# ECE 404 Homework #5 solution

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## Description

In this homework, you will become familiar with the ANSI X9.31 pseudo-random number generator (PRNG) and the Counter (CTR) mode for using block ciphers.
Both parts will require the use of your AES implementation from Homework 4. If for some
reason you did not finish Homework 4 and are unable to finish your AES implementation by the
deadline for Homework 5, you may use the implementation found in the PyCryptoDome/PyCrypto
package. If you import this package in your code, you will incur a 40% penalty to your
homework score.
Part 1: X9.31 Pseudo-Random Number Generator
Section 10.6 of Lecture 10 talks about the ANSI X9.31 cryptographically secure PRNGs. Your
task is to implement a more modern version of this PRNG with the following requirements:
1. Instead of using 3DES for encrypting the 64-bit vectors as indicated in the lecture notes, use
your implementation of AES from Homework 4 to encrypt 128-bit vectors. By the way, AES
is indeed used instead of 3DES in the newer implementations of X9.31.
2. Your script needs to define the PRNG function in the following manner:
def x931(v0, dt, totalNum, key_file):
’’’
* Arguments:
v0: 128-bit BitVector object containing the seed value
dt: 128-bit BitVector object symbolizing the date and time
totalNum: The total number of random numbers to generate
key_file: Filename for text file containing the ASCII encryption key for AES
* Function Description:
This function uses the arguments with the X9.31 algorithm to generate totalNum
random numbers as BitVector objects.
Returns a list of BitVector objects, with each BitVector object representing a
random number generated from X9.31.
’’’
3. For the sake of simplicity, you can use in this homework the same dt vector for each random
number generated in a given call.
4. Obviously, dt is supposed to contain the date and time. But for testing purposes, you can set
it to a predetermined value (hence, dt is a specifiable argument to the x931(…). function).
How Your X9.31 Code Will Be Tested
Your x931 function will be tested with a script similar to the one below:
import x931
from BitVector import *
v0 = BitVector(textstring=’computersecurity’) #v0 will be 128 bits
#As mentioned before, for testing purposes dt is set to a predetermined value
dt = BitVector(intVal=501, size=128)
listX931 = x931.x931(v0,dt,3,’keyX931.txt’)
#Check if list is correct
print(’{}\n{}\n{}’.format(int(listX931[0]),int(listX931[1]),int(listX931[2]))
The script would be run on its own, and can be found in the Homework Section of the ECE 404
website. The correct result for this script (as well as the keyX931.txt file) is also provided .
Part 2: AES Encryption in Counter Mode
In Homework 2, the sudden changes in the image of the helicopter allowed you to see the helicopter’s
outline even after encrypting the image. To prevent this from happening, implement AES in CTR
mode as described in Section 9.5.5 of the lecture notes. Use your implementation of AES from
Homework 4 as a starting point. In the real world, you would possibly use a random number
generated from X9.31 as the initialization vector. But for testing purposes, you can use a BitVector
containing the ASCII encoding of the textstring ‘computersecurity’ for the CTR mode initialization
vector.
1. The encryption function should have the following format:
def ctr_aes_image(iv, image_file=’image.ppm’, out_file=’enc_image.ppm’,
key_file=’key.txt’):
’’’
* Arguments:
iv: 128-bit initialization vector
image_file: input .ppm image file name
out_file: encrypted .ppm image file name
key_file: Filename containing encryption key (in ASCII)
* Function Description:
This function encrypts image_file using CTR mode AES and writes the encryption
to out_file. No return value is required.
’’’
2. For those who are unaware: the above Python syntax for function definition that involves the
equals sign in the arguments is for indicating the default arguments for a Python function
definition. For example, when calling ctr aes image(…), if no value is specified for the
image file argument, the value ’image.ppm’ is used by default.
3. 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 slowdown due to the size of the image).
4. As in Homework 2, the encrypted image should still be a viewable image file and as such
should have an image header (But since you have used the CTR mode encryption, the
contents of the original image should be imperceptible in the encrypted image).
How Your CTR AES Code Will Be Tested
Your ctr aes image function will be tested with a script similar to the one below:
from AES_image import ctr_aes_image
from BitVector import *
iv = BitVector(textstring=’computersecurity’) #iv will be 128 bits
ctr_aes_image(iv,’image.ppm’,’enc_image.ppm’,’keyCTR.txt’)
Further testing can be done by comparing your encrypted image with the encrypted image found
on the ECE 404 homework page (which is an encrypted version of the helicopter image from
homework 2). You can use
xxd enc image.ppm | less
to view the encrypted image data in hexadecimal and compare with what encrypted image your
code generates (you can also use the diff command to see if the two images are identical).
Submission Instructions
• For this homework you will be submitting 2 files electronically. Your submission must include:
– The file x931.py/pl containing your code for Part 1.
– The file AES image.py/pl containing your code for Part 2.
– Since this homework requires the use of AES, you may include in your submission
code in one of the above files).
• As previously mentioned, you can use the AES implementation in PyCryptoDome or PyCrypto if you are somehow unable to finish implementing AES. However, if you import either
package in your code, you will incur a 40% penalty to your homework score. As an example, if you would otherwise get 100% for this homework, but used the PyCryptoDome/PyCrypto implementation of AES, your final grade for this homework would instead be 60%.
– For those who are curious: PyCrypto was first released around 2002, and for many years
has been used in Python applications for cryptographic needs. However, PyCrypto is
no longer actively maintained by its creator as vulnerabilities have been discovered
in its code. PyCryptoDome is a “drop-in replacement” for PyCrypto that is actively
maintained.
• In your program file, include a header as described on the ECE 404 Homework Instructions.
• If using Python, please denote the Python version in your code with a shebang line (e.g.
#!/usr/bin/env python3)