Apply poker test to the following sequence with level of significane α = 0.05. (4) 1001101000010000101111011 01110100101101100100110.
c) Apply runs test to the following sequence
Let's solve both parts numerically and manually as requested. --- ## Part (a): Poker Test ### Given sequence: ``` 1001101000010000101111011 01110100101101100100110 ``` First, write the full sequence without spaces: ``` 100110100001000010111101101110100101101100100110 ``` ### Step 1: Break into groups of 4 bits (quadruples) Total number of bits = 52 We need non-overlapping groups of 4 bits → total groups = ⌊52 / 4⌋ = 13 Split into: 1. 1001 2. 1010 3. 0001 4. 0000 5. 1011 6. 1101 7. 1011 8. 1010 9. 0101 10. 1011 11. 0010 12. 0110 13. 0110 ### Step 2: Count frequency of each distinct 4-bit group There are $2^4 = 16$ possible 4-bit combinations (0000 to 1111). Now, count ______ ______ _________ _______ _________.
______ ___ _______ ______ ___ _____ ___ __________ __________ ___ ______ ____.
__________ ________ _________ ________ _____ ____ _________.
____ _______ __________ _______ _________ ____ _________ _______.
________ ____ _______ _______ _____ ___ ______.
________ __________ ___ ________ ______ _________ ________.
_________ ___ __________ ___ __________ _______ _____ ______.
___ ________ ___ ______ ______.
___ _________ __________ __________ ______.
_________ _____ __________ _________ ________ ________ _______ _______.
_____ ______ ______ ____ ____ _________ ______ _______.
_______ _________ _______ ______ ________ ______ _______.
_____ ______ _______ __________ _________ ____ ___.
_______ _________ ___ __________ ____.
______ ________ ____ _________ _____.
________ ________ _______ ______ ____ ________ _________ __________ ___ __________ __________.
_____ ________ _____ ___ ________ ____ ________.
_______ ___ ____ ___ _________ _____ ______ ___ _________ ___ __________ _____.
_________ ________ ____ ___ ____.
____ ___ ___ ___ ___ _____ _____ ______.
________ _______ ______ ____ ________ ____ _______ _____ ________ ___ _____.
____ ______ ________ ___ ______ __________ _______ ________ ___ _______ ________ ____.
________ ___ ______ ________ ____ ________.
__________ ____ _________ _________ ________ ________ _____ ______ _________ ____ __________ _______.
_________ __________ _____ ___ ___ ___ __________.
________ ______ _______ _____ _________ ______ ___ ________.
__________ ___ _________ ______ __________ ___.
__________ ______ ______ _________ _____ ___ ____ _________ _____.
____ ____ _________ ____ ____ ________ ________ __________ ______ ______.
__________ ____ ______ _______ _________.
__________ __________ __________ ____ ___ ___ ____ _____.
______ ___ ___ ________ _____.
______ ________ ______ _________ ___ _________ _______ _______ ____ ________ _______ ___.
______ _____ ___ __________ ________ _______ _______.
_______ _____ ____ ____ _____ ______ _________.
________ ______ __________ ______ _____ _______ __________ _________.
_______ ____ ___ _________ ________.
__________ _________ ___ ______ ____ ________ ___ _________.
___ _________ __________ _______ ________ ___ _____ _____ __________.
____ _____ _____ ______ ________ ___.
____ _______ __________ _____ ___.
______ ________ _____ _______ _________ _______ _____ _____ ___ ___.
_________ ___ ______ ______ ___ _________ ___ _____ ____ ______.
____ ____ ____ __________ __________.
_______ ___ ____ _____ _____ ___ ____ ______ ___ ______ ______.
________ _________ _______ __________ ________ _______ _________ __________ _______ _____.
_________ _________ _____ __________ ______ _____ _______ ___ ________ __________ ___ ___.
________ _________ _____ _______ _______ __________ _______ ___ _____ _______ ___.
________ __________ _______ _______ ________ _____ _________ ____ ________ _______.
___ __________ __________ ___ _____ ___ ___ __________.
______ _______ _____ ______ _____ ______ ______ ________ ________ __________ ____.
_____ __________ ________ ____ ________ ________ ______.
___ ___ ___ _______ ________ __________.
____ __________ ____ ___ ___ _______ ________ _____ __________ ______ ___ ____.
___ _____ ___ _______ ____ _____ ________ __________ ___ ________ ______ ___.
_______ _______ _____ _______ _______ _______ ____ ______ ___ _________ ____.
_________ _________ __________ __________ ____ ___ __________ ____ ____.
____ ____ ________ ____ _____ __________ _________ ______ __________.
_____ __________ ______ _________ _________ ___ ______.
__________ ___ ________ _________ _________.
__________ ________ ______ ________ _________.
____ ____ _______ _____ __________ ________ _________ ____ ______ __________ ______ ________.
_________ ________ _____ ________ ________ ___ ______ __________ _______.
_________ ________ __________ __________ _______ ___ __________.
________ ________ _________ ____ ____ _______ _________ _______ ___ ____ __________.
____ ____ ______ ____ ________ ____.
________ _________ _____ _________ ____ _________ _________.
____ _______ ___ ____ _______.
______ _____ ____ ___ __________ ___ _____ _______ ________.
____ ____ ______ _____ ___.
____ _______ ______ ___ _____ _________ _____ ____ ________ _____.
Get Full Answer on WhatsApp
Decrypt the ciphertext 101000111001 which was encrypted with the Toy block cipher once using the key 101010010. Show all the steps.
Use Miller-Rabin test to check whether 75521 is a strong pseuodprime to the base 2.
Considering the bytes 10001001 and 10101010 as elements of the field F2[X]/hg(X)i, where g(X) is the polynomial X 8 +X 4 +X 3 +X +1, find their product and quotient.
a) Find the inverse of 13 (mod 51) using extended euclidean algorithm.
b) A 64 bit key for the DES is given below
i) Check whether the key is error free using the parity bits.
ii) Find the keys for the second round.
Let f (x) = x4 + x + 1 ∈ F2[x]. We represent the field F24 by F2[x]/( f (x)). Let us write γ = x + ( f (x)). The table of values is given below:
| i | γ i | Vector | i | γ i | Vector |
| 0 1 2 3 4 5 6 7 | 1 γ γ 2 γ 3 γ +1 γ 2 +γ γ 3 +γ 2 γ 3 +γ +1 | (0,0,0,1) (0,0,1,0) (0,1,0,0) (1,0,0,0) (0,0,1,1) (0,1,1,0) (1,1,0,0) (1,0,1,1) | 8 9 10 11 12 13 14
| γ 2 +1 γ 3 +γ γ 2 +γ +1 γ 3 +γ 2 +γ γ 3 +γ 2 +γ +1 γ 3 +γ 2 +1 γ 3 +1
| (0,1,0,1) (1,0,1,0) (0,1,1,1) (1,1,1,0) (1,1,1,1) (1,1,0,1) (1,0,0,1)
|
Alice wants to use the Digital Signature algorithm for signing messages. She chooses p = 83, q = 41, g = 2 and a = 3. Alice wants to sign the message M = 20. She chooses the secret value k = 8. Explain the procedure that Alice will use for computing the signature. What information will she send Bob?