the her ng tem como in which transaction records are added to the blockchain in its called blocks via the repeated solut

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The Her Ng Tem Como In Which Transaction Records Are Added To The Blockchain In Its Called Blocks Via The Repeated Solut 1 (58.71 KiB) Viewed 108 times

the her ng tem como in which transaction records are added to the blockchain in its called blocks via the repeated solution of a computationally difficult cryptographie problem. Miners receive a reward every time they successfully solve this problem. Currently, this reward is set at 6.25 bitcoins plus any voluntary) foes that are paid within the transactions To explain the mining process further, it is necessary to have a brief discussion of how data is stored in computers and how this data can be operated on by a hos function Computers store data in bituary (or base2) form, with each sumber consisting of a string of ones and serve. The binary numbers of relevance to Bitcoin are of length 256. Reverting to our normal bue 10 counting systet, there are appreciately 1.16 x 10 binary numbers of length 256 The important thing about a hoh function is that it is easy to calculate its value at a given input, but it is impossible in a practical sense) to even the calculation and produce the input if you know only the output number The process of bitcoin mining involves applying a hush function to the concate nation of three binary numbers: the hash number of the block at the head of the current blockchain, . a hash number that summarises information about the transaction that the miner wants to include in the current block. • A random number, called the mone (a) The hash function he used in Bitcoin maps any set of data stored in binary form to an integer in the set 0,2274 - 11. Let the random variable X denote the output of h when it is applied to some arbitrary input data. What type of distribution should give a good model for X? What are its parameters! (b) What type of random experiment is a miner performing when it applies to the concatenation of the three numbers described above and observes whether the result is less than the threshold (c) Define an appropriate randot variable to describe the outcome of this experi- ment and give its distribution, including defining any wary parameters (d) If the output of the bush function is greater than the threshold , mint adjusts the once and tries again, the performing an independent repeat of the random experiment in (b). If the output of the halfunction is still greater than the miner again adjust the notice and trece more, and so on. Let the random variable N denote the number of times that the miner has to repeat the experiment in (b) before observing an output value that is less than Name the distribution of the random variable N and give the values of its parameter(s) (e) What are the mean and variance of N? (f) Bitcoin miners around the world are currently performing evaluations of the hash function at a total rate of 5/3x10 per second, which means that they perform 6 x 10hash function evaluations in an hour. Let M be the sumber of hash evaluations less than the threshold that occur in 6x 10 hesh function calculations. Name the distribution of the random variable and give the values of its parameter(s). (8) What are the mean and variance of ar? (h) In the original white paper [3] that defined the Bitcoin system, Sets Nakamoto (whose name is a preudonym) recommended that a vendor who has just a cepted payment in Bitcoins for some goods should wait until the transaction has been incorporated in a block and then that block and five more are mined before despatching the goods. Let R be the mumber of times that the randon experiment in (b) has to be performed before six blocks are mined worldwide. Name the distribution of the random variable R. give the value of its parameter(s) and specify its mean and rinn