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The function E(x) = (ax + b)MOD26 defines a valid affine cipher if a is relatively prime to 26, and b is an integer between 0 and 25, inclusive. If b = 0, then we refer to this cipher as a decimation cipher.
To set up an affine cipher, you pick two values a and b, and then set ǫ(m) = (am + b) (mod 26). For example, if we take a = 3 and b = 8, then the encryption function is. ǫ(m) = (3m + 8) (mod 26). To encrypt the letter “C”, we first note that “C” corresponds to the number 02.
Affine cipher keys must have a multiplicative inverse for successful decryption! Euclid’s Division Theorem: For any integers ,𝑑there are unique integers , such that =𝑑∙ + and r≤ <𝑑.
An affine cipher, (like a shift cipher), is an example of a substitution cipher: In encryption using a substitution cipher, each time a given letter occurs in the plaintext, it always is replaced by the same ciphertext letter.
Cryptography Worksheet — The Affine Cipher 1 The Affine Cipher is a cipher that uses Maths to encode the message. It works by conver ng every le ©er in the alphabet into a number, performing a func on on that number, and turning the result back into a le ©er.
From our point of view, equation (4) is the decryption equation, since it converts ciphertext into plaintext, while equation (3) is the encryption equation. The conditions 0 p 25 and 0 c 25 are needed in order thatpandccan be assigned a letter of the alphabet.
Affine Cipher. Addition (shifting) and multiplication can be combined to give an Affine transformation. Encryption: C=E( , , p)=( x p +. ) mod n = ( x p +. ) mod 26 ........(7) Decryption: p=D( , , C)= − (C - ) mod n = − (C - ) mod 26 ........(8) Example: Encrypt the plaintext: “affine cipher”, using the key: Ans. : C=E( , , p)=(5 p +8) mod 26
