Recall that encryption under the Vigen`ere cipher just corresponds to m shift ci
ID: 3587822 • Letter: R
Question
Recall that encryption under the Vigen`ere cipher just corresponds to m shift ciphers, one for each of the letters in the key word.
(i) (2 marks) Suppose you apply a Vigen`ere cipher using the key word WORD, followed by a second Vigen`ere cipher using the key word CIPHER. Is the result again a Vigen`ere cipher? If yes, provide the resulting key word and explain how you obtained it.
(ii) (4 marks) In general, suppose a Vigen`ere double encryption is performed using first a key word of length m1, followed by a key word of length m2. Is the result again a Vigen`ere cipher? If yes, how do you obtain the corresponding key word, and what is its length?
Explanation / Answer
a. Let the plaintext be: "Plaintext"
Conversion to number equivalent starting at 0: 15 12 0 8 13 19 4 23 19
Number equivalent of "WORD": 22 14 17 3
Divinding plaintext in 4 parts: 15 12 0 8 13 19 4 23 19 0 0 0 (Appneding 3 a's to make a complete set)
Adding WORD: 37 31 17 11 35 31 21 26 41 14 17 3
Cipher text 1: 11 5 17 11 9 5 21 0 15 14 17 3
Dividing in parts of 6: 11 5 17 11 9 5 21 0 15 14 17 3
Number equivalent of CIPHER: 2 8 15 7 4 17
Adding CIPHER: 13 13 32 18 13 22 23 8 30 21 21 20
Ciphertext=13 13 6 18 13 22 23 8 8 21 21 20
Subtracting Ciphertext-Plaintext(to look for a pattern): -2 1 -6 10 0 3 19 15 -11 21 21 20
Adding 26 as required: 24 1 20 10 0 3 19 15 15 21 21 20
There is no pattern there hence we dont get a Vigenere cipher again.
b. We will not get a Vignere cipher always if we use 2 keys of different lengths. We might but we cannot say we always get it. But if the key lengths are same then we get a Vigenere Cipher with key as the sum of the two keys, that is the master key.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.