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

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UTtDUkFCREVGTVpYWVNOT1BRS0dVVkhJTEpUVzYi

plaintext:="This is the text we want to encode 111"; LowerCase(plaintext);

UUdUaGlzfmlzfnRoZX50ZXh0fndlfndhbnR+dG9+ZW5jb2RlfjExMTYi

UUd0aGlzfmlzfnRoZX50ZXh0fndlfndhbnR+dG9+ZW5jb2RlfjExMTYi

Exercise: Create a function that encodes a given message. encode:=plaintext->CharacterMap(alphabet,cibet,LowerCase(plaintext));

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cyphertext:=encode(plaintext);

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Exercise: Create a function that deciphers a given message. decode:=x->CharacterMap(cibet,alphabet,x);

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decode(cyphertext);

UUd0aGlzfmlzfnRoZX50ZXh0fndlfndhbnR+dG9+ZW5jb2RlfjExMTYi

What are the weaknesses of substitution method? Caesar cipher ASCII and the convert command. convert("abc",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([[..,seq(i,i=0..9)],seq([10*j,seq(convert([10*j+i],bytes),i=0..9)],j=0..12)]);

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Exercise: Create a function that takes a list of integers and returns a list of the cubes of those integers. f:=numlist->map(x->x^3,numlist);

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f([2,6,7,8,1000]);

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Make 3 procedures that takes a plain message and perform 1, 1 and 2 and 1 and 2 and 3. 1converts each of its characters into the ASCII equivalent, 2 adds a number n to each of the number of the characters 3 converts the list of numbers into the ASCII equivalent characters. caesar1:=proc(text) convert(text,bytes); end;

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caesar1(plaintext);

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caesar12:=proc(text,n) map(x->modp(x+n,127),convert(text,bytes)); end;

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caesar12(plaintext,10);

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caesar123:=proc(text,n) convert( map(x->modp(x+n-1,127)+1,convert(text,bytes)), bytes); end;

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caesar123(plaintext,10);

UUdecnN8aHIqc3xocip8aXJybyp8aXJvfCR8aXIqfCNvKnwja3h8aXIqfGlyeSpveG15bm8qOzs7NiI=

caesar123(plaintext,1000);

UUdEWFljfDFZY3wxZFhVfDFkVWhkfDFnVXwxZ1FeZHwxZF98MVVeU19UVXwxISEhNiI=

caesar123(caesar123(plaintext,-94),94);

UUdUaGlzfmlzfnRoZX50ZXh0fndlfndhbnR+dG9+ZW5jb2RlfjExMTYi

Exercise: Describe all the solutions of the following congruences. Remember that 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means that under division by q, the reminder of a and the reminder of b are equal (Hint: to find the appropriate Maple command, start by looking at the "solve" command help). . xLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEoJmVxdWl2O0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDRi8=23 (mod 7) -xLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiK0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JFEiMkYnRi8tRiw2LVEoJmVxdWl2O0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZORi8=13 (mod 6) 4xLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiK0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JFEiMUYnRi8tRiw2LVEoJmVxdWl2O0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZORi8=23 (mod 11) 3x-6LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEoJmVxdWl2O0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDRi8=-23 (mod 11) 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 msolve(x=23,7);

PCMvSSJ4RzYiIiIj

msolve(-x+2=13, 6 );

PCMvSSJ4RzYiIiIi

msolve(4*x+1=23,11);

PCMvSSJ4RzYiIiIh

msolve(3*x-6=-23,11);

PCMvSSJ4RzYiIiIq

msolve(4*x=4,12);

NiY8Iy9JInhHNiIiIiI8Iy9GJSIiJTwjL0YlIiIoPCMvRiUiIzU=

msolve(3*x-4,12); Ceasar with our own alphabeth Exercise: Store in a variable named "Alphabet" a string containing all printable symbols. [seq(convert([i],bytes),i=1..127)];

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Implode([seq(convert([i],bytes),i=1..127)]);

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Alphabet:=cat("\134t\134n", Select( IsPrintable , Implode([seq(convert([i],bytes),i=1..127)])));

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Exercise: 1. Design a procedure that takes a string of characters as input and replaces each character with the number corresponding to that character in Alphabet. 2. Repeat 1. with the condition that the first character of the Alphabet should get the number 0. Exercise: 1. Design a procedure that takes as input list of integers and replaces each entry of the list with character in that position position in Alphabet. 2. Repeat 1. with the condition that the first character of the Alphabet should get the number 0. Exercise: Using the two procedures above, create a new implementation of Ceaser method using the alphabet stored in "Alphabet". How would you decode an encoded message?