ECE404_Spring24_HW05

ECE404 Introduction to Computer Security: Homework 05 Spring 2024 Due Date: 5:59pm, February 20, 2024 1 Introduction This homework assignment consists of two part, the first of which is in re- gards to using block ciphers in the counter (CTR) mode. The second is in regards to cryptographically-safe pseudo-random number generators. Both parts of the assignment will require the use of your AES implemenation from homework 05. As always, please read the homework document in its entirety before coming to office hours with your questions. The teaching staff have spent a long time writing the assignment to cover many common questions you might have. 2 Problem 1: AES Encryption In Counter Mode In homework 02, the sudden changes in the image of the helicopter allowed you to see the helicopter’s outline even after encrypting the image. To pre- vent this from happening, encrypt the same helicopter image using AES in the counter mode as described in Section 9.5.5 of the lecture notes [ 2 ]. In a real-world implementation, you would normally choose a random 16 byte number, however for testing and reproducibility purposes, please use a BitVector containing the ASCII encoding of the textstring ‘counter-mode- ctr’. as your initialization vector. Please note that your solution must be an object oriented python program. The bullet points below should give you an idea of how your solution should be written as an extension of the AES class from homework 04. • The method that performs AES encryption in the CTR mode has the following format. Note that this function should be an AES class method . 1 def ctr_aes_image (self , iv , image_file , enc_image) : 2 """ 3 Inputs: 4 iv (BitVector): 128 -bit initialization vector 5 image_file (str): input .ppm file name 6 enc_image (str): output .ppm file name 1

7 8 Method Description: 9 * This method encrypts the contents in image_file using CTR mode AES and writes the encrypted content to enc_image 10 * Method returns void 11 """ • To ensure that the encryption does not take too long, write each block to the output image file as you encrypt it. Do not store the entire encrypted image in a BitVector as you encrypt it (this will cause a noticeable slowdown to the size of the image). • As in homework 02, the encrypted image should still be a viewable image file and as such should have an image header • The command line syntax to invoke your ctr aes image method should be the following: 1 python3 AES.py -i image.ppm key.txt enc_image.ppm • Note here that the key used is the same as the one used in homework 04 • Modify your if name equals main guard to hand the above command line syntax. Example shown below: 1 if __name__ == "__main__" : 2 cipher = AES(keyfile = sys.argv [ 3 ] ) 3 if sys.argv [ 1 ] == "-e" : 4 cipher.encrypt(plaintext = sys.argv [ 2 ] , ciphertext = sys.argv [ 4 ] ) 5 elif sys.argv [ 1 ] == "-d" : 6 cipher.decrypt(ciphertext = sys.argv [ 2 ] , recovered_plaintext = sys. argv [ 4 ] ) 7 elif sys.argv [ 1 ] == "-i" : 8 cipher. ctr_aes_image (iv = BitVector(textstring = " counter -mode -ctr" ), image_file = sys.argv [ 2 ] , enc_image = sys.argv [ 4 ] ) 2

• The command line syntax to invoke your x931 method should be the following: 1 python3 AES.py -r 3 key.txt random_numbers .txt • The argument directly following the ‘-r’ flag indicates the number of random numbers to generate. For this assignment please generate 5 cryptographically secure random numbers. • Note here that the key used is the same as the one used in homework 04 • Modify your if name equals main guard to handle the above command line syntax. Example shown below: 1 if __name__ == "__main__" : 2 cipher = AES(keyfile = sys.argv [ 3 ] ) 3 if sys.argv [ 1 ] == "-e" : 4 cipher.encrypt(plaintext = sys.argv [ 2 ] , ciphertext = sys.argv [ 4 ] ) 5 elif sys.argv [ 1 ] == "-d" : 6 cipher.decrypt(ciphertext = sys.argv [ 2 ] , recovered_plaintext = sys. argv [ 4 ] ) 7 elif sys.argv [ 1 ] == "-i" : 8 cipher. ctr_aes_image (iv = BitVector(textstring = " counter -mode -ctr" ), image_file = sys.argv [ 2 ] , enc_image = sys.argv [ 4 ] ) 9 else: 10 cipher.x931(v0 = BitVector(textstring = "counter -mode - ctr" ), dt = BitVector(intVal = 501 ,size = 128), totalNum = int (sys.argv [ 2 ] ), outfile = sys.argv [ 4 ] ) • Using the given dt and v 0 values, your program should generate the five following numbers: 1 331374527193731622526773163027689011175 2 26263303708022960927873924862754889187 3 6213881104399286406150948824157995508 4 317525806849049200816126045738729418009 5 240080400546264647934751409092776671804 4

4 Submission Instructions Make sure that the program requirements and submission instructions are followed. Failure to follow these instructions may result in loss of points! • For this homework you will be submitting a zip file to Brightspace titled hw05 <last name> <first name>.zip containing: – The modified AES.py file containing your solutions for problems 1 and 2 – A PDF titled hw05 <last name> <first name>.pdf containing: ∗ a brief explanation of your code for both problems ∗ the encrypted image from problem 1 ∗ the 5 pseudo-random numbers generated from problem 2 References [1] NIST-Recommended Random Number Generator Based on ANSI X9.31 Appendix A.2.4 Using the 3-Key Triple DES and AES Algorithms. URL https://csrc.nist.rip/cryptval/rng/931rngext.pdf . [2] ECE 404 Lecture Notes. URL https://engineering.purdue.edu/kak/ compsec/Lectures.html . 5