This paper introduces an approach to constructing ledger structures for cryptocurrency systems with basic category theory. Compositional theories of resource convertibility allow us to express the material history of virtual goods, and ownership is modelled by a free construction. Our notion of ownership admits an intuitive graphical representation through string diagrams for monoidal functors.
Sean Braithwaite, Ethan Buchman, Ismail Khoffi, Igor Konnov · 7 authors
In Tendermint blockchains, the proof-of-stake mechanism and the underlying consensus algorithm entail a dynamic fault model that implies that the active validators (nodes that sign blocks) may change over time, and a quorum of these validators is assumed to be correct only for a limited period of time (called trusting period). The changes of the validator set are under control of the blockchain application, and are committed in every block. In order to check what is the state of the blockchain application at some height h, one needs to know the validator set at that height so that one can verify the corresponding digital signatures and hashes. A naive way of determining the validator set for height h requires one to: (i) download all blocks before h, (ii) verify blocks by checking digital signatures and hashes and (iii) execute the corresponding transactions so the changes in the validator sets are reproduced. This can potentially be very slow and computationally and data intensive. In this paper we formalize the dynamic fault model imposed by Tendermint, and describe a light client protocol that allows to check the state of the blockchain application that, in realistic settings, reduces significantly the amount of data needed to be downloaded, and the number of required computationally expensive signature verification operations. In addition to mathematical proofs, we have formalized the light client protocol in TLA+, and checked safety and liveness with the APALACHE model checker.
Recursive Length Prefix (RLP) is used to encode a wide variety of data in Ethereum, including transactions. The work described in this paper provides a formal specification of RLP encoding and a verified implementation of RLP decoding, developed in the ACL2 theorem prover. This work has led to improvements to the Ethereum documentation and additions to the Ethereum test suite.
Abstract We condense the theory of UTxO blockchains down to a simple and compact set of four type equations (Idealised EUTxO), and to an algebraic characterisation (abstract chunk systems), and exhibit an adjoint pair of functors between them. This gives a novel account of the essential mathematical structures underlying blockchain technology, such as Bitcoin.
Fault-tolerant distributed systems move the trust in a single party to a majority of parties participating in the protocol. This makes blockchain based crypto-currencies possible: they allow parties to agree on a total order of transactions without a trusted third party. To trust a distributed system, the security of the protocol and the correctness of the implementation must be indisputable. We present the first machine checked proof that guarantees both safety and liveness for a consensus algorithm. We verify a Proof of Stake (PoS) Nakamoto-style blockchain (NSB) protocol, using the foundational proof assistant Coq. In particular, we consider a PoS NSB in a synchronous network with a static set of corrupted parties. We define execution semantics for this setting and prove chain growth, chain quality, and common prefix which together imply both safety and liveness.
Rob van Glabbeek, Vincent Gramoli, Pierre Tholoniat
We consider the problem of cross-chain payment whereby customers of different escrows---implemented by a bank or a blockchain smart contract---successfully transfer digital assets without trusting each other. Prior to this work, cross-chain payment problems did not require this success, or any form of progress. We demonstrate that it is possible to solve this problem when assuming synchrony, in the sense that each message is guaranteed to arrive within a known amount of time, but impossible to solve without assuming synchrony. Yet, we solve a weaker variant of this problem, where success is conditional on the patience of the participants, without assuming synchrony, and in the presence of Byzantine failures. We also discuss the relation with the recently defined cross-chain deals.
Derivatives are a special type of financial contracts used to hedge risks or to speculate on the market fluctuations. In order to avoid ambiguities and misinterpretations, several domain specific languages (DSLs) for specifying such derivatives have been proposed. The recent development of the blockchain technologies enables the automatic execution of financial derivatives. Once deployed on the blockchain, a derivative cannot be modified. Therefore, more caution should be taken in order to avoid undesired situations. In this paper, we address the formal verification of financial derivatives written in a DSL for blockchain, called Findel. We identify a list of properties that, once proved, they exclude several security vulnerabilities (e.g., immutable bugs, money losses). We develop an infrastructure that provides means to interactively formalize and prove such properties. To provide a higher confidence, we also generate proof certificates. We use our infrastructure to certify non-trivial examples that cover the most common types of derivatives (forwards/futures, swaps, options).
Events in the Solidity language provide a means of communication between the on-chain services of decentralized applications and the users of those services. Events are commonly used as an abstraction of contract execution that is relevant from the users' perspective. Users must, therefore, be able to understand the meaning and trust the validity of the emitted events. This paper presents a source-level approach for the formal specification and verification of Solidity contracts with the primary focus on events. Our approach allows specification of events in terms of the on-chain data that they track, and predicates that define the correspondence between the blockchain state and the abstract view provided by the events. The approach is implemented in solc-verify, a modular verifier for Solidity, and we demonstrate its applicability with various examples.
In the blockchain-based, distributed computing platform Ethereum, programs called smart contracts are compiled to bytecode and executed on the Ethereum Virtual Machine (EVM). Executing EVM bytecode is subject to monetary fees---a clear optimization target. Our aim is to superoptimize EVM bytecode by encoding the operational semantics of EVM instructions as SMT formulas and leveraging a constraint solver to automatically find cheaper bytecode. We implement this approach in our EVM Bytecode SuperOptimizer ebso and perform two large scale evaluations on real-world data sets.
The paper develops a logical understanding of processes for signature of legal contracts, motivated by applications to legal recognition of smart contracts on blockchain platforms. A number of axioms and rules of inference are developed that can be used to justify a ``meeting of the minds'' precondition for contract formation from the fact that certain content has been signed. In addition to an ``offer and acceptance'' process, the paper considers ``signature in counterparts'', a legal process that permits a contract between two or more parties to be brought into force by having the parties independently (possibly, remotely) sign different copies of the contract, rather than placing their signatures on a common copy at a physical meeting. It is argued that a satisfactory account of signature in counterparts benefits from a logic with syntactic self-reference. The axioms used are supported by a formal semantics, and a number of further properties of the logic are investigated. In particular, it is shown that the logic implies that when a contract has been signed, the parties do not just agree, but are in mutual agreement (a common-knowledge-like notion) about the terms of the contract.
Abstract Solidity is the dominant programming language for Ethereum smart contracts. This paper presents a high-level formalization of the Solidity language with a focus on the memory model. The presented formalization covers all features of the language related to managing state and memory. In addition, the formalization we provide is effective: all but few features can be encoded in the quantifier-free fragment of standard SMT theories. This enables precise and efficient reasoning about the state of smart contracts written in Solidity. The formalization is implemented in the SOLC-VERIFY verifier and we provide an extensive set of tests that covers the breadth of the required semantics. We also provide an evaluation on the test set that validates the semantics and shows the novelty of the approach compared to other Solidity-level contract analysis tools.
The exploitation of smart-contract vulnerabilities can have catastrophic consequences such as the loss of millions of pounds worth of crypto assets. Formal verification can be a useful tool in identifying vulnerabilities and proving that they have been fixed. In this paper, we present a formalisation of Solidity and the Ethereum blockchain using the Solid language and its blockchain; a Solid program is obtained by explicating/desugaring a Solidity program. We make some abstractions that over-approximate the way in which Solidity/Ethereum behave. Based on this formalisation, we create Solidifier: a bounded model checker for Solidity. It translates Solid into Boogie, an intermediate verification language, that is later verified using Corral, a bounded model checker for Boogie. Unlike much of the work in this area, we do not try to find specific behavioural/code patterns that might lead to vulnerabilities. Instead, we provide a tool to find errors/bad states, i.e. program states that do not conform with the intent of the developer. Such a bad state, be it a vulnerability or not, might be reached through the execution of specific known code patterns or through behaviours that have not been anticipated.
Decentralized techniques are becoming crucial and ubiquitous with the rapid advancement of distributed ledger technologies such as the blockchain. Numerous decentralized systems have been developed to address security and privacy issues with great dependability and reliability via these techniques. Meanwhile, formalization and verification of the decentralized systems is the key to ensuring correctness of the design and security properties of the implementation. In this paper, we propose a novel method of formalizing and verifying decentralized systems with a kind of extended concurrent separation logic. Our logic extends the standard concurrent separation logic with new features including communication encapsulation, environment perception, and node-level reasoning, which enhances modularity and expressiveness. Besides, we develop our logic with unitarity and compatibility to facilitate implementation. Furthermore, we demonstrate the effectiveness and versatility of our method by applying our logic to formalize and verify critical techniques in decentralized systems including the consensus mechanism and the smart contract.
We implement two versions of a simple but illustrative smart contract: one in Solidity on the Ethereum blockchain platform, and one in Plutus on the Cardano platform, with annotated code excerpts and with source code attached. We get a clearer view of the Cardano programming model in particular by introducing a novel mathematical abstraction which we call Idealised EUTxO. For each version of the contract, we trace how the architectures of the underlying platforms and their mathematics affects the natural programming styles and natural classes of errors. We prove some simple but novel results about alpha-conversion and observational equivalence for Cardano, and explain why Ethereum does not have them. We conclude with a wide-ranging and detailed discussion in the light of the examples, mathematical model, and mathematical results so far.
Rob van Glabbeek, Vincent Gramoli, Pierre Tholoniat
In this paper, we consider the problem of cross-chain payment whereby customers of different escrows -- implemented by a bank or a blockchain smart contract -- successfully transfer digital assets without trusting each other. Prior to this work, cross-chain payment problems did not require this success or any form of progress. We introduce a new specification formalism called Asynchronous Networks of Timed Automata (ANTA) to formalise such protocols. We present the first cross-chain payment protocol that ensures termination in a bounded amount of time and works correctly in the presence of clock skew. We then demonstrate that it is impossible to solve this problem without assuming synchrony, in the sense that each message is guaranteed to arrive within a known amount of time. We also offer a protocol that solves an eventually terminating variant of this cross-chain payment problem without synchrony, and even in the presence of Byzantine failures.
We present a model/executable specification of smart contract execution in Coq. Our formalization allows for inter-contract communication and generalizes existing work by allowing modelling of both depth-first execution blockchains (like Ethereum) and breadth-first execution blockchains (like Tezos). We represent smart contracts programs in Coq's functional language Gallina, enabling easier reasoning about functional correctness of concrete contracts than other approaches. In particular we develop a Congress contract in this style. This contract -- a simplified version of the infamous DAO -- is interesting because of its very dynamic communication pattern with other contracts. We give a high-level partial specification of the Congress's behavior, related to reentrancy, and prove that the Congress satisfies it for all possible smart contract execution orders.
In December 2015, a bounty emerged to establish both reliable communication and secure transfer of value between the Dogecoin and Ethereum blockchains. This prized "Dogethereum bridge" would allow parties to "lock" a DOGE coin on Dogecoin and in exchange receive a newly minted WOW token in Ethereum. Any subsequent owner of the WOW token could burn it and, in exchange, earn the right to "unlock" a DOGE on Dogecoin. We describe an efficient, trustless, and retrofitting Dogethereum construction which requires no fork but rather employs economic collateral to achieve a "lock" operation in Dogecoin. The protocol relies on bulletproofs, Truebit, and parametrized tokens to efficiently and trustlessly relay events from the "true" Dogecoin blockchain into Ethereum. The present construction not only enables cross-platform exchange but also allows Ethereum smart contracts to trustlessly access Dogecoin. A similar technique adds Ethereum-based smart contracts to Bitcoin and Bitcoin data to Ethereum smart contracts.
Danil Annenkov, Jakob Botsch Nielsen, Bas Spitters
We present a new way of embedding functional languages into the Coq proof assistant by using meta-programming. This allows us to develop the meta-theory of the language using the deep embedding and provides a convenient way for reasoning about concrete programs using the shallow embedding. We connect the deep and the shallow embeddings by a soundness theorem. As an instance of our approach, we develop an embedding of a core smart contract language into Coq and verify several important properties of a crowdfunding contract based on a previous formalisation of smart contract execution in blockchains.
In paper describes the new logic programming language Delta, which have a many good properties. Delta-programs is p-computable, verifiable and can translation on other languages. Also we describe the Delta-methodology for constructing p-computable programs in high-level languages such as PHP, Java, JavaScript, C++, Pascal, Delphi, Python, Solidity and other. We would like to especially note the use of the Delta methodology for creating Smart Contracts and for Internet of things. We change the concept of the formula and define D-formulas(or Delta programs) are special list-formulas. Then we define the execution of a program how is the process of checking truth D-formula on a dynamic model. Main idea our paper consider program how list-formula from another formulas on dynamic models. And we created by iterations new Delta-programs use simple base formulas for this. Also we entered a dynamic models how models where we save final values of variables when check formula on this model.
We present solc-verify, a source-level verification tool for Ethereum smart contracts. Solc-verify takes smart contracts written in Solidity and discharges verification conditions using modular program analysis and SMT solvers. Built on top of the Solidity compiler, solc-verify reasons at the level of the contract source code, as opposed to the more common approaches that operate at the level of Ethereum bytecode. This enables solc-verify to effectively reason about high-level contract properties while modeling low-level language semantics precisely. The contract properties, such as contract invariants, loop invariants, and function pre- and post-conditions, can be provided as annotations in the code by the developer. This enables automated, yet user-friendly formal verification for smart contracts. We demonstrate solc-verify by examining real-world examples where our tool can effectively find bugs and prove correctness of non-trivial properties with minimal user effort.
Ethereum smart contracts are public, immutable and distributed and, as such, they are prone to vulnerabilities sourcing from programming mistakes of developers. This paper presents SAFEVM, a verification tool for Ethereum smart contracts that makes use of state-of-the-art verification engines for C programs. SAFEVM takes as input an Ethereum smart contract (provided either in Solidity source code, or in compiled EVM bytecode), optionally with assert and require verification annotations, and produces in the output a report with the verification results. Besides general safety annotations, SAFEVM handles the verification of array accesses: it automatically generates SV-COMP verification assertions such that C verification engines can prove safety of array accesses. Our experimental evaluation has been undertaken on all contracts pulled from etherscan.io (more than 24,000) by using as back-end verifiers CPAchecker, SeaHorn and VeryMax.
A bug or error is a common problem that any software or computer program may encounter. It can occur from badly writing the program, a typing error or bad memory management. However, errors can become a significant issue if the unsafe program is used for critical systems. Therefore, formal methods for these kinds of systems are greatly required. In this paper, we use a formal language that performs deductive verification on an Ethereum Blockchain application based on smart contracts, which are self-executing digital contracts. Blockchain systems manipulate cryptocurrency and transaction information. Therefore , if a bug occurs in the blockchain, serious consequences such as a loss of money can happen. Thus, the aim of this paper is to propose a language dedicated to deductive verification, called Why3, as a new language for writing formal and verified smart contracts, thereby avoiding attacks exploiting such contract execution vulnerabilities. We first write a Why3 smart contracts program; next we formulate specifications to be proved as absence of RunTime Error properties and functional properties, then we verify the behavior of the program using the Why3 system. Finally we compile the Why3 contracts to the Ethereum Virtual Machine (EVM). Moreover, we give a set of generic mathematical statements that allows verifying functional properties suited to any type of smart contracts holding cryptocurrency, showing that Why3 can be a suitable language to write smart contracts. To illustrate our approach, we describe its application to a realistic industrial use case.
Smart contracts are a special type of programs running inside a blockchain. Immutable and transparent, they provide means to implement fault-tolerant and censorship-resistant services. Unfortunately, its immutability causes a serious challenge of ensuring that a business logic and implementation is correct upfront, before publishing in a blockchain. Several big accidents have indeed shown that users of this technology need special tools to verify smart contract correctness. Existing automated checkers are able to detect only well known implementation bugs, leaving the question of business logic correctness far aside. In this work, we present a symbolic model-checking technique along with a formal specification method for a subset of Solidity programming language that is able to express both state properties and trace properties; the latter constitutes a weak analogy of temporal properties. We evaluate the proposed technique on the MiniDAO smart contract, a young brother of notorious TheDAO. Our Proof-of-Concept was able to detect a non-trivial error in the business logic of this smart contract in a few seconds.
Blockchain systems and smart contracts provide ways to securely implement multi-party transactions without the use of trusted intermediaries, which currently underpin many commercial transactions. However, they do so by transferring trust to computer systems, raising the question of whether code can be trusted. Experience with high value losses resulting from incorrect code has already shown that formal verification of smart contracts is likely to be beneficial. This note investigates the specification and verification of a simple form of multi-party transaction, atomic swaps. It is argued that logics with the ability to express properties of strategies of players in a multi-agent setting are conceptually useful for this purpose, although ultimately, for our specific examples, the less expressive setting of temporal logic suffices for verification of concrete implementations. This is illustrated through a number of examples of the use of a model checker to verify atomic swap smart contracts in on-chain and cross-chain settings.