Another version of the columnar transposition cipher is the cipher using a key word. In this cipher, we encrypt as follows: Given a key word, we remove all the duplicate characters in the key word. For example, if the key word is ‘SECRET’, we remove the second ‘E’ and use ‘SECRT’ as the key word. To encrypt, we form a table as follows: In the first row, we write down the key word. In the following rows, we write the plaintext. Suppose we want to encrypt the text ‘ATTACKATDAWN’. We make a table as follows:
| S | E | C | R | T |
| A | T | T | A | C |
| K | A | T | D | A |
| W | N | X | X | X |
Then we read off the columns in alphabetical order. We first read the column under ‘C’, followed by the columns under ‘E’, ‘R’, ‘S’ and ‘T’. We get the cipher text TTX TAN ADX AKW CAX. To decrypt, we reverse the process. Note that, since we know the length of the keyword, we can find the length of the columns by dividing the length of the message by the length of the keyword.
Given the ciphertext ‘HNDWUEOESSRORUTXLARFASUXTINOOGFNEGASTORX’ and the key word ‘LANCE’, find the plaintext.
The given ciphertext is: ``` HNDWUEOESSRORUTXLARFASUXTINOOGFNEGASTORX ``` The key word is LANCE. First, remove duplicates (none here), so the key remains LANCE. Step 1: Determine the column order Alphabetically, the letters in the key LANCE are: ``` A C E L N ``` So the column order is: 1. A → 2nd column 2. C → 3rd column 3. E → 5th column 4. L → 1st column 5. N → 4th column Step 2: Determine column lengths Ciphertext length = 42 Keyword length = 5 Rows = ceil(42 / 5) = 9 (since 5 × 8 = 40 < 42, so we need 9 rows) So the table has 9 rows × 5 columns = 45 cells. Ciphertext has 42 letters, so last 3 cells are padding (X or ____ _____ ___ ________ __________.
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Solve the discrete logarithm problem 5x ≡ 22 (mod 47) using Baby-Step, Giant-Step algorithm.
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.
ii) Compute using the logarithm an antilogarithm tables
Apply poker test to the following sequence with level of significane α = 0.05. (4) 1001101000010000101111011 01110100101101100100110.
a) Apply the frequency test, serial test and autocorrelation test to the following sequence at level of significance α = 0.05: 011001110000110010011100
Use Miller-Rabin test to check whether 75521 is a strong pseuodprime to the base 2.
Apply runs test to the following sequence:
1001101000010000101111011
0111010010110110010011010
0110011100001100100111000
1100001101010111101001110
0010001111000001101010010
1000110100000110100101101
1110001001