1. () Given finite field Z17 and two elements a = 10 Î Z17 and b = 12 Î Z17. Please compute a + b,...

Question

1.  () Given finite field Z17 and two elements a = 10 Î Z17 and b = 12 Î Z17. Please compute a + b, a - b, a´b, and a / b.   2.  () Given Z7, irreducible polynomial m(x) = x3 + 3, and two elements f(x) = 2x2 + 1Î GF(73) and g(x) = 3x+2Î GF(73). Please compute f(x) + g(x), f(x) – g(x), f(x) ´g(x), and f(x) / g(x).   3.  Given matrix M =  and column vector C = , consider the affine transformation f(v) = M×v + C over Z11where v is2-dimensional column vector.  XXXXXXXXXXpoints) Compute f(v) for v = . (2)  (Bonus 10 points) The inverse of f is also an affine transformation. Compute the matrix and column vector of f-1.   4.  Given the original AES encryption and decryption:  Consider the variations AES-V1 and AES-V2.  XXXXXXXXXXAES-V1 only has the initial AddRoundKey. Please design an attack against AES-V1. You need to specify the attack objective, type ofattack, and the detailed cryptanalysis.  XXXXXXXXXXAES-V2 only has the initial AddRoundKey and the next one round of encryption (i.e. Round 1). Please design an attack against AES-V2.   5.  Problem 6.4 ():With the ECB mode,if there is an error in a block of the transmitted ciphertext,onlythe corresponding plaintext block is affected. However, in the CBC mode, this errorpropagates. For example, an error in the transmittedC1 (Figure 6.4) obviouslycorrupts P1 and P2. (1)  Are any blocks beyond P2 affected? (2)  Suppose that there is a bit error in the source version of P1. Through how many ciphertext blocks is this error propagated? What is the effect at the receiver?   6.  Problem XXXXXXXXXXIn discussing the CTR mode, it was mentioned that if any plaintext block that is encrypted using a given counter value is known, then the output of the encryption function can be determined easily from the associated ciphertext block. Show the calculation.

Robert · Accepted Answer

1. 
Given : 
a=10, b=12 
Modulo 17 
So 
i)  
(   )       (     )
(  )       (  )        ( )
(  )
So  (   )         
ii) 
(   )       (     )
(  )       (     )        (  )
(  )
So  (   )          
iii) 
(   )       (     )
(   )       (    )        ( )
(   )
So  (   )
2. 
i) 
 ( )  (    )     
So 
(    )    
i)  
 ( )   ( )  ((      )  (     ))
 ( )   ( )  (          ))      
 ( )   ( )
ii)  
 ( )   ( )  ((      )  (     ))
 ( )   ( )  (       (     )         ))      
 ( )   ( )
iii)  
 ( )   ( )  ((      )  (     ))
 ( )   ( )  (               )
 ( )   ( )  (                  )      
 ( )   ( )  ( (    )            )      
By m(x) 
 ( )   ( )  (  ( )            )      
 ( )   ( )  (          )      
iv)  
 ( )  ( )  ((     ) (    ))
 ( )
 ( )
 (
 
 

 
)
 

    

3. 
M = (
  
  
), C = (
 
 
),
f(v) = Mv + C 
1. v = (
 
 
). 
So
f(v) = Mv + C 
 ( )  (
  
  
) (
 
 
)  (
 
 
)
 ( )  (
  
 
)  (
 
 
) 
 ( )  (
  
  
)
4.  
1. AES-V1 
When AES has initial round key
Attack 
Attack Objective:  To design a method that could get data out of provided data after 
rearrangement using initial add key round. 
Type of Attack: 
Brute force attack : We can use Brute force for designing attack. Brute force includes hit and trial 
method. We need to try every possible solution to design attack. It may be needing some 
iterations. 
Detailed Cryptanalysis 
The ultimate goal of the cryptanalyst is to derive the key so that all ciphertext can be easily 
deciphered. A brute-force attack is one way of doing so. In this type of attack, the cryptanalyst 
tries every possible combination until the correct key is identified. Although using longer keys 
make the derivation less statistically likely to be successful, faster computers continue to make 
brute-force attacks feasible. Networking a set of computers together in a grid combines their 
strength, and their cumulative power can be used to break long keys.
2. AES-V2 : The initial Add Round Key and the next one round of encryption (i.e. 
Round 1).
Attack Objective:  To design a method that could get data out of provided data after two 
steps that is rearrangement using initial add key round and encryption step. 
Type of Attack:  DPA (Differential Power Analysis attack)
Detailed Cryptanalysis 
 Collect Data  
 Use DPA to attack the two low-order bytes of the counter (first round).

1. () Given finite field Z 17 and two elements a = 10 Î Z 17 and b = 12 Î Z 17 . Please compute a + b , a - b , a ´ b , and a / b . 2. () Given Z 7 , irreducible polynomial m ( x ) = x 3 + 3, and two...

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