Project #2: Linear Feedback Shift Register

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1 BHSEC Queens Object-Oriented Programming Spring 2015 Project #2: Linear Feedback Shift Register Introduction1 A register is a small amount of storage on a digital processor. In this project, we will think of a register as a string of N ones and zeros stored in order. A linear feedback shift register (LFSR) is a special type of register used primarily for generating pseudo-random numbers. In this project, we will use the sequence of pseudorandom numbers generated from an LFSR to encrypt and decrypt an image. encrypt decrypt Linear Feedback Shift Register Technical Details Below is an example of an 11-bit LFSR. To go from one pseudo-random number to the next, the LFSR performs a step, which consists of the following two operations: 1. Shift all bits one position to the left. 2. The new rightmost bit is the exclusive or of the old leftmost bit and a bit at a given position, called the tap. Submission 1 Project adapted from 1

2 On Dropbox, create a folder called LFSR. You will submit a total of three java files that should be named XOR.java, LFSR.java, PhotoMagic.java. Grading To get a 60: Successfully implement and test XOR.java. To get a 70: Define the LFSR class. Write the constructor and tostring methods, and test each one. To get an 80: Correctly implement and test the step() method in the LFSR class. To get a 90: Correctly implement and test the generate() method in the LFSR class. To get a 100: Encrypt and decrypt images by correctly implementing the PhotoMagic class. Possible 10 point deduction: You must include a block comment at the start of each Java file containing your name, date of last modification, and a sentence affirming that you did not receive or share your code from anyone else, including via . Amongst your three Java files, you also must include a total of at least 25 inline comments, each of which gives a brief, English description of one or more lines of code that is not obvious. Academic Honesty Policy It is academically dishonest to look at code written by anyone else. You are allowed to talk to other students in class and share ideas. You may ask them if they have experienced particular compiler errors or how they approached a portion of the project. However, you are not allowed to look at code, accept it, or send it to anyone else. The most common incidents of academic dishonesty in computer science involve the electronic sending/sharing of code with other students. Incidents of academic dishonest will be reported to the principal of the school. 2

3 APIs XOR: This class is composed of static methods (i.e. methods that do calculation); therefore, it should not contain any instance variables. A starter XOR.java class has been provided for you. Method Name xor Input Type boolean, boolean Return Type boolean xor String, String String xor int, int int dectobinary int String binarytodec String int main none String[] Comments Implements the exclusive OR function on two bits of data. Assumes that the two input strings are composed only of 0s and 1s. Outputs the bitwise exclusive OR of the two inputs. Your function should work even when the input strings are of different lengths. Outputs the bitwise exclusive OR of two base 10 integers. The integers should be converted to binary and the final result should be converted back to base 10. Make use of the decimaltobinary and binarytodecimal methods that have already been written. Already coded for you. This takes an integer in base 10 and converts it to binary. The input is an integer, and the output is a String of 1s and 0s. Already coded for you. This takes a binary number and converts it to an integer in base 10. The input is a string of 1s and 0s, and the output is an integer. This code has been started for you, and you must finish it. It should test each static method defined in the class. You are expected to comment the main method with expected outputs as is demonstrated in the starter code. 3

4 LFSR: This class is a template for an LFSR object. Your instance variables should all be private, and your methods should all be public. Re-read the LFSR technical details to help you decide what instance variables to use. Method Name Input Type Return Type Constructor String, int none tostring none String step none int generate int int main none String[] Here are some additional hints: Comments The constructor takes the initial seed as a String of 0s and 1s. The length of the register should be the same as the length of the initial seed. The constructor also takes the the position of the tap bit. Returns a string representation of the LFSR, which is simply the sequence of bits stored in the register. Simulates one step (i.e. one shift) of the LFSR. The method should modify the contents of the register and return the new bit that was shifted in. Simulates k steps of the LFSR where k is the input parameter. Returns the nonnegative integer (in base 10) that is represented by the 0s and 1s that have been shifted into the register in those k steps. Instantiates at least one LFSR object and tests all methods of the class. Instantiating and printing an LFSR object This should display: LFSR lfsr = new LFSR(" ", 2); System.out.println(lfsr); The following code will help you determine if your step method is working. This should display LFSR lfsr = new LFSR(" ", 2); for (int i = 0; i < 10; i++) { int bit = lfsr.step(); System.out.println(lfsr + " " + bit); } 4

5 The generate method should use a String to keep track of what bits have been shifted into the LFSR. It should take advantage of the binarytodec static method in the XOR class. To call a static method located in a different class, you write <class name>.<method name>(<parameters>). The following code will help you determine if your generate method is working. It should output LFSR lfsr = new LFSR(" ", 2); for (int i = 0; i < 10; i++) { int r = lfsr.generate(5); System.out.println(lfsr + " " + r); }

6 PhotoMagic: This class only contains static methods. It will use your LFSR and XOR classes to encrypt or decrypt a Picture. Method Name transform main Input Type Picture, LFSR none Return Type Comments Picture Returns a new picture that is the result of transforming the input picture using the input LFSR. How to use the LFSR to transform the picture is described below. String[] Reads in three command line arguments (input image name, initial seed, and the tap number for the LFSR). Displays the resulting encrypted image. You should also consider saving this encrypted image to make sure that your code can successfully decrypt it. Here are a few additional details: Transforming the image. First of all, make sure to create a new Picture object. Do not modify (i.e. overweight) the original image. Second, iterate through each pixel in the original image. For each pixel, do the following: 1. Extract the red component of the original image. Generate an 8-bit number from your LFSR. XOR the red component with the number from the LFSR. This is the new red value in the encrypted image. 2. Extract the green component of the original image. Generate an 8-bit number from your LFSR. XOR the green component with the number from the LFSR. This is the new green value in the encrypted image. 3. Extract the blue component of the original image. Generate an 8-bit number from your LFSR. XOR the blue component with the number from the LFSR. This is the new blue value in the encrypted image. The final product. Note that the second and third arguments can effectively thought of as a way to password protect your image. java PhotoMagic pipe.png Input Should Display Save the output image as Xpipe.png. 6

7 java PhotoMagic Xpipe.png Input Should Display 7

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