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ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 4 Even callable precompiled contracts can have an empty account state. This is because their account states do not usually contain the code describing its behavior. An account is dead when its account state is non-existent or empty: (15) DEAD(σ, a) ≡ σ[a] = ∅ ∨ EMPTY(σ, a) 4.2. The Transaction. A transaction (formally, T) is a single cryptographically-signed instruction constructed by an actor externally to the scope of Ethereum. The sender of a transaction can not be a contract. While it is as- sumed that the ultimate external actor will be human in nature, software tools will be used in its construction and dissemination1. There are two types of transactions: those which result in message calls and those which result in the creation of new accounts with associated code (known informally as ‘contract creation’). Both types specify a number of common fields: nonce: A scalar value equal to the number of trans- actions sent by the sender; formally Tn. gasPrice: A scalar value equal to the number of Wei to be paid per unit of gas for all computation costs incurred as a result of the execution of this transaction; formally Tp. gasLimit: A scalar value equal to the maximum amount of gas that should be used in executing this transaction. This is paid up-front, before any computation is done and may not be increased later; formally Tg. to: The 160-bit address of the message call’s recipi- ent or, for a contract creation transaction, ∅, used here to denote the only member of B0 ; formally Tt. value: A scalar value equal to the number of Wei to be transferred to the message call’s recipient or, in the case of contract creation, as an endowment to the newly created account; formally Tv. v, r, s: Values corresponding to the signature of the transaction and used to determine the sender of the transaction; formally Tw, Tr and Ts. This is expanded in Appendix F. Additionally, a contract creation transaction contains: init: An unlimited size byte array specifying the EVM-code for the account initialisation procedure, formally Ti. init is an EVM-code fragment; it returns the body, a second fragment of code that executes each time the account receives a message call (either through a trans- action or due to the internal execution of code). init is executed only once at account creation and gets discarded immediately thereafter. In contrast, a message call transaction contains: data: An unlimited size byte array specifying the input data of the message call, formally Td. Appendix F specifies the function, S, which maps trans- actions to the sender, and happens through the ECDSA of the SECP-256k1 curve, using the hash of the transaction (excepting the latter three signature fields) as the datum 1Notably, such ‘tools’ could ultimately become so causally removed from their human-based initiation—or humans may become so causally-neutral—that there could be a point at which they rightly be considered autonomous agents. e.g. contracts may offer bounties to humans for being sent transactions to initiate their execution. nonce: A scalar value equal to the number of trans- actions sent from this address or, in the case of accounts with associated code, the number of contract-creations made by this account. For ac- count of address a in state σ, this would be for- mally denoted σ[a]n. balance: A scalar value equal to the number of Wei owned by this address. Formally denoted σ[a]b. storageRoot: A 256-bit hash of the root node of a Merkle Patricia tree that encodes the storage con- tents of the account (a mapping between 256-bit integer values), encoded into the trie as a mapping from the Keccak 256-bit hash of the 256-bit integer keys to the RLP-encoded 256-bit integer values. The hash is formally denoted σ[a]s. codeHash: The hash of the EVM code of this account—this is the code that gets executed should this address receive a message call; it is immutable and thus, unlike all other fields, cannot be changed after construction. All such code fragments are contained in the state database under their corre- sponding hashes for later retrieval. This hash is formally denoted σ[a]c, and thus the code may be denoted as b, given that KEC(b) = σ[a]c. Since we typically wish to refer not to the trie’s root hash but to the underlying set of key/value pairs stored within, we define a convenient equivalence: ∗ (7) TRIE LI (σ[a]s) ≡ σ[a]s The collapse function for the set of key/value pairs in the trie, L∗I , is defined as the element-wise transformation of the base function LI, given as: (8) (9) where: LI(k, v) ≡ KEC(k), RLP(v) k ∈ B32 ∧ v ∈ N It shall be understood that σ[a]s is not a ‘physical’ member of the account and does not contribute to its later serialisation. If the codeHash field is the Keccak-256 hash of the empty string, i.e. σ[a]c = KEC(), then the node represents a simple account, sometimes referred to as a “non-contract” account. Thus we may define a world-state collapse function LS: (10) where (11) LS(σ) ≡ {p(a) : σ[a] ̸= ∅} p(a) ≡ KEC(a), RLP(σ[a]n, σ[a]b, σ[a]s, σ[a]c) This function, LS, is used alongside the trie function to provide a short identity (hash) of the world state. We assume: (12) ∀a:σ[a]=∅ ∨ (a∈B20 ∧ v(σ[a])) where v is the account validity function: (13) v(x) ≡ xn ∈ N256∧xb ∈ N256∧xs ∈ B32∧xc ∈ B32 An account is empty when it has no code, zero nonce and zero balance: (14) EMPTY(σ, a) ≡ σ[a]c = KEC()∧σ[a]n = 0∧σ[a]b = 0PDF Image | ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION
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