Question 1 (a) The hash function h used in Bitcoin maps any set of data stored in binary form to an integer in the set (

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Question 1 A The Hash Function H Used In Bitcoin Maps Any Set Of Data Stored In Binary Form To An Integer In The Set 1 (55.22 KiB) Viewed 63 times

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Question 1 (a) The hash function h used in Bitcoin maps any set of data stored in binary form to an integer in the set (0,225 – 1]. 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 h to the concatenation of the three mmbers described above and observes whether the result is less than the threshold L? (c) Define an appropriate random variable to describe the outcome of this experi- ment and give its distribution, including defining any necessary parameters. (d) If the output of the hash function is greater than the threshold l, a miner naljusts the nonce and tries again, thus performing an independent repeat of the random experiment in (b). If the output of the hash function is still greater than , the miner again adjusts the once and tries one 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 1. 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? (1) Bitcoin miners around the world are currently performing evaluations of the hash function at a total rate of 5/3 x 101% per second, which means that they perform 6 x 1021 hash function evaluations in an hour. Let M be the number of
hash evaluations less than the threshold that occur in 6 x 1021 hash function calculations. Name the distribution of the random variable M and give the values of its parameter(s). (g) What are the mean and variance of M? (h) In the original white paper [3] that defined the Bitcoin system, Satoshi Nakamoto (whose name is a pseudonym) recommended that a vendor who has just ac 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 number of times that the random experiment in (b) has to be performed before six blocks are mined worldwide. Name the distribution of the random variable R give the values of its parameter(s) and specify its mean and variance.