Section 1: Division Algorithms and Modular Arithmetic Let ????, ????, ????, ???? be integers and ????, ????, ???? are positive integers. Then there exists a unique expression such that ????/???? = ???? ... ????, where d is the divisor, a is the dividend, q is the quotient, and r is the remainder, and the remainder must be positive 0 ????Question 1: What are the quotient and remainder when 101 is divided by 11? Express it using division algorithms. Question 2: What are the quotient and remainder when 101 is divided by 11? The remainder is positive and 0 ???? Question 3: Rewrite 101 is divided by 11 and 101 is divided by 11 using the modular arithmetic notation. Section 2: Introduction to Caesar Cipher The legendary Roman emperor Julius Caesar created a process of making messages secret to protect his military communications. He shifted each letter three letters forward in the alphabet. In a Caesar cipher with a shift key of 3, A becomes D, B becomes E, C becomes F, etc. When the alphabet ends, it cycles around, so X becomes A, Y becomes B, and Z becomes C. Here is how the Caesar Cipher encryption process works: Use integer ???????? from 0 to 25 representing the English alphabet from A to Z. The encryption function is ????(????) = (???? + ????) mod 26. It replaces each integer p in the set {0, 1, 2, ..., 25} by ????????(????????) in the set {0, 1, 2, ..., 25}, where ???? is the shift key. Then find the corresponding English alphabet for each ????(????). ???? is ???? = 0. ????(0) = (0 + 3) mod 26 = 3. A becomes D after encryption. ???? is ???? = 24. ????(24) = (24 + 3) mod 26 = 1. Y becomes B after encryption. Question 4: Encrypt the message "Leave by dawn" using a shift key of 3? To recover the original message, use ????1(????) = (???? ????)mod 26. So, each letter in the coded message is shifted backward k letters in the alphabet, with the first three letters sent to the last three letters when the shift key is 3. This process of recovering the original message from the encrypted message is called decryption. Question 5: Decrypt the messages "XYWNPJ UFHPFLJ F" with a shift key of 5? Provide a step-by-step explanation of the decryption process. Question 6: Please choose your own shift key to encrypt messages "NOW IS THE TIME TO DECIDE". Section 3: Reflection Questions Is the Caeser Cipher encryption method susceptible to cracking? Can the Caeser Cipher encryption be applied to all languages? Provide an example to support your thoughts?