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ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 3 Sometimes, a path follows a new protocol from a par- ticular height (block number). This document describes one version of the protocol, namely the Berlin version defined by Beiko et al. [2021]. In order to follow back the history of a path, one must reference multiple versions of this document. Here are the block numbers of protocol updates on the Ethereum main network: Name First Block Number FHomestead 1150000 FTangerineWhistle 2463000 FSpuriousDragon 2675000 FByzantium 4370000 FConstantinople 7280000 FPetersburg 7280000 FIstanbul 9069000 FMuirGlacier 9200000 FBerlin 12244000 FLondon 12965000 Occasionally actors do not agree on a protocol change, and a permanent fork occurs. In order to distinguish be- tween diverged blockchains, EIP-155 by Buterin [2016b] introduced the concept of chain ID, which we denote by β. For the Ethereum main network (5) β=1 3. Conventions We use a number of typographical conventions for the formal notation, some of which are quite particular to the present work: The two sets of highly structured, ‘top-level’, state val- ues, are denoted with bold lowercase Greek letters. They fall into those of world-state, which are denoted σ (or a variant thereupon) and those of machine-state, μ. Functions operating on highly structured values are denoted with an upper-case Greek letter, e.g. Υ, the Ethereum state transition function. For most functions, an uppercase letter is used, e.g. C, the general cost function. These may be subscripted to denote specialised variants, e.g. CSSTORE, the cost func- tion for the SSTORE operation. For specialised and possibly externally defined functions, we may format as typewriter text, e.g. the Keccak-256 hash function (as per version 3 of the winning entry to the SHA-3 contest by Bertoni et al. [2011], rather than the final SHA-3 specification), is denoted KEC (and generally referred to as plain Keccak). Also, KEC512 refers to the Keccak-512 hash function. Tuples are typically denoted with an upper-case letter, e.g. T, is used to denote an Ethereum transaction. This symbol may, if accordingly defined, be subscripted to refer to an individual component, e.g. Tn, denotes the nonce of said transaction. The form of the subscript is used to denote its type; e.g. uppercase subscripts refer to tuples with subscriptable components. Scalars and fixed-size byte sequences (or, synonymously, arrays) are denoted with a normal lower-case letter, e.g. n is used in the document to denote a transaction nonce. Those with a particularly special meaning may be Greek, e.g. δ, the number of items required on the stack for a given operation. Arbitrary-length sequences are typically denoted as a bold lower-case letter, e.g. o is used to denote the byte sequence given as the output data of a message call. For particularly important values, a bold uppercase letter may be used. Throughout, we assume scalars are non-negative inte- gers and thus belong to the set N. The set of all byte sequences is B, formally defined in Appendix B. If such a set of sequences is restricted to those of a particular length, it is denoted with a subscript, thus the set of all byte sequences of length 32 is named B32 and the set of all non-negative integers smaller than 2256 is named N256. This is formally defined in section 4.3. Square brackets are used to index into and reference individual components or subsequences of sequences, e.g. μs[0] denotes the first item on the machine’s stack. For subsequences, ellipses are used to specify the intended range, to include elements at both limits, e.g. μm[0..31] denotes the first 32 items of the machine’s memory. In the case of the global state σ, which is a sequence of accounts, themselves tuples, the square brackets are used to reference an individual account. When considering variants of existing values, we follow the rule that within a given scope for definition, if we assume that the unmodified ‘input’ value be denoted by the placeholder then the modified and utilisable value is denoted as ′, and intermediate values would be ∗, ∗∗ &c. On very particular occasions, in order to maximise readability and only if unambiguous in meaning, we may use alpha-numeric subscripts to denote intermediate values, especially those of particular note. When considering the use of existing functions, given a function f, the function f∗ denotes a similar, element-wise version of the function mapping instead between sequences. It is formally defined in section 4.3. We define a number of useful functions throughout. One of the more common is l, which evaluates to the last item in the given sequence: (6) l(x) ≡ x[∥x∥ − 1] 4. Blocks, State and Transactions Having introduced the basic concepts behind Ethereum, we will discuss the meaning of a transaction, a block and the state in more detail. 4.1. World State. The world state (state), is a map- ping between addresses (160-bit identifiers) and account states (a data structure serialised as RLP, see Appendix B). Though not stored on the blockchain, it is assumed that the implementation will maintain this mapping in a modi- fied Merkle Patricia tree (trie, see Appendix D). The trie requires a simple database backend that maintains a map- ping of byte arrays to byte arrays; we name this underlying database the state database. This has a number of benefits; firstly the root node of this structure is cryptographically dependent on all internal data and as such its hash can be used as a secure identity for the entire system state. Secondly, being an immutable data structure, it allows any previous state (whose root hash is known) to be recalled by simply altering the root hash accordingly. Since we store all such root hashes in the blockchain, we are able to trivially revert to old states. The account state, σ[a], comprises the following four fields:PDF Image | ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION
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