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!

The Formula: Sample Chapters

A book, lost for centuries, is said to recount the intimate conversations between Jesus Christ and Mary Magdalene, providing evidence regarding the divinity of Christ (or lack thereof). When the book is rediscovered, the events that unfold threaten to shake the vary foundations of civilization. These events are the subject of my soon-to-be-published novel, The Formula, a thriller akin to The Da Vinci Code, but with a twist.

Sample chapters from The Formula can be viewed by clicking on the link below:

The Formula: Sample Chapters

The Ladies Club

What do you get when you cross Jerry Mahoney with The Stepford Wives? You get my first entry in the Fiction section of my website, my short story, “The Ladies Club.” The following is a link to this short story:

The Ladies Club

This short story is meant to be a companion to the first entry in the Neuroscience section of this site, “The Simple Response Machine.” The connection between my short story and this neuroscience article is that the neuroscience article, more or less, parallels the content of “the lecture” given by a character in my short story, psychologist Dr. Robert Baker. More importantly, the animations associated with “The Simple Response Machine” provide a visualization of many of “the slides” that Baker uses in his lecture. My recommendation would be to read “The Simple Response Machine” first, then read “The Ladies Club.”

I considered incorporating the animations into the lecture portion of the short story but, when I tried it, it just didn’t work.

Finally, as pointed out in my post introducing “The Simple Response Machine,” the reason that this neuroscience article and my short story are the first real content offered on this site is because they typify the types of issues that this site will address (especially, the relationships between science and philosophy and the use of literature to explore philosophical subject matter).

I hope you enjoy it.

The Simple Response Machine

After considerable trial and tribulation, the introductory entry to my Neuroscience section, “The Simple Response Machine” is ready for publication and can be accessed by clicking the link below:

The Simple Response Machine

It describes how neurons work and how they might be linked together to make a simple machine able to discriminate red light from green light. The intended implication of this exercise is that the principles on which this simple machine operates are the same as those employed by a much more complex machine, the human brain. While this article is certainly intended as an introduction to the complicated science behind neural function, it is just as much (maybe more) meant to be an introduction to two important philosophical issues, issues that are outlined in the article’s conclusion. Indeed, it is no accident that this article is being published simultaneously with my short story, “The Ladies Club” as it gives background crucial to complete understanding of the story. I suggest that readers peruse “The Simple Response Machine” prior to reading “The Ladies Club,” especially if their knowledge of neuroscience is limited.

That short story and this article typify the types of issues that this site will address (especially, the relationships between science and philosophy and the use of literature to explore philosophical subject matter). Thus, they constitute the first real pieces of content published on this site.

I began this project in November 2017. It’s taken 8 months to publish it because of the animations it contains. To make the animations, I had to learn to program with p5.js; it was a challenge, to say the least. The animations are two-dimensional and somewhat crude. Some of the animations are not as accurate as I would have liked simply because programing the necessary details was a hassle. (These inaccuracies are pointed out in the description of the animations, where appropriate.) In retrospect, my time may have been better spent learning a higher-level graphics program. However, learning to program with p5.js was an interesting and instructive adventure, and I feel that the animations, as they are, convey the basic concepts well enough.

The links to animations are designed to open in separate tabs. The best way to view them is to set your browser for new pages to open in a new window, then resize the windows and place them side-by-side such that you can look at the animation and read its description (always depicted in red) simultaneously. Setting your browser to open links in a new window isn’t always easy. However, an easy way to get this done is to allow the link to open in a new tab, then drag the tab off the browser, onto the desktop. References also are set to open in new tabs.

A final word about references before closing this post. First, I chose only references that can be accessed online, for free. I did this because I hope readers will check them out and I know that there’s no chance of this happening if they’d have to buy a textbook, go to the library for textbooks or journals or paying in the range of $35 for access to a reference online. Second, most of the references are reviews of subjects rather than original work, in keeping with the introductory nature of my article. Finally, references range in difficulty from general to quite technical. However, readers can often glean some information, even from the more technical references, often because they contain useful diagrams. I believe, also, that it’s important to show them, because they provide more precise and detailed information in instances where my animations and descriptions fall short.

I hope that you find my article to be of interest.

 

 

Animation test success

I finally got an animation to display correctly on my website. I’m so ecstatic about this that I decided to publish it. A link to this animation is:

Animation Test

Now that I’ve got the animation thing going, I plan to insert animated illustrations into my short story, The Ladies Club, and post that short story when I’m done (the story makes much more sense with the illustrations). I’m not too facile with the programming involved in creating those illustrations so it may take a while. However, I’m happy to have at least taken this small step forward.