Tag: modular arithmetic

Update to The Formula, Chapter 62 (Long Version)

Just a short detour before moving on to an introduction to quantum encryption. I’ve updated the long version of Chapter 62 of my novel The Formula. You can navigate to that chapter by clicking on the following link

Chapter 62 Long Version

Also, here are some acknowledgements/references for that chapter.

The general overviews from which I generated most of this article can be found at the following sites:

https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/the-fundamental-theorem-of-arithmetic-1

https://en.wikipedia.org/wiki/RSA_(cryptosystem)

The discussions on Euler’s Totipotent Theorem were derived from the following sources:

http://artofproblemsolving.com/wiki/index.php?title=Euler%27s_Totient_Theorem

https://www.chegg.com/homework-help/definitions/eulers-theorem-33

http://www.math.uconn.edu/~kconrad/blurbs/ugradnumthy/fermatlittletheorem.pdf

Information on Euler’s Totipotent Function was gleaned from several sources. The main one was:

http://mathworld.wolfram.com/TotientFunction.html

Proof of the multiplicity rule in modular arithmetic was largely taken from:

https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/modular-multiplication

The proof of phi function multiplicity follows the arguments outlined in:

http://www.oxfordmathcenter.com/drupal7/node/172

The discussion of Euclid’s Algorithm was taken from:

https://en.wikipedia.org/wiki/Euclidean_algorithm

The proof that the Euclidean Algorithm works come from this source (document will be downloaded by clicking on the link)

www.cs.ucf.edu/~dmarino/ucf/cot3100h/lectures/COT3100Euclid01.doc

 

RSA Encryption 1

As promised in my last post, I have created an article on the first of my “next 4 topics,” – an article on RSA encryption.

I couldn’t get my equations to format correctly by using an equation plugin or by embedding an odt document like I’ve done previously. Therefore, I embedded a PDF of the article using a plugin, PDF Embedder.

To be able to use links, you need the premium (paid) version. However, just a tip for others who might be having similar difficulties, if you an MS Word for Mac 2011 document to pdf, links (both internal and external) that worked in the Word document will not work in the pdf. The workaround I used was to convert my Word document to a Google Docs document. I had to rewrite many of the equations, and after several revisions, it appears that I have a workable document.

Not ideal though.

I suppose I might need to break down and learn LaTex.

At any rate, you can find the first installment of my discussion of RSA encryption topic by clicking on the following link:

RSA Encryption 1