Problem 1 (Authentication): Consider the following authentication protocol, which uses a classical cryptosystem. Alice generates a random message r, enciphers it with the key k she shares with Bob, and sends the enciphered message {r}k to Bob. Bob deciphers it, adds 1 to r, and sends {r + 1}k back to Alice. Alice deciphers the message and compares it with r. If the difference is 1, she knows that her correspondent shares the same key k and is therefore Bob. If not, she assumes that her correspondent does not share the key k and so is not Bob. Does this protocol authenticate Bob to Alice? If so, Why? Otherwise, explain why not.

answer: when the substance contain the two parts (polar and non-polar) like soap.

explanation:

soap is produced from the basic hydrolysis of ester "saponification", it is considered as a salt of hydrocarbons. the soap molecule contains the two parts: a polar group   (-coo-na+) and a non-polar group (r-hydrocarbon part). the polar group is called the head and the tail is the non-polar group. the polar group is hydrophilic in nature (water loving) and the non-polar group is hydrophobic in nature (water repelling).the polar/non-polar nature of a substance is useful that it can dissolve the non-polar substances by the polar part and also can dissolve the polar substances by the non-polar part. it commonly used in detergents and soaps.