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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