problem 2 I need a clear solution to this problem

problem 2 I need a clear solution to this problem
CS466, University of Massachusetts, Amherst, Spring 2019Instructor: Adam O’Neill people.cs.umass.edu/ ~adamo/sp19466 Instructions Before attempting this homework, be sure to review the cours e’s Academic Honesty policy on the course syllabus , and be certain to abide by it and the homework policies discu ssed in class. This homework is due on Friday, February 8that11:59pm , by which time you should have submitted your solutions as a PDF to Gradescope. Since we aren’t using real paper here, please use at least one page per solution (in this case at least four pages: at least one each for Problem 1, Problem 2A, Problem 2B, and Problem 2C). Please al solabel your solution pages correctly on Gradescope ! If you do not, you will bededucted up to 10 points , so make sure you leave yourself about ve minutes to upload, especially i f you are unfamiliar with the process. Problem 1.(30 points.) In a recent interview with astrophysicist Neil Degrasse Tyson,1 Edward Snowden suggested a reason why humans have not observed alie n communication is that aliens’ use of “good” encryption would make such communication look ran dom and therefore indistinguishable from cosmic background radiation. (NB: He is talking about a liens communicating amongst them- selves, not attempts to contact humans.) Critique this argu ment from a cryptographic standpoint. Problem 2. (70 points.) Let Z 10 = {0,1 , . . . , 9}. Consider the symmetric-key encryption scheme SE = ( K,E ,D ) with message-space ( Z 10 )4 (that is, messages are four decimal digits) de ned as follows. Key-generation algorithm Koutputs a uniformly random Perm (Z 10 ), where Perm(Z 10 ) is the set of permutations on Z 10 , and encryption algorithm Eis de ned by Algorithm E ( M ): Parse MasM[1]M [2]M [3]M [4] where each M[i ] Z 10 For i= 1 to 4 do: P [i ] M[i ] + imod 10 C [i ] (P [i ]) Return C[1] C[2] C[3] C[4] (Part A -10 points.) Finish the description of SE. That is, specify a decryption algorithm Dsuch that SE= ( K,E ,D ) is a correct symmetric-key encryption scheme with K,E as de ned above. (Part B – 30 points.) Is SEa substitution cipher? Why or why not? (Part C – 30 points.) Is SEa Shannon-secure? Why or why not? 1 See http://www.startalkradio.net/show/a- conversation- with- edward- snowden- part- 1/ . 1