Abstract
Bitcoin and Ethereum, hosting the two currently most valuable and popular cryptocurrencies, use two rather different ledger models, known as the UTXO model and the account model, respectively. At the same time, these two public blockchains differ strongly in the expressiveness of the smart contracts that they support. This is no coincidence. Ethereum chose the account model explicitly to facilitate more expressive smart contracts. On the other hand, Bitcoin chose UTXO also for good reasons, including that its semantic model stays simple in a complex concurrent and distributed computing environment. This raises the question of whether it is possible to have expressive smart contracts, while keeping the semantic simplicity of the UTXO model.
In this paper, we answer this question affirmatively. We present Extended UTXO (EUTXO), an extension to Bitcoin’s UTXO model that supports a substantially more expressive form of validation scripts, including scripts that implement general state machines and enforce invariants across entire transaction chains.
To demonstrate the power of this model, we also introduce a form of state machines suitable for execution on a ledger, based on Mealy machines and called Constraint Emitting Machines (CEM). We formalise CEMs, show how to compile them to EUTXO, and show a weak bisimulation between the two systems. All of our work is formalised using the Agda proof assistant.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
- 3.
- 4.
That these match up is enforced by Rules 7 and 8 in Fig. 6.
- 5.
Cardano will provide a mechanism in this vein.
- 6.
Adding such fields might require amending Rule 4 to ensure value preservation.
- 7.
- 8.
The result may be Nothing, in case no valid transitions exist from a given state/input.
- 9.
A user can run the step function locally to determine the correct next state off-chain.
- 10.
In our formal development, we enforce validity statically at compile time.
- 11.
We cannot provide a correspondence proof in case the target state is final, as explained in the previous note.
References
Andrychowicz, M., Dziembowski, S., Malinowski, D., Mazurek, Ł.: Modeling bitcoin contracts by timed automata. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 7–22. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10512-3_2
Atzei, N., Bartoletti, M., Lande, S., Zunino, R.: A formal model of Bitcoin transactions. In: Meiklejohn and Sako [10], pp. 541–560. https://doi.org/10.1007/978-3-662-58387-6_29
Bartoletti, M., Zunino, R.: BitML: a calculus for bitcoin smart contracts. In: Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, pp. 83–100. ACM (2018)
Ethereum Foundation: Solidity documentation (2016–2019). https://solidity.readthedocs.io/
Falkon, S.: The story of the DAO – its history and consequences (2017). medium.com. https://medium.com/swlh/the-story-of-the-dao-its-history-and-consequences-71e6a8a551ee
IETF: RFC 7049 - Concise Binary Object Representation (CBOR), October 2013. https://tools.ietf.org/html/rfc7049 . Accessed 01 Jan 2020
Larsen, K.G., Pettersson, P., Yi, W.: UPPAAL in a nutshell. Int. J. Softw. Tools Technol. Transfer 1(1–2), 134–152 (1997). https://doi.org/10.1007/s100090050010
Mavridou, A., Laszka, A.: Designing secure Ethereum smart contracts: a finite state machine based approach. In: Meiklejohn and Sako [10], pp. 523–540. https://doi.org/10.1007/978-3-662-58387-6_28
Mealy, G.H.: A method for synthesizing sequential circuits. The Bell Syst. Tech. J. 34(5), 1045–1079 (1955)
Meiklejohn, S., Sako, K. (eds.): FC 2018. LNCS, vol. 10957. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-662-58387-6
Melkonian, O., Swierstra, W., Chakravarty, M.M.: Formal investigation of the Extended UTxO model (Extended Abstract) (2019). https://omelkonian.github.io/data/publications/formal-utxo.pdf
Möser, M., Eyal, I., Gün Sirer, E.: Bitcoin covenants. In: Clark, J., Meiklejohn, S., Ryan, P.Y.A., Wallach, D., Brenner, M., Rohloff, K. (eds.) FC 2016. LNCS, vol. 9604, pp. 126–141. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53357-4_9
Nanevski, A., Ley-Wild, R., Sergey, I., Delbianco, G.A.: Communicating state transition systems for fine-grained concurrent resources. In: Shao, Z. (ed.) ESOP 2014. LNCS, vol. 8410, pp. 290–310. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54833-8_16
Sangiorgi, D.: Introduction to Bisimulation and Coinduction. Cambridge University Press, Cambridge (2012)
Lamela Seijas, P., Thompson, S.: Marlowe: financial contracts on blockchain. In: Margaria, T., Steffen, B. (eds.) ISoLA 2018. LNCS, vol. 11247, pp. 356–375. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03427-6_27
Sergey, I., Nagaraj, V., Johannsen, J., Kumar, A., Trunov, A., Hao, K.C.G.: Safer smart contract programming with Scilla. In: Proceedings of the ACM on Programming Languages 3(OOPSLA) (2019). Article No: 185
Zahnentferner, J.: An abstract model of UTxO-based cryptocurrencies with scripts. IACR Cryptology ePrint Archive 2018, p. 469 (2018). https://eprint.iacr.org/2018/469
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Chakravarty, M.M.T., Chapman, J., MacKenzie, K., Melkonian, O., Peyton Jones, M., Wadler, P. (2020). The Extended UTXO Model. In: Bernhard, M., et al. Financial Cryptography and Data Security. FC 2020. Lecture Notes in Computer Science(), vol 12063. Springer, Cham. https://doi.org/10.1007/978-3-030-54455-3_37
Download citation
DOI: https://doi.org/10.1007/978-3-030-54455-3_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-54454-6
Online ISBN: 978-3-030-54455-3
eBook Packages: Computer ScienceComputer Science (R0)