COS 126

Linear Feedback Shift Register
Programming Assignment

Write a program that produces pseudo-random bits by simulating a linear feedback shift register, and then use it to implement a simple form of encryption for digital pictures.

LFSR review.  A linear feedback shift register is a register of bits that performs discrete step operations that

A LFSR has three parameters that characterize the sequence of bits it produces: the number of bits N, the initial seed (the sequence of bits that initializes the register), and the the tap position tap. As in the example in Lecture 1, the following illustrates one step of an 11-bit LFSR with initial seed 01101000010 and tap position 8.


LFSR data type.  Your first task is to write a data type that simulates the operation of a LFSR by implementing the following API:

public class LFSR
public             LFSR(String seed, int tap)  //  create LFSR with the given initial seed and tap
public         int step()                      //  simulate one step and return the least significant (rightmost) bit as 0 or 1
public         int generate(int k)             //  simulate k steps and return k-bit integer
public      String toString()                  //  return a string representation of the LFSR
public static void main(String[] args)         //  test all of the methods in LFSR

To do so, you need to choose the internal representation (instance variables), implement the constructor, and implement the three instance methods. These are interrelated activities and there are several viable approaches.

A client to encrypt and decrypt images.  Your final task is write a LFSR client that can encrypt and decrypt pictures, by implementing the following API:

public class PhotoMagic
public static Picture transform(Picture picture, LFSR lfsr)  //  transform picture using lfsr
public static    void main(String[] args)                    //  read in the name of a picture and the description of an LFSR
                                                             //  from the command-line and encrypt the picture with the LFSR
The Picture class should already be available on your system. It is part of the stdlib.jar file that was required to use the Std* classes from previous weeks.

Useful files.   Download the contents of the directory lfsr to your system, or this .zip of the directory. It contains a template file, which you can either use to get started (see the checklist), or you can delete it and start from scratch. It also contains pipe.png, the readme.txt file, and some other encrypted images.

Submission.   Submit and Also, submit a readme.txt file and answer the questions.

Extra credit.  Using a short binary password is weak protection and using a long one is inconvenient. For extra credit, write a client with the same API as, but use an alphanumeric password instead of a binary one. Assume that the password contains only characters from the 64-character alphabet:

String base64 = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
Interpret an N-character alphanumeric password as a 6N-character binary password, where the ith character in the 64-character alphabet is expanded to the 6-bit binary representation of i. For example, the 10-character alphanumeric password OPENSESAME corresponds to the 60-character binary password 001110001111000100001101010010000100010010000000001100000100.

To earn extra credit, you must work modularly. Do not copy huge chunks of code from to Instead, call PhotoMagic.transform().

Challenge for the bored.  Write a program that the name of an encrypted picture and the number of bits N in the password as command-line arguments, tries all possible binary passwords of length N and all possible taps, and decrypts the picture.

Hint: all but the correct seed and tap will produce pseudo-random colors, so you can track the frequencies of each 8-bit value and pick the seed and tap that results in the frequencies that deviate the most from 128.

Warning: this program can take a very long time to run; we recommend debugging it using pictures transformed with binary passwords of length 5 or 6.

This assignment was created by Robert Sedgewick.
Copyright © 2008.