Problem 1750. Modular multiplicative inverse

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>Modular multiplicative inverse is used for</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>The Chinese Remainder Theorem</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:i/></w:rPr><w:t>RSA algorithm</w:t></w:r><w:r><w:t>. You can visit</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Modular_multiplicative_inverse\"><w:r><w:t>Wikipedia.</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Normal Modulus</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>X = M (mod Y)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You can solve that with M = mod(X,Y)</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>Inverse Modulus</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>X.B = M (mod Y)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>given X,M,Y calculate B</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>B = inverse_modulus(X,M,Y)</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>"}]}

Solve

Solution Stats

84 Solutions
19 Solvers

Last Solution submitted on Mar 27, 2022

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Rafael S.T. Vieira on 12 Oct 2020

The inverse modulus would be to find X such that mod(X,Y) = M where M and Y are known (or X === M (mod Y)); this is the chinese remainder theorem which is generalized for any number of Y's and M's when all have the same X and the GCD of all Y = 1 (greatest common divisor). The author is actually requesting Y*Z + M = X*B, which is not the same thing, or the inverse modulus.

Solution Comments

Solution 290802

1 Comment

1 Comment

Claudio Gelmi on 27 Jul 2013

Sorry about that...it was only for learning purposes...

Problem Recent Solvers19

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 1750. Modular multiplicative inverse

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers19

Suggested Problems

More from this Author76

Problem Tags

Community Treasure Hunt

Problem 1750. Modular multiplicative inverse

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers19

Suggested Problems

More from this Author76

Problem Tags

Community Treasure Hunt

Players