Construct the multiplication table modulo 8. Then find all the integers k, 0 k 7 that...

  

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Construct the multiplication table modulo 8. Then find all the integers k, 0 k 7 that are invertible under modulo 8 and give their inverses. (b.) (5 points) Suppose I want to send the note SEND MONEY to my parents, but I don't want my brother to read it. Encrypt my message using an affine cipher (mod 26) with a = 11 and b = 4. (c.) Suppose the ciphertext QJ KE SRE OG HGXXREOXEO has been encrypted using an affine cipher. However, we do not know the key (a, b) that was used. Fortunately, we know that the plaintext letter T becomes ciphertext H and the plaintext letter O becomes E. Find (c.1.) (4 points) The encryption formula E (r) and the decryption formula D(y). (c.2.) (3 points) Decrypt the message 2 - (d.) (Bonus 2 points) Suppose we use the affine cipher on an alphabet with 143 letters. Find K, the size of the key space for this cipher. Construct the multiplication table modulo 8. Then find all the integers k, 0 k 7 that are invertible under modulo 8 and give their inverses. (b.) (5 points) Suppose I want to send the note SEND MONEY to my parents, but I don't want my brother to read it. Encrypt my message using an affine cipher (mod 26) with a = 11 and b = 4. (c.) Suppose the ciphertext QJ KE SRE OG HGXXREOXEO has been encrypted using an affine cipher. However, we do not know the key (a, b) that was used. Fortunately, we know that the plaintext letter T becomes ciphertext H and the plaintext letter O becomes E. Find (c.1.) (4 points) The encryption formula E (r) and the decryption formula D(y). (c.2.) (3 points) Decrypt the message 2 - (d.) (Bonus 2 points) Suppose we use the affine cipher on an alphabet with 143 letters. Find K, the size of the key space for this cipher.