ASSIGNMENT 2 Cryptography Solution

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Description

You must do this assignment individually and, unless otherwise speci ed, you should follow all the instruc-tions. Graders have the discretion to deduct up to 15% of the value of this assignment for deviations from the general instructions and regulations.

Before starting this assignment, you need to download the les web2.txt and SentenceChecker.java from mycourses. These les should be placed in the same folder as the le you will create called Cryptography.java

If you are working using Dr. Java, you need to open SentenceChecker.java at the same time. However, when you click compile and then run, you must ensure that you run your le Cryptography.java by leaving this window open.

Part 1: 0 points

Part 2, Question 1: 15 points

Part 2, Question 2: 10 points

Part 2, Question 3: 20 points

Part 2, Question 4: 15 points

Part 2, Question 5: 10 points

Part 2, Question 6: 30 points

100 points total

Free pass usage

If you wish to use your \free pass” (see the course webpage for more details), you are required to email the TA who is marking your assignment before the deadline. Please see the table below, which is referenced by the last name of the student, to determine your TA. Note that this is also the person whom you should see if you have questions or other complains about your marks.

1

TA Name

Email Address

Student Last Name Range

Xiaozhong Chen

xiaozhong.chen@mail.mcgill.ca

A-BAN

Stephanie La amme

stephanie.la amme@mail.mcgill.ca

BAO-BUDD

Teng Long

teng.long@mail.mcgill.ca

BUDE-CHR

Andrew Holliday

andrew.holliday@mail.mcgill.ca

CHS-DOW

Carlos Gonzalez Oliver

carlos.gonzalezoliver@mail.mcgill.ca

DOX-GAG

Hua Qun (Robin) Yan

huaqun.yan@mail.mcgill.ca

GAH – HARB

Feras Abu Talib

ta feras@hotmail.com

HARC – JON

David Bourque

david.bourque@mail.mcgill.ca

JOO – KOR

Paul Husek

paul.husek@mail.mcgill.ca

KOS – LI, H

Babak Samari

babak@cim.mcgill.ca

LI,I-MA

Seyyed Mozafari

sh.mozafari@mail.mcgill.ca

MAC – MUR

Egor Katkov

egor.katkov@mail.mcgill.ca

MUS – PARE

Chenghui Zhou

chenghui.zhou@mail.mcgill.ca

PARF – RENT

Jonathan Campbell

jonathan.campbell@mail.mcgill.ca

RENU – SHIM

Neeth Kunnath

neeth.kunnath@mail.mcgill.ca

SHIN – TANG

Ayush Jain

ayush.jain@mail.mcgill.ca@mail.mcgill.ca

TANN – WANG, Q

Tzu-Yang (Ben) Yu

tzu-yang@mail.mcgill.ca

WANG, T – YANI

Mohammad Patoary

mohammad.patoary@mail.mcgill.ca

YAY- Z (end)

Part 1 (0 points): Warm-up

Do NOT submit this part, as it will not be graded. However, doing these exercises might help you to do the second part of the assignment, which will be graded. If you have di culties with the questions of Part 1, then we suggest that you consult the TAs during their o ce hours; they can help you and work with you through the warm-up questions.

Warm-up Question 1 (0 points)

Write a method printTypeOfChar. This method should take as input a char and print the type of character. If the char is upper case, your method should print UPPERCASE. If the char is lower case, your method should print LOWERCASE. If the char is any other symbol, your method should print SYMBOL. Note that it is not necessary to make 52 di erent cases if you consider the order of the Unicode chart and the fact that you can use the < and > operators on them.

Warm-up Question 2 (0 points)

Write a method countUppercase. Your method should take as input a String and return an int representing the number of upper case letters in the String. Now add a main method where you use the Scanner class to read a String from the user and call your method, outputting the returned result.

Warm-up Question 3 (0 points)

Write a method toUpperCase which takes as input a String and returns another String which is the original String but with all lower case letters converted to upper case. Any letters that are not lower case should remain the same. Do NOT use any methods in the Character class or the .toUpperCase() method in the String class

For example the input String of \Hi!” should become \HI!”

Warm-up Question 4 (0 points)

Write a method reverseString which takes as input a String and returns the string in reverse order. For example if the input String is \Comp 202 is awesome” the result should be \emosewa si 202 pmoC”

Hint: Use a new String called reverse and initially store into it the empty String. Then read the input String in reverse by using the method .charAt(int i) to get a speci c element.

Warm-up Question 5 (0 points)

A prime number is a positive number whose only even divisors are 1 and itself. Write a method isPrime

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that takes as input an integer n and returns a boolean representing whether n is prime or not. Make sure to handled cases where the integer is negative. (Your method should return false in these cases.)

Warm-up Question 6 (0 points)

Write a method firstPrimeNumbers which takes as input an int n and returns an int[] . The int[] should contain the rst n prime numbers.

Warm-up Question 7 (0 points)

Practice using the utility code we have provided by calling the method countEnglishWords() from the SentenceChecker class. To ensure things work, put all les (web2.txt, SentenceChecker.java, and your new class) into the same directory. You can then leave both SentenceChecker.java and your new class open at the same time in Dr. Java.

The method countEnglishWords takes as input a String and returns how many English words are part of it, using a list of words provided in the le web2.txt. Try calling this method to check how many English words are in the sentence The laydee hit teh man wit the bay bee.

Warm-up Question 8 (0 points)

Practice using the Random class: Question four requires using the Random class. In this warmup question, you will generate random numbers.

Write a method that takes as input an int n and an int max and returns an int[]. The array you return should be an array of size n and lled with n random numbers between 0 and max, counting 0, but not counting max. Assume max is a positive number.

See the instructions within question 4 for help using Random class.

Warm-up Question 9 (0 points)

Same question as before except your method should now take as input three values: int n , int min, and int max. Instead of ranging from 0 to max, you should range from min to max.

Again, you may assume both min and max are positive numbers as well as assume that min is less than max.

Warm-up Question 10 (0 points)

x is a factor of y if y is a multiple of x. as input an int n and return an int[]

Write a method calculateFactors. The method should take containing all the factors of the number n

Warm-up Question 11 (0 points)

Write a method that takes as input an array of Strings and prints all of the Strings on separate lines.

Warm-up Question 12 (0 points)

Create a le called Counting.java, and in this le, declare a class called Counting. This class should ask the user when the computer should stop counting.

When should I stop counting to?

10 <—- User typed this

I am counting until 10: 1 2 3 4 5 6 7 8 9 10

Warm-up Question 13 (0 points)

For this question you have to generalize the last question. The user will give you the number they want the computer to count up to and the step by which it will do so.

When should I stop counting to?

25 <—-

Which step should I use?

3 <—-

I am counting to 25 with a step of 3:

147101316192225

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Warm-up Question 14 (0 points)

This program should ask the user how big she wants a square to appear. Using two loops, you should be able to describe the outline of a square like the following.

How big do you want your square to be?

10 <—- User typed this

##########

# #

# #

# #

# #

# #

# #

# #

# #

##########

N.B. It is normal that it does not output a perfect square as the width and the length of the characters are not equal.

How would you extend your program to output a rectangle with width and length speci ed by the user?

Part 2

The questions in this part of the assignment will be graded. All of your code in this assignment should go into a class Cryptography.

Beginning in this assignment, a 75% non-compilation penalty will apply. This means that if your code does not compile, you will receive a maximum of 25% for the question. If you are having trouble getting your code to compile, please contact your instructor or one of the TAs or consult each other on the discussion boards.

For this assignment, you will be writing several methods to help you practice using arrays. As such you are not allowed to use any methods from the Java library class Arrays.

Encrypting a String With a Shift Schema

Question 1: Encrypting a String with a Caesar shift (15 points)

A simple way to encrypt things is by shifting all of the letters by a xed amount n. This is known as a Caesar shift. The letters are \cycled” and all characters other than letters (e.g. numbers, punctuation, etc. remain the same).

For example, when employing a Caesar shift of 3 on the String go Rangers! you would get jr Udqjhuv!. Note that the letter ‘j’ comes three letters after the letter ‘g’ in the alphabet. The letter ‘U’ comes three letters after the letter ‘R’, and is upper-case, because the letter ‘R’ in this example is also upper case. We consider the alphabet of upper-case letters to be a loop (a shift of 3 applied to the letter ‘Z’ would give ‘C’), and similarly with lower-case letters (a shift of 3 applied to the letter ‘z’ would give ‘c’).

Julius Caesar famously used this method of encoding messages. At the time, very few people were literate and those that could read simply assumed it was a foreign language! If interested, you can read more about it at https://en.wikipedia.org/wiki/Caesar_cipher#History_and_usage

Write a method caesarEncrypt which takes as input a String originalMessage and an int shift and returns the String created by applying a shift of size shift to the original message. Note that your

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method should work with all non-negative integers. That is, you can assume that the input will never be smaller than zero. In the case that shift is greater than 25, you should cycle over the alphabet an additional time. For example the letter a shifted by 30 is the same as the letter a shifted by 4, which would be e.

Two useful methods that you can use are charAt() and length() from the String class. In order to use them, write the name of the String type variable, then a dot, and then the method name followed by arguments. For example, if you have:

String s = ‘‘hello’’

then

s.charAt(x)

will return the xth character in s. The counting starts from 0. So for example:

System.out.println(s.charAt(0))

will print the letter h.

System.out.println(s.charAt(3))

will print the letter l.

System.out.println(s.charAt(5))

will give you a run time error because the String s does not have a character at index 5.

In addition, you can obtain the length (number of characters) of a String by using the method .length(). To do this, for example, write

int length = s.length()

In order to add a number to a character and have the result be a character, you will have to be careful with type-casting. For example:

char d = (char)(‘A’ + 3)

will will store the unicode for the letter ‘D’ in the variable d. Clari cation: The casting must be done after the addition in order for the types to work properly.

For this question, do not use any methods from the Java Character class. Additionally you may not use any methods from the String class other than those listed above (charAt and length).

Question 2: Decrypting a String (10 points)

Write a method caesarDecrypt which takes as input a String encoded and an int shift and returns the String created by applying a reverse shift of shift to the original message.

caesarEncrypt() is the inverse of caesarDecrypt(). This means that for any String s, caesarDecrypt(caesarEncrypt(s)) is the same as s

Hint: Can you use the method encrypt() that you wrote in the previous question to help for this part?

Question 3: Cracking the code! (20 points)

Write a method crackCipher() which takes as input a String encoded and an int numberLetters. It should then call the method caesarDecrypt() with all di erent shifts from 0…numberLetters 1. After getting the result from this call, it should call the method countEnglishWords() given in the le SentenceChecker. This method takes as input a String and outputs the number of English words it contains. The method provided to you will take care of things such as removing punctuation. This means, for example, that he!!!!!!llo will count as one English word and hello, world 🙂 counts as two English words.

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Your method should return a String representing the message decryption with the most English words.

In the case of a tie, you can pick whichever one you like.

To make this work correctly, you will have to make sure that you put the le web2.txt as well as SentenceChecker.java in the same directory as your code. Both of these les can be found on My-Courses. To compile your code from the terminal, you should type javac SentenceChecker.java Cryptography.java. See the instructions in the warm up question if you are having trouble using this method.

Generating a better code using permutations

Caesar’s method of encryption is clearly insecure with computers. Now we will generate a more robust code, that is much more di cult to crack.

The rst step is to shu e letters in an array.

Question 4: Shu ing (15 points)

Write a method shuffle that takes an array of characters as input and returns void. This method should shu e the elements in the array (remember that arrays are reference types, so any changes you make to the contents of the array in the method will apply in other methods as well). If you are having confusion over this, please read the class notes and examples or see a TA or instructor.

One way (and the way you will use on this assignment) to shu e the characters of the array is by repeatedly choosing two random elements (more on this below) and swapping them with each other. For an array of length n, you should use n4 random swaps.

To generate the two random numbers you will use Java’s Random class. First, import the class, which is part of java.util.

Then, to create a variable of type Random (a random number generator) you need to write the following line of code. To generate good random numbers, it is absolutely critical that the below line only be executed one time throughout your method. Otherwise, you will always generate the exact same number.

Random generator = new Random(12345);

Note that the number 12345 is not a suggestion. We require that all students use the same seed in order to simplify the marking process. The seed determines the order of the pseudo-random numbers. You will notice that if you run your code repeatedly, you will obtain the same sequence of numbers every time. While this is sub-optimal for generating true random numbers, it is very helpful in writing code with reproducible behaviour, and in grading assignments. 🙂

Once you have created the Random object, you should use the random number generator to generate a random number between 0 (inclusive) and n (exclusive) with the method generator.nextInt(n);.

Question 5: Generating a Random Mapping (10 points)

Still in the same class, write a method generatePermutation() which takes no input and outputs a random char[] . The char[] should be created and lled according to the following rules.

  1. It should have size of exactly 26

  1. It should contain each upper case English letter once and only once

Hint: You should use the shuffle() method that you wrote previously in order to do this.

Question 6: Encrypting Using a Random Permutation (30 points)

Write a method permuteEncrypt() which takes as input a String input and returns a String which represents an encoded String. You should do this by rst calling the method you wrote in the previous

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section generatePermutation(). Then, for every letter, you can gure out the mapping of the ith letter, by guring out the value of the ith element in the array.

For example, the letter A is the 0th letter in the alphabet. The character to which A maps is stored in the 0th element of the returned random char array.

Note that A is considered the 0th letter, B the 1st letter, etc until Z, which is the 25th letter.

Note that the generatePermutation method you wrote returns an array with only uppercase letters in it. Your method must work on lowercase letters, but it is allowed that the lowercase letters become uppercase. Any thing that is not a letter to begin with should keep the same value.

If you encrypt this way, it is extremely di cult to guess the code. Spiritual Growth Question (not for credit): How many possible encryptions are there in the rst method of encoding using shifts? How many possible encryptions are there in the random permutation scheme?

What To Submit

You have to submit one zip le with all your les in it to MyCourses under Assignment 1. If you do not know how to zip les, please ask any search engine or friends. Google might be your best friend with this, and a lot of di erent little problems as well.

These les should all be inside your zip.

Cryptography.java

confession.txt – You should write in this le any information that you think is useful for the

TA to mark the assignment. This should include things you were not sure of as well as parts of

your code that you don’t think it will work. Of course, like a confession, this will draw the TA’s

attention to the part of your code that doesn’t work, but he/she will probably be more lenient

than if he/she has to spend a lot of time looking for your error. It demonstrates that even though

you couldn’t solve the problem, you understand roughly what is going on.

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