The ISC International Journal of Information Security

Abstract The future of the IoT requires new methods of payment that can handle millions of transactions per second. IOTA cryptocurrency aims at providing such a solution. It uses a consensus algorithm based on directed acyclic graphs (DAG) that is called Tangle. A tip selection algorithm (TSA) is a part of Tangle that determine which unconfirmed blocks (tips) should be confirmed by new blocks. There is always a chance that a small number of valid blocks never get confirmed and become stale. If a significant part of blocks become stale, the Tangle is considered unstable. In this paper, we mathematically prove that a TSA is stable in all transaction rates if and only if the probability of selecting all tips is at least $1/2n$ in which $n$ is the total number of tips. Accordingly, we demonstrate that the MCMC TSA used in IOTA would not be stable in high transaction rates.