We propose the formal study of blockchains that are owned and controlled by organizations and that neither create cryptocurrencies nor provide incentives to solvers of cryptographic puzzles. We view such approaches as frameworks in which system parts, such as the cryptographic puzzle, may be instantiated with different technology. Owners of such a blockchain procure puzzle solvers as resources they control, and use a mathematical model to compute optimal parameters for the cryptographic puzzle mechanism or other parts of the blockchain. We illustrate this approach with a use case in which blockchains record hashes of financial process transactions to increase their trustworthiness and that of their audits.

For Proof of Work as cryptographic puzzle, we develop a detailed mathematical model to derive MINLP optimization problems for computing optimal Proof of Work configuration parameters that trade off potentially conflicting aspects such as availability, resiliency, security, and cost in this governed setting. We demonstrate the utility of such a mining calculus by applying it on some instances of this problem.

We hope that our work may facilitate the creation of domain-specific blockchains for a wide range of applications such as trustworthy information in Internet of Things systems and bespoke improvements of legacy financial services.