On Symbolic Verification of Bitcoin's script Language

Abstract

Validation of Bitcoin transactions rely upon the successful execution of scripts written in a simple and effective, non-Turing-complete by design language, simply called SCRIPT. This makes the validation of closed scripts, i.e. those associated to actual transactions and bearing full information, straightforward. Here we address the problem of validating open scripts, i.e. we address the validation of redeeming scripts against the whole set of possible inputs, i.e. under which general conditions can Bitcoins be redeemed? Even if likely not one of the most complex languages and demanding verification problems, we advocate the merit of formal verification for the Bitcoin validation framework. We propose a symbolic verification theory for of open SCRIPT, a verifier tool-kit, and illustrate examples of use on Bitcoin transactions. Contributions include 1) a formalisation of (a fragment of) the language; 2) a novel symbolic approach to SCRIPT verification, suitable, e.g. for the verification of newly defined and non-standard payment schemas; and 3) building blocks for a larger verification theory for the developing area of Bitcoin smart contracts. The verification of smart contracts, i.e. agreements built as transaction-based protocols, is currently a difficult to formalise and computationally demanding problem.