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(72) (73) (74) σ′ ≡ ∀i∈As :σ′[i] = ∀i∈At :σ′[i] = σ∗ except ∅ (84) ∅ if DEAD(σ∗, i) (85) σ∗≡σ except: = 1, v + v′, TRIE(∅), KEC() ∅ ifσ[s]=∅ ∧ v=0 a∗ otherwise (75) (76) (77) ≡ (σ[s]n,σ[s]b −v,σ[s]s,σ[s]c) it was previously in existence: 0 if σ[a]=∅ (88) v′ ≡ σ[a]b otherwise Finally, the account is initialised through the execution of the initialising EVM code i according to the execution model (see section 9). Code execution can effect several events that are not internal to the execution state: the account’s storage can be altered, further accounts can be created and further message calls can be made. As such, the code execution function Ξ evaluates to a tuple of the resultant state σ∗∗, available gas remaining g∗∗, the re- sultant accrued substate A∗∗ and the body code of the account o. (89) (σ∗∗, g∗∗, A∗∗, o) ≡ Ξ(σ∗, g, A∗, I) ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 9 Note we use Θ4 and Λ4 to denote the fact that only the first four components of the functions’ values are taken; the final represents the message-call’s output value (a byte array) and is unused in the context of transaction evalua- tion. After the message call or contract creation is processed, the refund counter has to be incremented for the accounts that were self-destructed throughout its invocation. (66) A′r ≡ Ar + Rselfdestruct i∈As Then the state is finalised by determining the amount to be refunded, g∗ from the remaining gas, g′, plus some allowance from the refund counter, to the sender at the original rate. Tg−g′ ′ 2 We define the creation function formally as the function Λ, which evaluates from these values, together with the state σ and the accrued substate A, to the tuple containing the new state, remaining gas, new accrued substate, status code and output (σ′, g′, A′, z, o): (79) (σ′, g′, A′, z, o) ≡ Λ(σ, A, s, o, g, p, v, i, e, ζ, w) The address of the new account is defined as being the rightmost 160 bits of the Keccak hash of the RLP encoding of the structure containing only the sender and the account nonce. For CREATE2 the rule is different and is described in EIP-1014 by Buterin [2018]. Combining the two cases, we define the resultant address for the new account a: (67) g ≡g +min ,Ar ∗ ′ ADDR(s, n, ζ, i) ≡ B96..255 KEC LA(s, n, ζ, i) RLP(s,n) if ζ =∅ The total refundable amount is the legitimately remain- ing gas g′, added to Ar, with the latter component being capped up to a maximum of half (rounded down) of the total amount used Tg − g′. Therefore, g∗ is the total gas that remains after the transaction has been executed. The Ether for the gas is given to the miner, whose address is specified as the beneficiary of the present block B. So we define the pre-final state σ∗ in terms of the provisional state σP: LA (s, n, ζ , i) ≡ (255) · s · ζ · KEC(i) otherwise (68) (69) (70) (71) σ∗ ≡ σ∗[S(T)]b ≡ σ∗[m]b ≡ σP except σP[S(T)]b +g∗Tp σP[m]b + (Tg − g∗)Tp m ≡ BHc The final state, σ′, is reached after deleting all accounts that either appear in the self-destruct set or are touched and empty: And finally, we specify Υg, the total gas used in this transaction Υl, the logs created by this transaction and Υz, the status code of this transaction: (86) (87) σ∗[a] σ∗[s] = Υg(σ,T) ≡ Tg −g∗ Υl(σ,T) ≡ Al Υz(σ,T) ≡ z a∗ where v′ is the account’s pre-existing value, in the event These are used to help define the transaction receipt and are also used later for state and nonce validation. 7. Contract Creation There are a number of intrinsic parameters used when creating an account: sender (s), original transactor4 (o), available gas (g), gas price (p), endowment (v) together with an arbitrary length byte array, i, the initialisation EVM code, the present depth of the message-call/contract- creation stack (e), the salt for new account’s address (ζ) and finally the permission to make modifications to the state (w). The salt ζ might be missing (ζ = ∅); formally, (78) ζ ∈ B32 ∪ B0 If the creation was caused by CREATE2, then ζ ̸= ∅. a ≡ ADDR(s, σ[s]n − 1, ζ, i) (80) (81) (82) where · is the concatenation of byte arrays, Ba..b(X) evalu- ates to a binary value containing the bits of indices in the range [a,b] of the binary data X, and σ[x] is the address state of x, or ∅ if none exists. Note we use one fewer than the sender’s nonce value; we assert that we have incre- mented the sender account’s nonce prior to this call, and so the value used is the sender’s nonce at the beginning of the responsible transaction or VM operation. The address of the new account is added to the set of accessed accounts: (83) A∗ ≡A except A∗a ≡Aa ∪{a} The account’s nonce is initially defined as one, the bal- ance as the value passed, the storage as empty and the code hash as the Keccak 256-bit hash of the empty string; the sender’s balance is also reduced by the value passed. Thus the mutated state becomes σ∗: 4which can differ from the sender in the case of a message call or contract creation not directly triggered by a transaction but coming from the execution of EVM-codePDF Image | ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION
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