Problem 45279. Cryptography with A Square Matrix : Encoding

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>Matrix inverse operation can be used to encode or decode of a message. For example</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ text = 'matlab & cody'.]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>numeric equivalent is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ num = [109 97 116 108 97 98 32 38 32 99 111 100 121]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>let</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ key = magic(3);]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>key</w:t></w:r><w:r><w:t> is an arbitrary square matrix and its inverse is exist.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>reshape the vector</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>num</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: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[ numMatrix = [109 108 32 99 121;\n 97 97 38 111 32;\n 116 98 32 100 32];]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Note that last two elements are filled with 32 which is the numeric equivalent of blank character ' '.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Finally multiply</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> with</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>numMatrix</w:t></w:r><w:r><w:t> (and reshape it) to obtain an encoded vector.</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]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>if you multiply</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>inverse of key</w:t></w:r><w:r><w:t> with reshaped</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> you can obtain the ascii numbers of secret message.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Next Problem :</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45282-cyrptography-with-a-square-matrix-decoding\"><w:r><w:t>Cryptography with A Square Matrix : Decoding</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Inspired from:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Barnett, R.A., Ziegler, M.R. and Byleen, K.E. (2015). Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences. Pearson, 13th (Global) Edition. p:245-247.</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>"}]}

Matrix inverse operation can be used to encode or decode of a message. For example<pre> text = 'matlab & cody'. </pre>numeric equivalent is<pre> num = [109 97 116 108 97 98 32 38 32 99 111 100 121]</pre>let<pre> key = magic(3);</pre>key is an arbitrary square matrix and its inverse is exist.reshape the vector num so it has the same number of rows with key matrix<pre> numMatrix = [109 108 32 99 121;
 97 97 38 111 32;
 116 98 32 100 32];</pre>Note that last two elements are filled with 32 which is the numeric equivalent of blank character ' '.Finally multiply key with numMatrix (and reshape it) to obtain an encoded vector.<pre> encodedVector= [1665 1624 1541 1549 1495 1501 486 510 534 1503 1552 1595 1192 747 836]</pre>if you multiply inverse of key with reshaped encodedVector you can obtain the ascii numbers of secret message.Next Problem : <a href = "https://www.mathworks.com/matlabcentral/cody/problems/45282-cyrptography-with-a-square-matrix-decoding">Cryptography with A Square Matrix : Decoding</a>Inspired from:Barnett, R.A., Ziegler, M.R. and Byleen, K.E. (2015). Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences. Pearson, 13th (Global) Edition. p:245-247.

Matrix inverse operation can be used to encode or decode of a message. For example

text = 'matlab & cody'.

numeric equivalent is

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

let

key = magic(3);

*key* is an arbitrary square matrix and its inverse is exist.

reshape the vector *num* so it has the same number of rows with *key* matrix

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

Note that last two elements are filled with 32 which is the numeric equivalent of blank character ' '.

Finally multiply *key* with *numMatrix* (and reshape it) to obtain an encoded vector.

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

if you multiply *inverse of key* with reshaped *encodedVector* you can obtain the ascii numbers of secret message.

Next Problem : <https://www.mathworks.com/matlabcentral/cody/problems/45282-cyrptography-with-a-square-matrix-decoding Cryptography with A Square Matrix : Decoding>

Inspired from:

Barnett, R.A., Ziegler, M.R. and Byleen, K.E. (2015). Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences. Pearson, 13th (Global) Edition. p:245-247.

Solve

Solution Stats

28 Solutions
8 Solvers

Last Solution submitted on Aug 29, 2022

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Alfonso Nieto-Castanon on 19 Sep 2020

it's a bit unclear why padding is necessary in the first two test cases, where the number of characters (15) is already a multiple of the key size (3 or 5, respectively)

ChrisR on 19 Jun 2021

I agree with Alfonso.

Dyuman Joshi on 19 Jun 2021

+1
@Mehmet can you explain why?

Problem Recent Solvers8

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 45279. Cryptography with A Square Matrix : Encoding

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers8

Suggested Problems

More from this Author92

Problem Tags

Community Treasure Hunt

Problem 45279. Cryptography with A Square Matrix : Encoding

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers8

Suggested Problems

More from this Author92

Problem Tags

Community Treasure Hunt

Players