Math application in smart contracts

Abstract

Smart contracts are blockchain-based algorithms that activate when specific conditions are fulfilled. They streamline the execution of agreements, allowing both parties to trust the outcome instantly without needing intermediaries or experiencing delays. To ensure secure and verified contract execution, cryptographic methods such as hash functions and digital signatures are used. Additionally, mathematical approaches like mathematical proofs and finite state machines are applied in designing and assessing smart contracts to guarantee their proper functionality. This paper explores the mathematical foundations of smart contracts, highlighting how they rely on mathematics to ensure immutability, security, and enforceability. A key technique behind their encryption methods is the pseudo-random number generator, which is based on chaotic maps. These chaotic maps generate highly random patterns depending on the initial seed value through complex mathematical operations. This work provides an overview of how chaotic maps are implemented in smart contracts. Additionally, the results obtained from these chaotic maps are presented showing that these maps achieve a high performance in digital signature algorithms.