exam3 - n = 143 and the enciphering exponent is e = 103 ,...

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MATH 4023 Exam 3 Name July 26, 2010 Score: Instructions: This is a closed book, closed notes exam. Please read all instructions carefully and complete all problems. Be sure to show your work in order to receive full credit, an answer with no supporting work will receive no credit. 1. This problem concerns arithmetic modulo 20 (in Z 20 ). All answers should only involve expressions of the form a with a an integer satisfying 0 a < 20 . (a) Compute 8 + 17 . (b) Compute 8 17 . (c) Compute 7 - 1 . (d) Find all zero divisors of Z 20 .
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2. Find the last 2 digits of 15 101 .
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3. This problem makes use of the following equation: 1 = 15 · 27 - 4 · 101 . Using this equation (not necessary to prove it!) answer the following. (a) Compute the multiplicative inverse of 15 in Z 101 . (b) Compute 15 101 mod 101. (c) Solve the equation 15 x = 8 mod 101 . (d) Solve the simultaneous linear congruences: x 7 mod 101 x 3 mod 27
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4. Assume that for an RSA cryptosystem
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Unformatted text preview: n = 143 and the enciphering exponent is e = 103 , where n = 143 = 11 13 . (a) Compute the deciphering exponent d. (b) Assume that the following letter to number translation table is used: J = 1 ,Q = 2 ,R = 3 ,L = 4 ,D = 5 ,A = 6 ,S = 7 ,Y = 8 ,T = 9 ,O = 0 Encrypt the message SO. (c) Assume that a message has been grouped into blocks of two letters, enciphered and send out as 10 03 . Decipher the message. 5. Let C be a binary code with generator matrix 1 1 1 1 1 1 1 1 1 (a) Find the Partity check matrix of C . (b) Find all of the codewords of C (c) How many redundant digits are there in a codeword? (d) What is the minimum distance d of C ? (e) How many errors can it detect? How many errors can it correct? (f) Use this coding to encode 101....
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exam3 - n = 143 and the enciphering exponent is e = 103 ,...

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