1. Computer and Data Security 4th Class
lec.3

2. Polyalphabetic
In this type of cipher, the relationship between the ciphertext substitution for plaintext symbols is variable. more than one substitution alphabet is used. This makes cryptanalysis used more alphabets to guess.
Polyalphabetic substitution cipher systems includes
Vigener cipher
Beaufort cipher
Running key cipher

3. Vigenere cipher
Popular form of periodic substitution cipher based on shifted alphabets is called Vigenere cipher.
The Vigenere cipher uses multiple mixed alphabets, each is a shift cipher.
The key is m letters long (usually a word).
Use each shift in turn to encrypt one letter, repeating from the start after m letters in the plaintext.
The number of possible keys in the Vigenere Cipher is 26m
Hw// Explain why the number of possible keys in the Vigenere Cipher is 26m
Define K=ki...kd, where ki (i = 1, , d) gives the amount of shift in the ith alphabet; that is,
C = (p + ki) mod n.

4. The encipherment of the word RENAISSANCE under the key BAND is shown next:
M =RENA ISSA NCE
K =BAND BAND BAN
Ek(M ) =SEAD JSFD OCR .
In this example, the first letter of each four-letter group is shifted (mod 26) by 1, the second by 0, the third by 13, and the fourth by 3.
Ex2: m = 5 and the key is fishy. Find the ciphertext for the following plaintext: ericthehalibut.
Ciphertxt: ?
Ex3: m = 6 and the key is cipher. Find the plaintext for the following received message: vpxzgiaxivwpubttmjpwizitwzt.

5. Beaufort cipher
This cipher similar to Vigener cipher ,where, the key is specified by a sequence of the letters, K=k1, k2,……..,kd, where ki(i=1,2,….,d) gives the amount of shift in the ith alphabet.
Beaufort cipher can be computed as following:
Ci = (ki - pi) mod n.
Note that the same function can be used to decipher; that is, for ciphertext letter ci,
pi = (ki - Ci) mod n.
encrypt the following message using key BAND
M =RENA ISSA NCE
K =BAND BAND BAN
EK(M ) =kw……

6. H.W encrypt the following message using key BAN M =RENA ISSA NCE
K =BAND BAND BAN
EK(M ) =

7. Variant Beaufort cipher
Variant Beaufort cipher is equivalent to a Vigenere cipher.
The Variant Beaufort cipher is inverse of the Vigenere cipher.
The Variant Beaufort cipher uses the substitution
C = (pi - ki) mod n.
encrypt the following message using key BAN
M =RENA ISSA NCE
K =BAND BAND BAN
EK(M ) =
DK(M ) =

8. Running key cipher
The security of a substitution cipher generally increases with the key length. In a running-key cipher, the key is as long as the plaintext message (assuming the key does not repeat).
One method uses the text in a book (or any other document) as a key sequence in a substitution cipher based on shifted alphabets (i.e., a nonperiodic Vigenere cipher).
The key is specified by the title of the book and starting position (section, paragraph, etc.).
Given the starting key: "Cryptography and Data Security, Section 2.3.1, paragraph 2," the plaintext message "THE TREASURE IS BURIED...“ is enciphered as
M = THETREASUREISBURIED...
K = THESECONDCI PHERISAN...
EK(M ) = MOILVGOFXTMXZFLZAEQ...

9. Cont…
Because perfect secrecy is possible using key sequences as long as the messages they encipher, one might expect a running key cipher to be unbreakable.