Hello. I am a new user and am watching the cryptography series. I have only watched 2 episodes. I already knew most of the history, but I think we should have started at public key. I still need to watch the algorithms section.
I wanted to share my lessons I made for a college course I took. Concentrate on the Lesson 1 slides. The equation to defeat RSA is there. The other lessons are about the background.
I share this with the community because I am an inspiring teacher. I am in school learning about adult education. That is when I developed these sides in an instruction class. I am only promoting my idea there is nothing to purchase here. Would it ever be considered to have student teachers at IT Pro TV?
I post this here because it breaks the factorization problem of public key. I am confused on what actually makes an N = NP, but obviously the factorization problem doesn’t. It would be like time travel. It appears to be impossible, but a future discovery might mean that N = NP in time travel. That is the best description I can come up with because once N = NP is proven the problem is no longer N does not = NP. I would like to have more discussion in cryptography and one way functions.
If I broke the message boards rules by posting my own content than just delete it. However, I urge you to look at it first and you will see it is relevant.
BTW, the audio to the first lesson is in Windows Media Format and will not play until downloaded and played in PowerPoint. The equations can still be viewed online. That is what I want you to see.
Thank you for your time and please read the following message and follow the links to the lesson.
The lesson is geared to anyone with an algebra 2 knowledge. The equation is number theory so complex patterns are described by simple algebra. Usually the audience is math literate. But even being math literate the way I describe the problem may sound complicated. The problem is broken down in these lesson to a way that will make the equations best understood.
- In Power Point Presentation: Introduction: Lecture: Create interest in math and explain overview of what is happening in math problem.
- In Power Point Presentation: Lecture: Brief background on theory of main equation students are learning
- In Power Point Presentation: Revel 1st equation and then 2nd equation and briefly describe what the equations do.
- In PowerPoint Presentation show equations set equal to each other.
- In PowerPoint Presentation show the result.
- In Class: Students type the main polynomial equation into Mathematica (a math programming software) and test various variables and output with error and without error.
- In Class: Students graph various answer plots using Mathematica. Students apply basic Calculus to look for what values graph is approaching.
- In Class: Explain to students how this equation in solved by Mathemtica and there is a margin of error in the equations. Explain how Mathematica saves time, but that doing this on paper would take great resources.
- In Class: Explain to students that you shouldn’t plug and chug. We are testing values here to get a “feel” of the equation. Mathematic helps us test values. A little plug and chug is necessary when pattern searches. Explain that Mathematic is excellent to test equations you don’t fully understand.
- Power Point Presentation: Show second equation set.
- In Class: answer questions. Ask if anyone wants to share their results. Offer bonus points for any worthy discovery.
- Give contact information.
- In Power Point Presentation: Explain why Wikipedia is an excellent math resource.
- In Power Point Presentations: Show patterns and closeness the 85.
- In Power Point Presentation: Show equations and patterns that help to present the margin of error.
- In Power Point Presentation: Request help.
- In Class: Note that this problem is only partially solved. The margin of error must be found.
- In Class: Assignment: Students are to create a mathematical notebook in Mathematic; create graphs; and an interactive CDF file (think math animation that is interactive). These results will be posted online with 5 comments on other students work mandatory. Assignment is due in 2 weeks.
- In Power Point Presentation: Show progression of where the patterns originated mathematically working backwards from end of pattern to beginning of derived equations.
- In Power Point Presentation: Show series of Wikipedia articles while original lecture is given. This lecture is about the history of cryptography and its modern connections. Also discuss one-way functions and the NP problem.
- In Power Point Presentation: Give figures of how many people have seen this math problem and how many have acted upon it.
- In Class: Challenge the class to share this with everyone they know and make it go viral.
- In Class: Set up teams that will work on factoring 256 bit and larger numbers.
- In Power Point Presentation: Show the numbers of the 768 bit number.
- In Class: Start the class collected RSA cryptography messages to store for future deciphering.
- Give contact information.
The technology used are computers, projects, and software. More specifically the technologies are Power Point and Mathematica. Mathematica is a math computation and programming software. Several of the Power Point slides have Mathematica code. The equations and their solutions where calculated in Mathematica. The entire math problem itself relies on Mathematica in its solution.
In Mathematica there are notebooks, formatted math which can be solved by pressing “shift-enter”. These notebooks can be shared. They are so versatile that entire textbooks can be written. Graphical plots can be made. Also interactive animations can be made that take input for variations and is customizable in real time.
In a computer lab after watching a Power Point presentation an instructor could follow this lesson plans with the students. The goal is to give the students something tangible right away. They will better understand the equation by testing with it with values in Mathematica. So when the student leaves the classroom they have something to work on. They can even share ideas with other students’ programming attempts over the internet.
So it is traditional math augmented with technology. This project would be great to show off Mathematica’s features, but also as a starting point to learn Mathematica. But my goal is to teach learning and research in math. This math problem is real and with a little luck it might even proof something.
The problem itself is about technology. It is math. It also relates to modern, public key cryptography. Today, cryptography is based on computers. Modern cryptography is public key. The result is the one-way function required for these keys to work. This is modern problem and cryptography is the main security feature of the internet and banks. The old school math is still the basis and describes modern technology.