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# ps1 - ECEN 5022 Cryptography Spring 2008 P Mathys Problem...

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ECEN 5022 Cryptography Spring 2008 1-23-08 P. Mathys Problem Set 1 (Solutions are due Wed. 1-30-08) 1) (a) Let Z = X + Y , where X , Y and Z are discrete random variables with probability mass functions (pmf) p X ( x ), p Y ( y ), and p Z ( z ). Express p Z ( z ) in terms of p X ( . ) and p Y ( . ), assuming that X and Y are statistically independent. Determine p Z ( z ) numerically for the case when Z is the sum, modulo 26, of statistically independent English letters (see Appendix for the relative frequencies of English letters). (b) Repeat (a) for Z = X - Y in the general case and the difference, modulo 26, for the case of statistically independent English letters. (z) How do the numerical results in (a) and (b) change for the modulo 26 sum and difference of English letters, if one of the two letters is drawn from a uniform distribution, rather than from the English letter distribution? What does the change mean in the context of cryptography? 2) Of the following five cryptograms one is a transposition cipher, one is a shift cipher, one is

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