Problem 45282. Cryptography with A Square Matrix : Decoding

Created by Mehmet OZC

Solve Later

{"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'

Previous Problem: <https://www.mathworks.com/matlabcentral/cody/problems/45279-cryptography-with-a-square-matrix-encoding Cryptography with A Square Matrix : Encoding>

Now decode a double vector to a (hopefully!) meaningful text.

Inputs are *encoded vector* and *key* matrix.

encodedVector = [1665 1624 1541 1549 1495 1501 486 510 534 1503 1552 1595 1192 747 836]

key = magic(3);

inverse of *key*

inverseKey = [0.147222222222222 -0.144444444444444 0.0638888888888889
               -0.0611111111111111 0.0222222222222222 0.105555555555556
               -0.0194444444444445 0.188888888888889 -0.102777777777778];

Reshape *encodedVector* so it has the same number of rows with *key*

reshapedVector = [1665 1549 486 1503 1192;
                     1624 1495 510 1552 747;
                     1541 1501 534 1595 836];

Multiply *inverseKey* and *reshapedVector*, round it and reshape it;

messageVector = [109 97 116 108 97 98 32 38 32 99 111 100 121 32 32];

char equivalent of message vector is 'matlab & cody'

Solve

Solution Stats

9 Solutions
6 Solvers

Last Solution submitted on Feb 16, 2021

Last 200 Solutions

Problem Comments

Problem Recent Solvers6

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 45282. Cryptography with A Square Matrix : Decoding

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers6

Suggested Problems

More from this Author72

Problem Tags

Community Treasure Hunt

Problem 45282. Cryptography with A Square Matrix : Decoding

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers6

Suggested Problems

More from this Author72

Problem Tags

Community Treasure Hunt

Players