[SOLVED] Homework 3 – csci 181

1. (30 points) Write a program that generates the RC4 keystream. The program has
three inputs: the integer n (as described in Rc4), the integer l which is the length
of plaintext or ciphertext (the number of characters) and the array of bits which is
the secret key. The output of the program should be an array of bits which is the
keystream (it should have length n ∗ l).
Your program must include two functions. 1) A function called DecimalToBinary(int
number, int n), with two integer inputs number and n. Its output is an array of length
n giving the binary representation of number. So DecimalToBinary(100, 8) should
output [0,1,1,0,0,1,0,0].
2) A function called ConvertBitArraytoInt(Array k, int n) should take an array of
bits and n, and output an array of integers with every n bits converted to its decimal
representation. So ConvertBitArraytoInt([1,0,0,0,0,0,1,1,1,0,0,1], 3) should output [4,
0, 7, 1]. This will be used to convert the secret key input to RC4 to its decimal
equivalent to be used in the RC4 algorithm.
Make sure to include lots of comments so that it is easy to follow your work.
Each function should have a description of what it does.
(a) Submit your code separately.
(b) Suppose you want to encrypt the message M = BACDDAH, with key K= [1 2 3
6] when n =3. Run your program for the these values to generate the keystream.
Write the keystream from your code in your writeup. Then use the keystream
to encrypt M and write down the result in your writeup. (you can leave the
ciphertext as a bit string).
(c) Have your program find the keystream for the inputs: n = 8, l = 24, key=[1, 0,
1, 1, 1, 0, 0, 1 , 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0,
0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1]. Write the keystream in your writeup.
(d) Then use this keystream to find the corresponding ASCII plaintext from the
ciphertext. Write the plaintext in ASCII letters in your writeup. Both the key
and the ciphertext are available in file hw3.txt so you can easily read or copy
from.
[1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0,
1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0,
0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0,
1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0,
1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0,
1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0]
2. (a) (5 points) Consider the CFB mode of operation. Alice has a message to send and
she breaks it into 10 blocks (M1,…,M10) and encrypts them using AES in CFB
mode and sends Bob C1, . . . , C10. Suppose during transmission of ciphertext,
1
there are two bit errors in the transmission of C2 and Bob knows that. Explain
which Mi
’s will Bob correctly decrypt? and which ones are completely wrong?
Briefly explain.
(b) (5 points) We said that If the value of IV used in CBC mode is not reused then
the encryption is CPA-secure (resistant against Chosen plaintext attack). Explain why CBC mode with a repeating IV is not CPA-secure. In order to show
that an ecnryption scheme is not CPA-secure, suppose Eve knows M and M’ and
has observed C and C’ (the corresponding ciphertexts), but does not know which
ciphertext corresponds to which message and she would like to learn this information. Eve can ask Bob to encrypt any message she chooses for her under the
chosen plaintext threat model. Show that Eve can choose a specific message and
ask Bob to encrypt it such that from the ciphertext Eve can determine whether
C was the encryption of M or M’.