Tag: binary decimal conversion

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.