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 20% 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 zip file provided. 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=’keyCTR.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 we produced. (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 Please read below. Failure to follow these instructions may result in loss of points!. • For this homework you will be submitting a zip file titled HW05 .pdf to Brightspace containing: – The file x931.py containing your code for Part 1. – The file AES image.py containing your code for Part 2.
– Since this homework requires the use of AES, you may include in your submission additional code files as needed for your AES implementation (or you can put your AES code in one of the above files). – A PDF titled HW05 .pdf containing: ∗ a brief explanation of your code for both programming tasks ∗ your encrypted ppm image from programming task 2 ∗ a one to two paragraph explanation detailing the differences between the encrypted image in this homework versus the one created in DES (HW02). Your answer should include a discussion of the modes used while encrypting the image.
• 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 20% 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 80%.
– 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.
