prelim208_solns - Mathematics 336 4 problems, 25 points...

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Mathematics 336 Prelim 2 April 4, 2008 4 problems, 25 points each No books, notes or electronic devices may be used. Your proofs may use anything that has been given in class or in the book, as long as you show clearly what you are using. You must EXPLAIN ALL ANSWERS! 1. Consider an RSA public key cryptosystem in which your public key is ( e 1 , n 1 ) = (27 , 55) and my public key is ( e 2 , n 2 ) = (7 , 22). (a) Your decoding key is ( d 1 , 55). Determine d 1 . Solution: φ ( n 1 ) = φ (5 · 11) = 40 , 3 · 27 = 81 so d 1 = 3 . (b) “Sign” the numerical message 02 03 06 so that I know it is from you. Soln.: 02 3 03 3 06 3 mod 55 = 082751 signed message (c) Encrypt the result of part (b) for transmission to me. (There is no need to carry out the arithmetic in this part; just indicate what has to be done.) Soln.: 08 7 27 7 51 7 mod 22 encrypted signed message 2. Let H = 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 1 be a parity check matrix for a binary code. (a) Determine a generator matrix
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prelim208_solns - Mathematics 336 4 problems, 25 points...

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