NAME: [1] Alice is using an Affine cipher with modulus 47; all letters a - z, di

Question

NAME: [1] Alice is using an Affine cipher with modulus 47; all letters a - z, digits 0-9, and the rest punctuation and space characters. The space= 0 and a = 1, b = 2, . . . , z = 26 with the other charecters making up the rest. She takes c 37m-17 (mod 47) as the encryption formula. a. What would be the decryption formula? b. Eve knows Alice is using an affine cipher with modulus 47 as above but she appears to have changed her key. She intercepts the ciphertext starting qaggr,4ef72!S .. meant for Bob. The "qaq" could very well be "bob". If she makes this assumption can she recover the key? and if so what is it? [Note that in the abov e b 15, q 17 . There is no need to recover the message.] 2, o (10 POINTS)

Explanation / Answer

a) Decryption formula will be = [(37)-1(c - 17)]mod 47 where c is cipher text , inverse of 37 modular 47.

b) 'b' changes to 'q'

17= a*2 + b

'o' changes to 'a'

1=a * 15 + b

Subtracting both equations

16= -13a

a= (-13)-1 * 16 modulo 47

Now aim is to find inverse of -13 modulo 47. Hence we are done.

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