IOTA is a revolutionary new transaction settlement and data transfer layer for the Internet of Things (IoT). It is based on a new distributed ledger technology, the Tangle, which overcomes the inefficiencies of current Blockchain designs and introduces a new way of reaching consensus in a decentralized peer-to-peer system. Using IOTA, for the first time ever, people and machines can transfer money and/or data without any transaction fees in a trustless, permissionless, and decentralized environment. This means that even nano-payments are possible without the need for a trusted intermediary of any kind.
In this paper we analyze the mathematical foundations of IOTA, a cryptocurrency for the Internet-of-Things (IoT) industry. The main feature of this novel cryptocurrency is the tangle, a directed acyclic graph (DAG) for storing transactions. The tangle naturally succeeds the blockchain as its next revolutionary step, and offers features that are required to establish a machineto-machine micropayment system. An essential contribution of this paper is a family of Markov Chain Monte Carlo (MCMC) algorithms. These algorithms select attachment sites on the tangle for a transaction that has just arrived .