Use the following information for the Question below: As of early 2022, the global bitcoin hashrate is 160∗1018 hashes per second. The Antminer S19 can compute 110 TH/s = 73∗1012 hashes per second. It costs $2600 and consumes 3.25kW when operating.   How many such devices would be needed in order to reach a 1% chance that you will receive the mining reward?

For hash functions, to avoid attacks based on the birthday paradox, it is required to have large number of output bits. Why are shorter length outputs used in MAC?

Use the following information for the Question below As of early 2022, the global bitcoin hashrate is 160∗1018 hashes per second. The Antminer S19 can compute 110 TH/s = 73∗1012 hashes per second. It costs $2600 and consumes 3.25kW when operating.   Suppose the devices required to achieve 1% market share as outlined in Question 14 above operate for one year. If the energy used to power the miners comes from a natural gas power plant, approximately how many kilograms of CO2 will be generated? Finally, this CO2 generated is equivalent to how many passenger flights between Dallas and London? Please cite sources for how you are calculating the CO2 amounts.