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Math Topics Affine (Linear) Ciphers Name ____________________________ A spy might be able to decode an additive or multiplicative cipher fairly easily because if he/she can figure out what type of cipher was used, there are really only 25 different keys possible for additive ciphers and 11 for multiplicative ciphers. (In both, using a key of 1 doesn’t change the plaintext, so they are not included here). We can make it harder by combining additive and multiplicative cipher techniques. Then we would have 11*25 = 275 keys. The combined additive and multiplicative cipher is called the affine, or linear, cipher. Ciphertext = (k*plaintext + x) where k = any of the possible multiplicative keys and x is any of the additive keys. 1. Let’s figure out the ciphertext for the affine cipher 5p+20. Complete the chart: Plaintext (p) position A B C D E F G H I J K L M N O P 1 9 5p+20 25 65 150 Mod26 25 13 20 ciphertext Y M T 16 2. Encipher a message using key 5p+20 here: 3. Trade with a partner and decode your partner’s message here: Q R S T U V W X Y Z 26 4. Now choose a different affine key and create its chart. Remember that in kp+b K can only be one of those 11 numbers that don’t share factors with 26. plaintext A position 1 B C D E F G H I J K 9 L M N O P Q R S T U V W 16 Mod26 ciphertext 5. Write a message in your new ciphertext: 6. Trade with a partner and decipher your partner’s message using his/her key here: 7. Tomorrow you will need a message at least one paragraph long to encipher using any of the ciphers we’ve learned. Then you will trade with a partner and see if your partner can decipher any of it WITHOUT knowing the key, but only using the cryptogram tips. You may want to pick out/write your paragraph ahead of time. X Y Z 26