# 2. You intercept the ciphertext message 9LIMKTOG5DNN which you know...

## Question

2. You intercept the ciphertext message 9LIMKTOG5DNN which you know was encrypted using an affine map on digraphs in the 37-letter alphabet {0, 1, . . ., 9, a, b, . .., z, }.The alphabet includes numerals 0 − 9, which are labeled by themselves (i.e.,by integers 0 − 9). The letters A-Z have numerical equivalents 10 − 35, and blank space = 36. A digraph whose two characters have numerical equivalents x and y corresponds to 37x+y. The statistical analysis of earlier ciphertexts that have been coded by the same enciphering map shows that the most frequently occurring digraphs are GW and R3 in that order. It is known that the most common digraphs in English are TH and HE in that order.Find the deciphering key and read the message.
3. a) Break the RSA code whose enciphering key is (n, e) = (8369428283, 1234567).
Find the deciphering key and then decipher the message AFTHVVNJARCSTZFZ under the assumption that the plaintext consists of 7-letter blocks in the 26-letter alphabet, converted to an integer between 0 and 26⁷− 1 in the usual way, and the ciphertext consists of 8-letter blocks in the same alphabet.
b) Are 8-letter blocks for the ciphertext really needed? Either explain why not or give an example of a number whose encryption requires 8 positions

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Question 2
We use the provided information that
• TH encrypted gives GW and
• HE encrypted gives R3.
We also use the decryption function P =a*C + b (mod 37*37), where P is the plaintext digraph and C is the ciphertext digraph.
P =a*C +b (mod 1369)
TH =37*29 + 17 = 1090
GW = 37* 16 + 32 = 624...

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