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The following ciphertexts represent the same plaintext encrypted using Cacsar, affine, Vigenere and substitution. 1) Determine which one is encrypted using Cacsar's 2) Pecryptit 3) Determine the encryption method for cach of the remaining texts 4) Use known plaintext attack to find the key. Text 1 ANWDCE ZEMGMEID B0 FQRJIFBHE VHLRSA THCT PEPM YOW SDHNCT NGVAV RWRGGT wS DMMEOBHVFPE TJQQE BHAV MDHQ GOU ILDHMTWAAS UIYMMBGR wS RWRGGTWLQ NRIGNGw FPAT RRRZQL UNVRXINCT DQ NRX RWRGGT WSDMMEOBHV FPOSG TKEP PAVG SwYOS BY AOXEXEAYU RHQQUBET TR JAZGEVTK[ FZOUDLHW FPAT JAYI BISSGD DAMGBUV NHZQz FOTGHX FW REQEPFQZTHG BOJEAINIS WLMB COOE HEOP DAA Text 2 DOZDBVUHPHPEHU WR IRUJHWWWH WKLQJV WKDW PDGH BRX VDGEXW QHYHU [RUJHW WR UHPHPEHUWKH WKLQJ\ WKDW PDGH BRX JODG UHPHPEHU WR [RUJHWWKH IULHQGV WKDW SURYHGXQWUXHEXW GR QRW [RUJHWWR UHPHPEH1WWRVH WKDW KDYH VWXFN EB BRXD(ZZDBV UHPHPEHU WR [RUJHw Text 3 IPTUPCQ KPQKRADJQKNQTNIPZH XDMNINMLNZJCPTPTUPCQHWHCpPQQKPWCRPAIJ QKNQOCHEPIXAQCxPUxQIHAHQWHCDPQQHC PTPTU HJPQKNQKNEPJQXBFUZZHXN MLNZJCPTPTUPCQHWHCPPQQKP QCHXUMPJQKNQKNEPON JPINLNZUXQAPEPCWHCDPQQ HCPTPTUPCQKPUMPJJRADJQKNQBHTPPNBKINZ Text 4 LB LRGL YGHO XBP KGHMPL TOQOJ NEJEOL LB JOYOYMO] LR0 LRCTEKLRGL YGH0 XBP ESGHGSvGxK JOYOYMOJ LB NBJEOLLRO NICOTHK LRGL FJBQOH PTLIPOMPL HB TBLNBJEOLLB JOYOYMOJLRBK0 LRGL RGQO KLPUA Mx xBPGSvGxK JOYOYMOI LB NBJEOL LR0 LJBPMSOK LRGL RGQ0 FGKKOH GvGxMPL TOQO) NBJEOL LB jOYOYMO LRO MSOKKCTEK LRGL UBY0 OGUR HGx Given the following ciphertext, determine the encryption method, find the key and decrypt. ptnvffuntshtarptymjwzirapplimhhqvsubwlzzygytyitarptyiougxtuydtgzhhvvmum shwkzgstfmckvmpkswdgbilvjlimglmifqwioiivknulvvfemioietno)tywdsajtwmtcgluy Problem 1. (a) Compute gcd( 4883,4369) (b) Factor 4883 and 4369 into products of primes Problem 2. (a) Let be prime Suppose a and b are integers such that ab modp. Show that either a = (b) Show thati a,b, are integers with nlab and ged(a, 1, then nlb. Problem 3. (i) Find: € z suchthat 17x + 257y = 1 (ii) Solve 17x = mod 257 Problem 4. Decrypt aphertext FLEWTDTOJHQRESUPGL encrypted by Hill Cipher Problem 5. Suppose we work mod 27 instead of mod 26 for affine ciphers How many keys are possible? What if we work mod 297 Problem 6. Suppose there is language that has only the letters and b. The frequency of the letter a is and the frequency of the letter bis .9. A message is encrypted using Vigen ere cipher (working mod2 instead of mod 26). The ciphertext is BABABAAABA. (a) Show that the key length probably 2 (b) Using the information < on the frequencies of the letters, determine the key and decrypt the message.

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Problem 1

a)
GCD(4883, 4369)
4883=1*4369+ 514
4369= 8*514+ 257
514= 2*257+0 => GCD(4883,4369)=257.
b)
Using part a) we decompose the two numbers into prime factors...

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