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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 nd 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 eect on your nal grade, so dont 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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This note was uploaded on 09/05/2011 for the course MATH 3360 taught by Professor Billera during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 BILLERA
 Math, Algebra

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