoW),

  • merkle trees,

  • elliptic curve cryptography,

  • cryptographic hash functions and final fields

Author: Vadim Gruzdev, analyst at Freedman Сlub Crypto News