Information Security: Principles and Practices A Vigenère cipher uses a sequence
ID: 3791354 • Letter: I
Question
Information Security: Principles and Practices
A Vigenère cipher uses a sequence of "shift-by-n" simple substitutions,
where the shifts are indexed using a keyword, with "A" representing
a shift-by-0, "B" representing a shift-by-l, etc. For example, if the
keyword is "DOG," then the first letter is encrypted using a simple
substitution with a shift-by-3, the second letter is encrypted using a
shift-by-14, the third letter is encrypted using a shift-by-6, and the
pattern is repeated—the fourth letter is encrypted using a shift-by-3,
the fifth letter is encrypted using a shift-by-14, and so on. Cryptanalyze
the following ciphertext, i.e., determine the plaintext and the key. This
particular message was encrypted using a Vigenère cipher with a 3-letter
English keyword:
CTMYR DOIBS RESRR RIJYR EBYLD IYMLC CYQXS RRMLQ FSDXF
OWFKT CYJRR IQZSM X
Explanation / Answer
Let P = C = Zm and let K = (a, b) Zm × Zm gcd(a, m) = 1
Then the encryption and decryption of the affine cipher are: eK(x) = (ax + b) mod m dK(y) = (a 1 (y b))
Variations • For a = 1, b Zm, we have a simple shift cipher or rotation cipher • For a = 1, b = 3, this is a classical “Caesar Cipher” • Fix a block size of length n and choose n keys: K = (k1, . . . , kn), then the encryption of a plaintext string x = x1, . . . xn is eK(x) = (x1 + k1) mod m,(x2 + k2) mod m, . . . ,(xn + kn) mod m This is known as a Vigenere Cipher