Question: Please help me with this question For both exercises below we use the 31-letter alphabet AZ (labeled by the numbers 0-25) together with the 'blank',

Please help me with this question

Please help me with this question For both exercises below we use

For both exercises below we use the 31-letter alphabet AZ (labeled by the numbers 0-25) together with the 'blank', 'period', ?, l, and 'apostrophe', labeled by 26-30. 1. You and your friend communicate using afne enciphering transformations p H up | b, where (1,?) E F31 2 2/312. Consider the eld F312 2 F951 realized as F := F31 [X] / (X 2 + 1). The key (a, b) for the enciphering transformation is viewed as the class of a + bX in F. You exchange keys using the Dife-Hellman system with the group Fx and g = 4 + X | (X 2 + 1) E F x. As your secret exponent you choose a : 209. Your friend sends you her gb = 1 | 19X + (X2 | 1) E F. (a) Find the element in F x that describes your common enciphering key. (b) What is the element 9\" E F X you send your friend, so she also can compute the enciphering. (c) What is the key ((1,1)) that both of you are using for the afne single letter crypto system? ((31) Read the message 'BUVCFIWOUJTZ!H.\" from your friend

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