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ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 15 If there are collisions of the beneficiary addresses be- tween ommers and the block (i.e. two ommers with the same beneficiary address or an ommer with the same bene- ficiary address as the present block), additions are applied cumulatively. We define the block reward in Wei: (171) Finally, we define Π as the new state given the block re- ward function Ω applied to the final transaction’s resultant state, l(σ): (181) Π(σ, B) ≡ Ω(B, l(σ)) Thus the complete block-transition mechanism is de- fined, except for PoW, the proof-of-work function. 11.5. Mining Proof-of-Work. The mining proof-of- work (PoW) exists as a cryptographically secure nonce that proves beyond reasonable doubt that a particular amount of computation has been expended in the deter- mination of some token value n. It is utilised to enforce the blockchain security by giving meaning and credence to the notion of difficulty (and, by extension, total dif- ficulty). However, since mining new blocks comes with an attached reward, the proof-of-work not only functions as a method of securing confidence that the blockchain will remain canonical into the future, but also as a wealth distribution mechanism. For both reasons, there are two important goals of the proof-of-work function; firstly, it should be as accessible as possible to as many people as possible. The requirement of, or reward from, specialised and uncommon hardware should be minimised. This makes the distribution model as open as possible, and, ideally, makes the act of mining a simple swap from electricity to Ether at roughly the same rate for anyone around the world. Secondly, it should not be possible to make super-linear profits, and especially not so with a high initial barrier. Such a mechanism allows a well-funded adversary to gain a troublesome amount of the network’s total mining power and as such gives them a super-linear reward (thus skewing distribution in their favour) as well as reducing the network security. One plague of the Bitcoin world is ASICs. These are specialised pieces of compute hardware that exist only to do a single task (Smith [1997]). In Bitcoin’s case the task is the SHA256 hash function (Courtois et al. [2014]). While ASICs exist for a proof-of-work function, both goals are placed in jeopardy. Because of this, a proof-of-work func- tion that is ASIC-resistant (i.e. difficult or economically inefficient to implement in specialised compute hardware) has been identified as the proverbial silver bullet. Two directions exist for ASIC resistance; firstly make it sequential memory-hard, i.e. engineer the function such that the determination of the nonce requires a lot of mem- ory and bandwidth such that the memory cannot be used in parallel to discover multiple nonces simultaneously. The second is to make the type of computation it would need to do general-purpose; the meaning of “specialised hardware” for a general-purpose task set is, naturally, general purpose hardware and as such commodity desktop computers are likely to be pretty close to “specialised hardware” for the task. For Ethereum 1.0 we have chosen the first path. More formally, the proof-of-work function takes the form of PoW: (182) 5 Rblock = 1018 × 3 2 if Hi < FByzantium if FByzantium Hi < FConstantinople if Hi FConstantinople 11.4. State & Nonce Validation. We may now define the function, Γ, that maps a block B to its initiation state: (172) Γ(B) ≡ σ0 σi : TRIE(LS(σi)) = P (BH)Hr if P(BH)=∅ otherwise Here, TRIE(LS(σi)) means the hash of the root node of a trie of state σi; it is assumed that implementations will store this in the state database, which is trivial and efficient since the trie is by nature an immutable data structure. And finally we define Φ, the block transition function, which maps an incomplete block B to a complete block B′: (173) Φ(B) ≡ B′ : n : m B B′ = B∗ x 2256 Hd except: (174) (175) (176) Bn′ = Bm′ = B∗ ≡ with (x,m) = PoW(Bn∗ ,n,d) except: Br∗ = r(Π(Γ(B), B)) With d being a dataset as specified in Appendix J. As specified at the beginning of the present work, Π is the state-transition function, which is defined in terms of Ω, the block finalisation function and Υ, the transaction- evaluation function, both now well-defined. As previously detailed, R[n]z, R[n]l and R[n]u are the nth corresponding status code, logs and cumulative gas used after each transaction (R[n]b, the fourth component in the tuple, has already been defined in terms of the logs). We also define the nth state σ[n], which is defined simply as the state resulting from applying the corresponding transaction to the state resulting from the previous trans- action (or the block’s initial state in the case of the first such transaction): (177) σ[n] = Γ(B) Υ(σ[n − 1], BT[n]) if n<0 otherwise In the case of BR [n]u , we take a similar approach defin- ing each item as the gas used in evaluating the correspond- ing transaction summed with the previous item (or zero, if it is the first), giving us a running total: 0 g niently defined in the transaction execution function. (179) R[n]l =Υl(σ[n−1],BT[n]) We define R[n]z in a similar manner. (180) R[n]z =Υz(σ[n−1],BT[n]) Υ (σ[n−1],BT[n]) +R[n − 1]u if n<0 otherwise (178) R[n]u = For R[n]l, we utilise the Υl function that we conve- m = Hm ∧ n 2256 with (m,n) = PoW(Hn,Hn,d) Hd Where Hn is the new block’s header but without the nonce and mix-hash components; Hn is the nonce of the header; d is a large data set needed to compute the mix- Hash and Hd is the new block’s difficulty value (i.e. thePDF Image | ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION
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