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ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION LEDGER BERLIN VERSION 39 Appendix J. Ethash J.1. Definitions. We employ the following definitions: Name Jwordbytes Jdatasetinit Jdatasetgrowth Jcacheinit Jcachegrowth Jepoch Jmixbytes Jhashbytes Jparents Jcacherounds Jaccesses Value Description 4 Bytes in word. 230 Bytes in dataset at genesis. 223 Dataset growth per epoch. 224 Bytes in cache at genesis. 217 Cache growth per epoch. 30000 Blocks per epoch. 128 mix length in bytes. 64 Hash length in bytes. 256 Number of parents of each dataset element. 3 Number of rounds in cache production. 64 Number of accesses in hashimoto loop. J.2. Size of dataset and cache. The size for Ethash’s cache c ∈ B and dataset d ∈ B depend on the epoch, which in turn depends on the block number. Hi (327) Eepoch(Hi) = Jepoch The size of the dataset growth by Jdatasetgrowth bytes, and the size of the cache by Jcachegrowth bytes, every epoch. In order to avoid regularity leading to cyclic behavior, the size must be a prime number. Therefore the size is reduced by a multiple of Jmixbytes, for the dataset, and Jhashbytes for the cache. Let dsize = ∥d∥ be the size of the dataset. Which is calculated using (328) dsize = Eprime(Jdatasetinit + Jdatasetgrowth · Eepoch − Jmixbytes, Jmixbytes) The size of the cache, csize, is calculated using (329) csize = Eprime(Jcacheinit + Jcachegrowth · Eepoch − Jhashbytes, Jhashbytes) on the cache size csize and the seed hash s ∈ B32. J.3.1. Seed hash. The seed hash is different for every epoch. For the first epoch it is the Keccak-256 hash of a series of 32 bytes of zeros. For every other epoch it is always the Keccak-256 hash of the previous seed hash: (331) s = Cseedhash(Hi) x if x/y∈N Eprime(x − 2 · y, y) otherwise (330) Eprime(x, y) = J.3. Dataset generation. In order to generate the dataset we need the cache c, which is an array of bytes. It depends (332) Cseedhash(Hi) = With 032 being 32 bytes of zeros. 032 if Eepoch(Hi) = 0 KEC(Cseedhash(Hi − Jepoch)) otherwise J.3.2. Cache. The cache production process involves using the seed hash to first sequentially filling up csize bytes of memory, then performing Jcacherounds passes of the RandMemoHash algorithm created by Lerner [2014]. The initial cache c′, being an array of arrays of single bytes, will be constructed as follows. We define the array ci, consisting of 64 single bytes, as the ith element of the initial cache: KEC512(s) if i = 0 KEC512(ci−1 ) otherwise c′[i]=ci ∀ iPDF Image | ETHEREUM: A SECURE DECENTRALISED GENERALISED TRANSACTION
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