Explain how using SHA3-512 as the hashing algorithm Alice and Bob can implement the bit commitment algorithm. Make sure you explain how Bob verifies Alices commitment.

below is the bit number:

00011011 01000111 00000011 11111010 (last digit is Heads)

Suppose Alice and Bob are talking on the phone, and Alice flips a coin to determine which of them will get to keep the house after their divorce. Bob will call "heads" or "tails". Alice will reveal the result of the coin flip. The problem with that protocol is that if Bob tells Alice which he chooses (say, "heads"), then Alice can say "It was tails" (regardless of what the coin flip actually was). If instead, Alice reveals the result of the coin flip before Bob reveals which he chose and she says that the result was heads, then Bob can say "I chose heads." Bit commitment is a very clever solution to this dilemma. Alice reveals a quantity that commits her to the coin-flip value but does not reveal to Bob what the value is. Alice chooses a random number R and sends the hash of R to Bob. If the low order bit of R is 0 , Alice is committing to heads, and if 1, to tails. Alice sends hash (R) to Bob. Alice can't change her mind, since she cannot find two numbers that have the same hash. Knowing hash (R) does not help Bob choose. Bob makes the choice of heads or tails, and then Alice must reveal R (the jargon is that Alice opens the commitment)