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Unformatted text preview: 33 34 35 36 (a) Find the decoding exponent d . (b) Decode the 3letter message 46, 23, 29. You may use the following table giving a 1 , a 2 , a 4 , and a 8 mod 51 for a = 46 , 23 , 29. 1 2 4 8 46 46 25 13 16 23 23 19 4 16 29 29 25 13 16 You must show all your work to receive credit. 6 (20 points) . How many solutions does the equation x 2 = 1 have in the ring Z 136 ? Justify your answer. [You do not have to ﬁnd the solutions.] This is the end of the exam. If you have the time and inclination, there is an extra credit problem on the back. It will have only a marginal eﬀect on your ﬁnal grade, so don’t work on it unless you want to. The purpose of the following problem is to explain the “coincidence” that all entries in the last column of the exponentiation table are 16 in the RSA problem above. 7 (e.c.) . For any integer a relatively prime to 51, show that a 8 ≡ 1 or 16 (mod 51)....
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 Spring '08
 BILLERA
 Math, Algebra, Cryptography, Prime number, Linear code, binary linear code, ternary linear code, usual translation table

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