A.Multiply x by x7 + x5 + x3 + 1 in GF(28)mod x8+ x4+x3+x+1.
B. i) Verify that x6 + x is the inverse of x5 + x4+x2+ x +1in GF (28) mod x8+ x4+x3+x+1.
ii) Using the given matrices A and B for the affine transformation AY+ B, (i), and the input byte 0011 0111(37 in hex), compute the corresponding entry in the RijndaelS-box.
![935_Rijndael Algorithm.png](https://www.mywordsolution.com/CMSImages/935_Rijndael%20Algorithm.png)
C. Apply the Shift Row transformation of the Rijndael Algorithm to the following state:
87
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F2
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4D
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97
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EC
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6E
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4C
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90
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4A
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C3
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46
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E7
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8C
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D8
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95
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A6
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D. Use the Blum-Blum-Shub pseudorandom number generator to create a sequence of 6 bits, using p = 11, q = 13 and s = 3 (seed= x0).
E. Use the Chinese Remainder Theorem to solve for x if:
x ≡ 2 (mod 5), x ≡ 3 (mod 13), and x ≡ 1 (mod 7).
F. Given p = 17, q = 11, e = 7, Using the RSA algorithm,
a) Find n and d. Find the public key and private key.
b) Encrypt m = 6.
c) Decrypt c = 2.
G. Compute 6666 mod 11 using Fermat's Little Theorem.
H. Compute 5123 mod 13 using Euler's Theorem.
I. Use Fermat's Test for primality to test the following numbers:
a) n = 31
b) n = 187
J. Complete the following table of values of 2x mod 21:
x
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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15
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16
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17
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18
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19
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20
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2x
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Solve for x:
a) 2x ≡ 8 mod 21 L2(8) =
b) 2x ≡ 11 mod 21 L2(11) =
K. a) Is 2 a primitive root of 7?Explain.
b) Is 3 a primitive root of 7? Explain.