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ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 8 6. Transaction Execution The execution of a transaction is the most complex part of the Ethereum protocol: it defines the state transition function Υ. It is assumed that any transactions executed first pass the initial tests of intrinsic validity. These include: (1) The transaction is well-formed RLP, with no addi- tional trailing bytes; (2) the transaction signature is valid; (3) the transaction nonce is valid (equivalent to the sender account’s current nonce); (4) the sender account has no contract code deployed (see EIP-3607 by Feist et al. [2021]); (5) the gas limit is no smaller than the intrinsic gas, g0, used by the transaction; and (6) the sender account balance contains at least the cost, v0, required in up-front payment. Formally, we consider the function Υ, with T being a transaction and σ the state: (52) σ′ =Υ(σ,T) Thus σ′ is the post-transactional state. We also define Υg to evaluate to the amount of gas used in the execution of a transaction, Υl to evaluate to the transaction’s accrued log items and Υz to evaluate to the status code resulting from the transaction. These will be formally defined later. 6.1. Substate. Throughout transaction execution, we ac- crue certain information that is acted upon immediately following the transaction. We call this the accrued transac- tion substate, or accrued substate for short, and represent it as A, which is a tuple: (53) A ≡ (As, Al, At, Ar, Aa, Ak) The tuple contents include As, the self-destruct set: a set of accounts that will be discarded following the trans- action’s completion. Al is the log series: this is a series of archived and indexable ‘checkpoints’ in VM code exe- cution that allow for contract-calls to be easily tracked by onlookers external to the Ethereum world (such as decen- tralised application front-ends). At is the set of touched accounts, of which the empty ones are deleted at the end of a transaction. Ar is the refund balance, increased through using the SSTORE instruction in order to reset contract storage to zero from some non-zero value. Though not immediately refunded, it is allowed to partially offset the total execution costs. Finally, EIP-2929 by Buterin and Swende [2020] introduced Aa, the set of accessed account addresses, and Ak, the set of accessed storage keys. We define the empty accrued substate A0 to have no self-destructs, no logs, no touched accounts, zero refund bal- ance, all precompiled contracts in the accessed addresses, and no accessed storage: (54) A0 ≡ (∅,(),∅,0,π,∅) where π is the set of all precompiled addresses. 6.2. Execution. We define intrinsic gas g0, the amount of gas this transaction requires to be paid prior to execution, as follows: (55)g0≡ (56) + Gtxcreate if Tt = ∅ (59) S(T) ̸= σ[S(T)] ̸= σ[S(T)]c = Tn = g0 v0 Tg ∅ ∧ ∅ ∧ KEC() ∧ σ[S(T)]n ∧ Tg ∧ σ[S(T)]b ∧ BHl − l(BR)u Gtxdatazero if i = 0 i∈Ti ,Td Gtxdatanonzero otherwise 0 + Gtransaction where action’s associated data and initialisation EVM-code, de- pending on whether the transaction is for contract-creation or message-call. Gtxcreate is added if the transaction is contract-creating, but not if a result of EVM-code. G is fully defined in Appendix G. The up-front cost v0 is calculated as: (58) v0≡TgTp+Tv The validity is determined as: (57) Ti , Td means the series of bytes of the trans- Note the final condition; the sum of the transaction’s gas limit, Tg, and the gas utilised in this block prior, given by l(BR)u, must be no greater than the block’s gasLimit, BHl. The execution of a valid transaction begins with an irrevocable change made to the state: the nonce of the account of the sender, S(T), is incremented by one and the balance is reduced by part of the up-front cost, TgTp. The gas available for the proceeding computation, g, is defined as Tg − g0. The computation, whether contract creation or a message call, results in an eventual state (which may legally be equivalent to the current state), the change to which is deterministic and never invalid: there can be no invalid transactions from this point. We define the checkpoint state σ0: (60) (61) (62) σ0 ≡ σ except: σ0[S(T)]b ≡ σ[S(T)]b − TgTp σ0[S(T)]n ≡ σ[S(T)]n + 1 Evaluating σP from σ0 depends on the transaction type; either contract creation or message call; we define the tuple of post-execution provisional state σP, remaining gas g′, accrued substate A and status code z: (63) (σP,g′,A,z) ≡ where Λ4(σ0, A∗, S(T ), S(T ), g, Tp,Tv,Ti,0,∅,⊤) ∗ if Tt =∅ otherwise otherwise Θ4(σ0,A ,S(T),S(T),Tt, Tt, g, Tp, Tv, Tv, Td, 0, ⊤) except A∗a ≡A0a ∪{S(T)} A∗ ≡A0 the basic amount required to pay for the existence of the transaction: (65) g≡Tg−g0 (64) and g is the amount of gas remaining after deductingPDF Image | ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION
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