b) 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.
Let keyword = LANCE → alphabetical order: A, C, E, L, N. Ciphertext length = 40; with 5 columns ⇒ 8 rows, no padding needed (except what may be in text). Split ______ _____ _________ __________ _____ _____ ______ ____.
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Find the inverse of 13 (mod 51) using extended euclidean algorithm.
b) 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 |
Use Miller-Rabin test to check whether 75521 is a strong pseuodprime to the base 2.
Find a recurrence that generates the sequence 110110110110110.
Find a recurrence that generates the sequence 110110110110110.
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.
b) Use Miller-Rabin test to check whether 75521 is a strong pseuodprime to the base 2.