We2Exercise2Part2assignment.docx
Please do the following all the questions thank you
We 2 Exercise 2 Part 2
4 questions
1.Show how to obtain the inverse permutation so as to use the program in the previous question to decrypt a ciphertext. Using this permutation and the transp program, decrypt the following ciphertexts: (a) GSOVQJDXJVTXCSIZFFHXSHFX (b) DDXGOVFFOX
2.Use the permutation formula to calculate the number permutations of the set {V, W, X, Y, Z} taken three at a time. Also list these permutations.
3.The goal of this assignment is to decrypt the following : fcvcvjcvecpdgtgcfcpfwpfgtuvqqfykvjqwvcpaurgekcnogcuwtgukuecnngfrnckpvgzvqtengctvgzvvjgogvjqfqhfkuiwkukpirnckpvgzvkpuwejcycacuvqjkfgkvuuwduvcpegkuecnngfgpetarvkqpgpetarvkpirnckpvgzvtguwnvukpwptgcf
Add the passwords to the case and decrypt the files inside FTK
4. How could you easily determine if a ciphertext
has
been obtained by using only a permutation of the plaintext?
5. Write a Sage program to do the statistical analysis, Ic and then to suggest a possible plain text
|
Question 1
Needs Grading
|
|
|
|
|
Sage Exercises
Using Sage's crt function, find an integer which has residues 1, 2, 3, 4, 5 modulo 3, 5, 7, 11 and 13 respect ively.
|
|
|
|
|
|
|
|
|
|
Question 2
Needs Grading
|
|
|
|
|
Suppose X is defined to be the absolute difference of the numbers obtained when two fair six-sided dice are tossed. What is the entropy of X?
|
|
|
|
|
|
|
|
|
|
Question 3
Needs Grading
|
|
|
|
|
Evaluate the following modular powers:
(a) 4723 (mod 53), (b) 1347 (mod 61),
(d) 217219 (mod 344).
|
|
|
|
|
|
|
|
|
|
Question 4
Needs Grading
|
|
|
|
|
Sage Exercises
Develop a simple Playfair-like cipher with the following encryption: for a pair of letters XY in a Polybius square, if the indices of X and Y are ( a, b) and ( c, d) respectively, then the ciphertext is the pair of letters whose indices are (a, d) and (b, c).
|
|
|
|
|
|
|
|
|
|
Question 5
Needs Grading
|
|
|
|
|
Sage Exercises
Develop a simple Playfair-like cipher with the following encryption: for a pair of letters XY in a Polybius square, if the indices of X and Y are ( a, b) and ( c, d) respectively, then the ciphertext is the pair of letters whose indices are (a, d) and (b, c).
|
|
|
|
|
|
|
|
|
|
Question 6
Needs Grading
|
|
|
|
|
Evaluate the following congruences, by first evaluating the individual terms:
(a) 83+47 (mod 17), (b) 83-47 (mod 17), (c) 83x47 (mod 17),
(d) 217 x 219 (mod 43).
|
|
|
|
|
|
|
|
|
|
Question 7
Needs Grading
|
|
|
|
|
By trial division, test each of the following numbers for primality:
(a) 289, (b) 541, (c) 2813, (d) 1583, (e) 14803,(f) 7919.
|
|
|
|
|
|
|
|
|
|
Question 8
Needs Grading
|
|
|
|
|
Apply the "Sieve of Eratosthenes" as follows. First write down all the numbers from 2 to 100. Circle the 2 and cross out all its multiples. Circle the next uncrossed number (this will be 3), and cross out all its multiples. Continue in this way circling the next uncrossed number and crossing out its multiples until all numbers are either circled or crossed out.
(a) What do you notice about the circled numbers?
(b) How many are there?
|
|
|
|
|
|
|
|
|
|
Question 9
Needs Grading
|
|
|
|
|
Using Euclid's algorithm, find the following modular inverses:
(a) 29 -1 (mod 47), (b) 39 -l (mod 315), (c) 105 -1 (mod 143),
(d) 54 -1 (mod 81).
|
|
|
|
|
|
|
|
|
|
Question 10
Needs Grading
|
|
|
|
|
Use the ADFGVX cipher with the array given on page 17 and the keyword
ENCRYPT to
(a) Encrypt GO SOUTH
(b) Decrypt AVAV VXXD VAVD VXDX VDVX GVFV GXXF
Decrypt the followings Ciphertext
FHVBIPMSEYTHESZLMEUTPYJMMKZXKTIACUXAMTUKCPQHRNFXQNNKRWQRZXKBZDVOHBZTYOPXMFCOWLEHIEFUQRPKRAAUISRMTEDYVGUNXLYMEIEMIWUNEOVFDSIOIWIHVXXAQRVGELZOTYQIMNPNMGQDVKVEKTYOGHXDNSRMQRNSRWTAULVHGGYDABFHZDGEAUUCWHEODLVXMNUKVTUNJYTXZEKBEMUNXDLTFFLBXAQRFEXWAOIOBXDCZCIPMSEYAHGTFPXAQQLOWMUOESATEGCKHHRIKSRXHEIVMDQDCYRZIACUWXEPVMMTXLPYRVTICVCTRTVBRHANJNVXMDWEPMAMVGELFHVMSFUNXRSFQIEDLXDANDABXIXRXPUTYXMIBEUPMGSEICEGPTFOWTZDRRITDTJKHWQNVNFRFHVMLBPIEQWHRBVCWBQTYORNDSVKRWTUDLPXPBPDLXOOECGBAUJXILEOWWCITYJSGTXIEPIKUOISXRFOVVMSMJFRRTZDXOSKSIRXEKQEUDLXEAZNIEUZRTSAZAENKXARXSEGMWVBIGAWTVYLFEIOHKAUENXAQIIWEFMIEDLXPRRGMGSRFYQLTECKCKQCCSRXPOEKWHRASIXAQFZBILUDVKRWIIKRLXDDRBPBZGJKFHGTYOVYARKRIMUMVXIBFHVBUNMRIOPEUNXXSKORPSRZXOFUIWBEIPIVFLPREIBYDOWAQHRNHBEPVXWXPFIYQCAIESRZFHVQVHGPJKCBZGJRIKQGIOXMQDKYFXGNUOVMTEEOGXESZDCHRKVOTBZGDOEMMDZCXTZCVLYMFHRDYGFICCLXTERBHYDODLILEIVKRWOOLVHWUSTYZXDBPRIKAWEYFLQRMKXBANKREMUWRCIGPERFSNDIEQMGSOFNITDNVCXMAATAYBDERWSKQSFMMTNLVKRWOHZVHEUKVNMLBOJSXBANRWSKQAKDVTOTZFITZDJZVBSHKVCFMNEOVLAMVDLBZGCSKAFEIPVTZKVBQHDEEKXNDACKWBFWVBILTEIOEEXYDEWMQXTVYWQMVPVHYPISZBXEXOWBZTVXHXPOEVCYARTYRMQNKOHAMPGIPBFTCOGAULUBIGIHRDHHQSSOWLUEJKCBTAMOHHZEZKWDQDAKRXUDFXXEUKVMEOULCOVLARHEILFIFXIKEBVCMWQSKRIKQIJCSFQTYSRZFRLVCYARSSHWUNXSRTOHZVHMMKZXKNBHVBIEPEICMGFHRDQTZNVBFXEERDIWEODOAAQRVKRWGNKSPRAUTKRLBERUTEQAJKRMXYIOQTUNJSPXZTRLVXMKWKWMDOFWEWVOZXIWFHVNVTIIEQVHAMZCPBBPVNMGFHVBIBFCFXXTUNVNEUAOBMELQIJYSGBOJCILEEUWCLQLWYJTHOCEQXFABSRZOAIOXAMTZDWAAUCNFXANVCXHDEUGMMTPZMXNDEJSQHGNKOHBZTFDLXIIENSPEERDKTFHVBMGSUGWCYQEKSWTFCIYWLXEXQIWXIBOEMGRBKRWTAMSRZPRRGRMTEIOHFARVORVGRKKMGZERBPROLFCIBIAJCLKUNVNMGPOLLPXDEKSVXYEEDJHXDJYJLOAIVIMPRRZIKKSYEXBZMPFMXITFDLXDIXRXAMNUDSMTECOJMIEIOXAQCCOEKBAEOWHRGCKWLBRFDIVFIEQFNFNFDWXBAIKXBZGDOJKAMKRIWDERBRHHEDLIKPAPKXBZTVBZTXSNRMEQTLBRBZGFFIKFHVVITHEJYJFKBFYOBETLNMXPTYOELBETDSYFHRDABZTVBEYFEIXSHZAWKVBFOWPIKQDRZEEQBCKRDAFDSWMMNUMPHGDEOEKMSTORXAFNOXEMWEKRWETFBQUQAKCLKGBNSXAOERCIEQSJBEBZSNOIIUNXKATKWZVHEKBVPSKQACYRZMNUVEFQNKKFEQBCKWMURVDYKZEUDSFKBFYOUQWZMOLTIJDSKKOWLVBFIJRFBDDJDLXXEKDIKBRVCWMTEIOSYUCRBIWXIKDPXROIQIGQRRVPREPVKOBZGRXHRQTKRIKQWVBIVQRKKMGUNKBSWGCKYVRBAXOWMTAKMLBXDRCMPMSZMSNXDEYXIMSJAYBFERCEUXAEUXAQYNOVXFHFCIPTITRXKQAKYJMTEYKYGFSFPWXMFFGPHRTYOWHXIKKVRDOTUWTZDGBSFANKYVBQSSIXAQMFXPRUNYKFBFEUYJMTETYELFOWXSKIAPCXNPDVNABFHZCPXEFIYQBFSJYYMTEIXIQFRVWMMKTYOPBZDVXILEOIXESQTFDLXZOIDLVMPVGLXDEKRIGARKRIKZOTOEGUNMKWMIHZBPLNOZVWKAUENXAQNRUIWYECKRVTOCIMLXEJYJYMRKRILFTYEPXMNUDLXMTCKRMUCJEVZQPFEVLUNRWSGSTYOWMARDILXNRZNILZOIMSNXDZZELEUEXSMUCVNXAQSLQKXETZYRHRTYOFEQABCLHDEJYJEMPCKRWEISOVBMSGSXSNEIQIGZOMKDXYBCKMVQLRXHZDEVXPTZDNSXAFHVFELFSNOIIAFKRITDCKSGSANVKRWFHFCIYARCYVGDEXSSGEOWNVXMRPCTTOEKREMDEJOVOAIIYJYDOJDEGPSEYAPTEIOJBDMWSIEPSFPMVQTYOEVOUDEPTFIFXSYOEEDYKUEJYJPUNKOVLSLRJIWUNRVTBZEYOMZTTJKFHHEYOMZTTJCYKDOLXHMTEGYPXMNUMSGOEEDVXFHVWYEFIGVMXPRZQSNDSFPIQFRVWIVALUYJMTEJOHXMTYGLBFEIOEEYSZPSKYEUKRBPERYJFKONXWAMDFGCEUKVKPEFHVREERCFWTKQHVXHXPNFDMHZSKREMRLFKXWUMKRVHGGYMLBXDIORLNRRSRLNUKCXKMNXOPRUMGBILEIMOXAQWFBHLUNKRILQIEDVHPUTDSKKPRQILOOEXIVFEUDLXYSVVZXEWZDLMTEJEGVQEUSRZHIXXIMFEJKRWSAMOWBSNZPMVMNTOXHFHVBSVWSKKRWUNXETTXOEOMGMSVKSYNICVSPMNUCTKMYKYXAQBIYOXZBFKXLFRRXHXPOEKHXEOCKXXOORCXMATYOGHXDRXHZTAJDPRYOFXKEMNTSRZFHIYYZTBRBWHRCCYYWMTRGVXOKAEWMEIEUMGSITKRGATKOPEIHRDWXZTZWIGFHRERMQDKRIJGIKOWHXIKKVROHLBGAKAINABFHZDWBZSTBMUQDYOEWETFXIBFSXKXXUTJDAHFRVOWBFSCYAAARZJSGSIINPXPBPKFKAKVXATXLRXHBFSEOAEKRZCIGORVCGXZTRDXXETZXKMTEYYYKAFVFIGFIUOXAQTNYWAUPJLIVMLDOHHZAKYVIUDJOEBNECSIOQDKYFXYAISRXBHRXXHYSKRIYUEENTBZNZXKWAWEDLXFHZOJLBATUFXTIENLBYIGKWLQDFFIKCUZMOEKIKGELMNFLNXOTFPXXDRFBWHIAJDLXNLRMOAAREOHMTIEQWXMTVNEEAOWYRTDOTUWNDVVIMGSAUSWMMNKMVHIDJEVKAUENMGSAXKPEAWJOEVTPZMXNDEKYPWMSKYVRYYJDIKUOLCSYFEEDSFKUENIOQLFZIWGNUOVLFAENMGSAENMFBEIPIVFFVOPBZGJIIMQVVBTKAFFERWXYZXXXDEJDMGSAJSRMQRVCXBZGRCXAQTRVILNEJCMXEODOXBYEJXEKDAKOHHZWZXXXDEMORBZGJGLXZSYOGAMNTOHMABVSRZAOURYFAUIKRWIHVXLTHIEQFKAUXRXAQRZBSGUNXDEUXEKYXAQNLBWXDYYOEKFHJRITXLFGIWGSKYWBFASYYMUTRXHPTICOWAQGFDYIYRJBIXPSCKGXRRZVPLMNUMVBYPVNLXDNZQLMOAGLSKPEICJXPOLBITSEIKXMQNKSSGIIKRTTESRQILAFCYZXMNUKHOQNKEVXFABORYDODYPWRAZBCMMLVCEGPOKRIKNACVEWEOIKWTFACKXXDPVBMHPIUSWVAVVBIWRRFWXAQPRQILAFGKQXXARXHAQNIIITDLFPQHDECKRWIIKRFXIITUSGYYBXIXUWRCXAQNYKTIKHRZTRMTCOELFIEWCPMYZPITDEUXSMTIEQFNFIEDIKDUGDMHZAENXAMTTKQXFOFCSHZTYOFKQABPELFRFYQWAOIYTXZEULSAYAUKQFAPVMVBQDKRIOAITOSYVOYXVXQDKRIGTEGKYLQDYOJHGNUDLXDOFWEIBAIORMXYVWTMKWYOVXFHVNMVWEECMLEHVRIVANKSRNQDCSDSKGVYVZKCRVPBZGKYLBESZCXXDSAYEGUSEYXAQRVDIEXMRWELTEZCVNZOLDMGFOKRIKMIELEWMNZWEEUTZCAXXLZNVXITYOGNDTRSRMTOLQLMUAENMPUSYOHYQRMORMXYYOQBSHKXSMPIJMSOQRDILBPIEQTEMCVXSKIOLVHCAHEBIXPHRFIYAUENMMAUKRMFEECPLXIAJXSMCUZMOXUTYOVHRVZCMHZOIMSGOEGDMHZBLDIEUZRTYLFPLDLXDHVKHBZAKDLXPOFBEGPSRSHTFOEMILTEZCMGFHVGMGPONCITFTFLILGRVTEVWAENMVMMVYYMUMDOHBMTVVCYARZDVXYBCOHTFTYOMWQAFPFXUNXNVTSGVNJHDTYLCMTEJKMWVATUAAMTUYCHGWRXXBMSBOHPUTYKADIAINHBRFZNIGOEJKCPTAKNSRAUNKRMYAJDIKDEVNATETYOEGEWVBMPMNKISNFOTYQXTEIOEGPSVKXBZGYSQLQLWSRTZAIWGAMIIRIBZTZWEMQDSIEZQSKEVXFHRDMPMSKYEIBRFKGAMNUCXTZDSOJHDEYSQ
|
|
|
|
|
|
|
|
|
|
|
ROJA
