Problem 45282. Cryptography with A Square Matrix : Decoding

Created by Mehmet OZC

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{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Previous Problem:</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45279-cryptography-with-a-square-matrix-encoding\"><w:r><w:t>Cryptography with A Square Matrix : Encoding</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Now decode a double vector to a (hopefully!) meaningful text.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Inputs are</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>encoded vector</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>key</w:t></w:r><w:r><w:t> matrix.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ encodedVector = [1665 1624 1541 1549 1495 1501 486 510 534 1503 1552 1595 1192 747 836]\n\n key = magic(3);]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>inverse of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>key</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ inverseKey = [0.147222222222222 -0.144444444444444 0.0638888888888889\n -0.0611111111111111 0.0222222222222222 0.105555555555556\n -0.0194444444444445 0.188888888888889 -0.102777777777778];]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Reshape</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>encodedVector</w:t></w:r><w:r><w:t> so it has the same number of rows with</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>key</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ reshapedVector = [1665 1549 486 1503 1192;\n 1624 1495 510 1552 747;\n 1541 1501 534 1595 836];]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Multiply</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>inverseKey</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>reshapedVector</w:t></w:r><w:r><w:t>, round it and reshape it;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ messageVector = [109 97 116 108 97 98 32 38 32 99 111 100 121 32 32];]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>char equivalent of message vector is 'matlab &amp; cody'</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Previous Problem: <a href = "https://www.mathworks.com/matlabcentral/cody/problems/45279-cryptography-with-a-square-matrix-encoding">Cryptography with A Square Matrix : Encoding</a>Now decode a double vector to a (hopefully!) meaningful text.Inputs are encoded vector and key matrix.<pre> encodedVector = [1665 1624 1541 1549 1495 1501 486 510 534 1503 1552 1595 1192 747 836]</pre><pre> key = magic(3);</pre>inverse of key<pre> inverseKey = [0.147222222222222 -0.144444444444444 0.0638888888888889
 -0.0611111111111111 0.0222222222222222 0.105555555555556
 -0.0194444444444445 0.188888888888889 -0.102777777777778];</pre>Reshape encodedVector so it has the same number of rows with key<pre> reshapedVector = [1665 1549 486 1503 1192;
 1624 1495 510 1552 747;
 1541 1501 534 1595 836];</pre>Multiply inverseKey and reshapedVector, round it and reshape it;<pre> messageVector = [109 97 116 108 97 98 32 38 32 99 111 100 121 32 32];</pre>char equivalent of message vector is 'matlab & cody'

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Problem 45282. Cryptography with A Square Matrix : Decoding

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