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ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 11 Aside from evaluating to a new state and accrued transaction substate, message calls also have an extra component—the output data denoted by the byte array o. This is ignored when executing transactions, however mes- sage calls can be initiated due to VM-code execution and in this case this information is used. (105) (σ′,g′,A′,z,o) ≡ Θ(σ,A,s,o,r,c,g,p,v,v ̃,d,e,w) Note that we need to differentiate between the value that is to be transferred, v, from the value apparent in the execution context, v ̃, for the DELEGATECALL instruction. We define σ1, the first transitional state as the orig- inal state but with the value transferred from sender to recipient: σ ifσ∗∗=∅ ≡ σ∗∗ otherwise (106) σ1[r]b ≡ σ[r]b + v ∧ σ1[s]b ≡ σ[s]b − v Ξ r o p d s v ̃ e w unless s = r. Throughout the present work, it is assumed that if σ1[r] was originally undefined, it will be created as an account (124) with no code or state and zero balance and nonce. Thus the previous equation should be taken to mean: (125) where (126) and (127) (107) (108) (109) (110) (111) σ1 ≡ σ′ 1 except: ΞECREC(σ1, g, A, I) ΞSHA256(σ1, g, A, I) ΞRIP160(σ1, g, A, I) ΞID(σ1, g, A, I) if c=1 if c=2 if c=3 if c=4 if c=5 if c=6 if c=7 if c=8 if c=9 σ1[s] ≡ Ξ ≡ ∅ ifσ′1[s]=∅ ∧ v=0 a1 otherwise ΞEXPMOD(σ1, g, A, I) ΞBN ADD(σ1, g, A, I) a1 ≡ σ′1[s]n, σ′1[s]b − v, σ′1[s]s, σ′1[s]c and σ′1≡σ except: Ξ(σ1, g, A, I) otherwise KEC(Ib) = σ[c]c ′ σ [r] ≡ (0,v,TRIE(∅),KEC(())) σ[r] = ∅ ∧ v ̸= 0 It is assumed that the client will have stored the pair (KEC(Ib),Ib) at some point prior in order to make the determination of Ib feasible. As can be seen, there are nine exceptions to the usage of the general execution framework Ξ for evaluation of the message call: these are so-called ‘precompiled’ contracts, meant as a preliminary piece of architecture that may later become native extensions. The contracts in addresses 1 to 9 execute the elliptic curve public key recovery function, the SHA2 256-bit hash scheme, the RIPEMD 160-bit hash scheme, the identity function, arbitrary precision modular exponentiation, elliptic curve addition, elliptic curve scalar multiplication, an elliptic curve pairing check, and the BLAKE2 compression function F respectively. Their full formal definition is in Appendix E. We denote the set of the addresses of the precompiled contracts by π: (128) π ≡ {1,2,3,4,5,6,7,8,9} 9. Execution Model The execution model specifies how the system state is altered given a series of bytecode instructions and a small tuple of environmental data. This is specified through a 1 σ′1[r]≡∅ σ′1[r] ≡ a′1 if if σ[r]=∅∧v=0 otherwise (112) a′1 ≡ (σ[r]n, σ[r]b + v, σ[r]s, σ[r]c) The account’s associated code (identified as the frag- ment whose Keccak hash is σ[c]c) is executed according to the execution model (see section 9). Just as with contract creation, if the execution halts in an exceptional fashion (i.e. due to an exhausted gas supply, stack underflow, in- valid jump destination or invalid instruction), then no gas is refunded to the caller and the state is reverted to the point immediately prior to balance transfer (i.e. σ). (113) (114) (115) (116) (117) (118) (119) (120) (121) (122) (123) σ′ g′≡ o=∅ A′ ≡ z ≡ (σ∗∗, g∗∗, A∗∗, o) ≡ Ia ≡ Io ≡ Ip ≡ Id ≡ Is ≡ Iv ≡ Ie ≡ Iw ≡ 0 ifσ∗∗=∅∧ g∗∗ otherwise A ifσ∗∗=∅ A∗∗ otherwise 0 if σ∗∗=∅ 1 otherwise Ξ (σ ,g,A,I) BNMUL 1 Ξ (σ ,g,A,I) SNARKV 1 Ξ (σ ,g,A,I) BLAKE2 F 1PDF Image | ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION
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