Month: September 2018

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 2

I have completed the second part of my article on the fundamentals of RSA encryption. It can be accessed by clicking on the following link:

RSA 2

There are many more topics in the field of encryption that I would like to learn about and write about. These include:

  • Practical implementation of RSA (padding, signatures, etc)
  • Other algorithms for factoring integers (esp. general number field sieve)
  • Proof of the prime number theorem
  • Attacks on RSA (e.g., timing, chosen ciphertext, side-channel, acoustic, etc)
  • Elliptical curve encryption

However, these are not for the faint of heart. Perhaps in the future.

Instead, right now, what I plan to do next is give a description of the basic theory behind quantum encryption.

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

Next 4 topics

The next 4 topics that I would like to discuss on this blog expand upon subjects described in my novel, The Formula. They are:

  1. RSA encryption
  2. Quantum encryption
  3. Bell’s Theorem
  4. Bohmian mechanics

An explanation of RSA encryption is given in the long version of Chapter 62 from The Formula. It can be found elsewhere on this website. My page on RSA encryption will be, for the most part, the discussion in Chapter 62 (Long Version) presented in expository form. In keeping with my attempt on this site to avoid “black boxes,” I have included a detailed but slow and step-by-step derivation of the mathematical formulas used in RSA encryption. I’ve done this so the reader isn’t left scratching his or her head, wondering where those formulas came from. Because mathematical proofs have never been my forte, I’ve relied heavily on information gleaned from several on-line sources.

Likewise, my page on quantum encryption is largely an expository version of the treatment on this subject given in Chapter 79 (Long Version) from The Formula. This chapter can also be found on this website and can be reached by clicking here.

Because my treatments of RSA  and quantum encryption are essentially reformulations of the descriptions found in the above-mentioned chapters, it shouldn’t take too long to produce them. On the other hand, I plan to expand considerably on the discussion of Bell’s Theorem given in Chapter 79 (Long Version). Thus, I expect that my page on Bell’s Theorem will take a little longer to produce. Finally, the last page I wish to create that relates to The Formula has to do with Bohmian mechanics. Development of this page, quite frankly, will take some doing.

So RSA encryption should be coming up next. Slightly before or after my page on this subject is released, I anticipate posting news of a promotion involving The Formula: for 5 days, The Formula will be given away-free! On amazon.com.

So stay tuned.

“The Formula” now available

My first novel, “The Formula”, is now available for purchase on amazon.com as an eBook or paperback. Links are as follows:

eBook: https://www.amazon.com/Formula-Sam-Artigliere-ebook/dp/B07GZ7PC2S/

Paperback: https://www.amazon.com/Formula-Sam-Artigliere/dp/1718144849/

Check back frequently for promotions, including free giveaways!