Learning Goal: I’m working on a computer science question and need an explanation and answer to help me learn.
1. Show that for all possible binary bit values of Mi and Si, Mi + Si mod 2 = Mi XOR Si (10 points)
2. Given a 3 bit key K=101 and a 3 bit initial seed S=001, encrypt M=11001010. Consider LFSR based stream cipher and show your work. (20 points)
3. Write one paragrapg note on RC4 (use web resources) (10 points)
S 1 through S 6 can be computed by XORing 6 bit message with the first 6 bits of ciphertext.Then formulate the following equations for S 4 through S 6 :
S m+1= S m × K m + S m-1 × K m-1 + …… S 2 × K 2 + S 1 × K 1 mod 2
S m+2= S m+1 × K m + S m × K m-1 + …… S 3 × K 2 + S 2 × K 1 mod 2
S m+3= S m+2 × K m + S m+1 × K m-1 + …… S 4 × K 2 + S 3 × K 1 mod 2
Number of units in the shift register determines the value of m.
Many of you may not feel comfortable solving systems of equation. You can apply the following brute force method:
Check, all possible sets of values of K 1, K 2 and K 3 listed in the following table to find out which set satisfies all the above equations (i.e., makes both sides of the equations equal) :
The attacker also knows that the plaintexts are composed of only English capital letters without any punctuations or space, and that part of the plaintexts contains the word: “PRESIDENT”. He was able to recover both the plaintexts. Show, how. (Points 25)
Hints: Slide ASCII for “PRESIDENT” over C1⊕C2 and XOR them. You can start from the left and keep sliding right, or start from the right and keep sliding left until you find a meaningful 9 letter phrase (since PRESIDENT is a 9 letter word). Once you retrieve the partial plaintexts, use your intuition and linguistic observations to complete the rest as much as possible.
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