Cryptography Substitution Method with(StringTools): alphabet:="abcdefghijklmnopqrstuvwxyz "; cibet:="CRABDEFMZXYSNOPQKGUVHILJTW ";

UTxhYmNkZWZnaGlqa2xtbm9wcXJzdHV2d3h5en42Ig==

UTxDUkFCREVGTVpYWVNOT1BRS0dVVkhJTEpUV342Ig==

Exercise: Create a function that encodes a given message. text:="hi this is text";

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length(text);

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text[1]; text[2];

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Search(text[1],alphabet); cibet[8];

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encode:=proc(plaintext) global alphabet, cibet; local position; position:=Search(text[1],alphabet); cibet[position]; end proc;

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encode1:=proc(plaintext,alphabet,cibet) local position; Implode([seq(cibet[Search(plaintext[i],alphabet)] ,i=1..length(plaintext))]); end proc;

Zio2JUkqcGxhaW50ZXh0RzYiSSlhbHBoYWJldEdGJUkmY2liZXRHRiU2I0kpcG9zaXRpb25HRiVGJUYlLV9JLFN0cmluZ1Rvb2xzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlSShJbXBsb2RlR0YlNiM3Iy1JJHNlcUdGLjYkJjkmNiMtX0YsSSdTZWFyY2hHRiU2JCY5JDYjSSJpR0YlOSUvRkA7IiIiLUknbGVuZ3RoR0YuNiNGPkYlRiVGJQ==

cytext:=encode1(text,alphabet,cibet);

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Exercise: Create a function that deciphers a given message. encode1(cytext,cibet,alphabet);

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How would you decode de following passage? 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 ?factorial; 26!;

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cipher:="PSAXJZUSNXVA HL JVK LPHKMPK ZG CSHJHMU HM LKPSKJ PZQK NMQ HL NM NMPHKMJ NSJ; JVK GHSLJ QZPTFKMJKQ TLK ZG PSAXJZUSNXVA HM CSHJHMU QNJKL ONPD JZ PHSPN 1900 O.P. CVKM NM KUAXJHNM LPSHOK TLKQ MZM-LJNMQNSQ VHKSZUEAXVL HM NM HMLPSHXJHZM. LZFK KRXKSJL NSUTK JVNJ PSAXJZUSNXVA NXXKNSKQ LXZMJNMKZTLEA LZFKJHFK NGJKS CSHJHMU CNL HMWKMJKQ, CHJV NXXEHPNJHZML SNMUHMU GSZF QHXEZFNJHP FHLLHWKL JZ CNS-JHFK ONJJEK XENML. HJ HL MZ LTSXSHLK, JVKM, JVNJ MKC GZSFL ZG PSAXJZUSNXVA PNFK LZZM NGJKS JVK CHQKLXSKNQ QKWKEZXFKMJ ZG PZFXTJKS PZFFTMHPNJHZML. HM QNJN NMQ JKEKPZFFTMHPNJHZML, PSAXJZUSNXVA HL MKPKLLNSA CVKM PZFFTMHPNJHMU ZWKS NMA TMJSTLJKQ FKQHTF, CVHPV HMPETQKL ITLJ NOZTJ NMA MKJCZSD, XNSJHPTENSEA JVK HMJKSMKJ.";

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Sort(cipher);

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What are the weaknesses of substitution method? Caesar cipher ASCII and the convert command. convert("a",bytes);

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convert([100],bytes);

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convert(alphabet,bytes);

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Exercise: Using Matrix, create a maple command that displays a matrix of all ASCII characters equivalent to numbers 0 to 127, matrix(20,10, [seq([seq( convert([10*j+i],bytes) , i=0..9)],j=0..19 )] );

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Exercise: Create a function that takes a list of integers and returns a list of the cubes of those integers. map(x->x^3,[2,3,4,5,10]);

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cube:=list->map(x->x^3,list);

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cube([3,4]);

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Make a procedure that takes a plain message and * converts each of its characters into the ASCII equivalent, * adds a number n to each of the number of the characters * converts the list of numbers into the ASCII equivalent characters. How do we decipher the ciphertext? This is not a good cryptosystem, find the flaws. (Hint: Have Maple print all the possible outputs for n =1,2,3... 200) Modify your procedure to solve the problem. Review: Modular arithmetic and the division algorithm Exercise: Describe all the solutions of the following congruences: 1. xLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEoJmVxdWl2O0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDRi8=23 (mod 7) 2. 4xLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEoJmVxdWl2O0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDRi8=23 (mod 11) 3. 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