# Thread: New One Way Function

1. Trurl,

First off thank you for the excellent response, very informative and you've cleared up some questions I had, I wish you luck with your quest to crack RSA, it's been breached earlier as my company had to buy 3500 new RSA token fobs after ours were compromised, so obviously it can be done, but that's far above my head.

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184

## Code explains it all; Trying to find exact way to calculate error. This is equation.

PNP = 3163007

NSolve[((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3) == ((PNP^2/x) + x^2)/
PNP + 0.287159517, x]

3163007

{{x -> 10766.8 + 18673. I}, {x ->
10766.8 - 18673. I}, {x -> -21533.6}, {x -> -953.082}, {x -> 953.}}

__________________________________________________ ___________________________________________
__________________________________________________ _________________________________________--

The equation below shows how to solve the error wich is 0.287

PNP = 3163007

NSolve[((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3) == ((PNP^2/x) + x^2)/
PNP + 0.28, x]

3163007

{{x -> 10767.00553406246` + 18672.685351161595` I}, {x ->
10767.00553406246` -
18672.685351161595` I}, {x -> -21533.93266812111`}, {x -> \
-941.1247294994954`}, {x -> 941.0463294956866`}}

The error of 0.28 is a starting point. Each side of the NSolve equation. These equations equal the Prime product within this error. I know it isn't exact yet, but I am working on it.

__________________________________________________ _____________________
x = 941 from previous equation

PNP = 3163007

((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3) - ((PNP^2/x) + x^2)/PNP

941

3163007

8859632789683911270/31644661843413961343

N[8859632789683911270/31644661843413961343, 11]

0.27997242737

3. Registered User
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## The final semi-Prime post. 3 PowerPoint Presentation

Hello. Here is a post I have been posting on a couple of message boards. This will be my final post on semi-primes. I am working on other problems. I know the message boards at 3D Buzz have slowed. I recommend branching out on engineering topics. For example, designing the body of a car to be aerodynamic, yet fit the inner mechanisms. Math is also an area to explore. I think the game design has been done so well that newer projects are more difficult to teach. I have the same problem with my semi-Prime factorization problem. I have tried to create a math and engineering with my site. But it takes more know-how and resources.

This will probably be my last Prime number post, which is probably much waited for. If you watch my 3 lessons you will learn about cryptography. The lecture speech isn’t terrific but the ideas are clear. So if these videos teach you anything please post here and let me know.

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.

Lesson 1
https://onedrive.live.com/redir?resi...nt=file%2cpptx

1. In Power Point Presentation: Introduction: Lecture: Create interest in math and explain overview of what is happening in math problem.
2. In Power Point Presentation: Lecture: Brief background on theory of main equation students are learning
3. In Power Point Presentation: Revel 1st equation and then 2nd equation and briefly describe what the equations do.
4. In PowerPoint Presentation show equations set equal to each other.
5. In PowerPoint Presentation show the result.
6. 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.
7. In Class: Students graph various answer plots using Mathematica. Students apply basic Calculus to look for what values graph is approaching.
8. 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.
9. 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.
10. Power Point Presentation: Show second equation set.
11. In Class: answer questions. Ask if anyone wants to share their results. Offer bonus points for any worthy discovery.
12. Give contact information.

Lesson 2
https://onedrive.live.com/redir?resi...nt=file%2cpptx

1. In Power Point Presentation: Explain why Wikipedia is an excellent math resource.
2. In Power Point Presentations: Show patterns and closeness the 85.
3. In Power Point Presentation: Show equations and patterns that help to present the margin of error.
4. In Power Point Presentation: Request help.
5. In Class: Note that this problem is only partially solved. The margin of error must be found.
6. 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.

Lesson 3
https://onedrive.live.com/redir?resi...nt=file%2cpptx

1. In Power Point Presentation: Show progression of where the patterns originated mathematically working backwards from end of pattern to beginning of derived equations.
2. 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.
3. In Power Point Presentation: Give figures of how many people have seen this math problem and how many have acted upon it.
4. In Class: Challenge the class to share this with everyone they know and make it go viral.
5. In Class: Set up teams that will work on factoring 256 bit and larger numbers.
6. In Power Point Presentation: Show the numbers of the 768 bit number.
7. In Class: Start the class collected RSA cryptography messages to store for future deciphering.
8. Give contact information.

Conclusion
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.

4. Who Dat!
Join Date
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934
I'm impressed with your perseverance, trurl_, even though I have not had the motivation to break this all down to see what you were trying to do. I agree that, since activity here has slowed, you're probably not reaching much of an audience. But here's an active forum where lots of scientists and scientific-minded (and skeptical) folks hang out: http://www.internationalskeptics.com/forums/

There's a subforum for science and math here.

Edit: I will say, though, it can be slightly less friendly than 3dbuzz at times.
Last edited by pellea72; 09-13-2015 at 10:15 PM.

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## Take time to see the pattern!

Thank you for the input. You are right I am not an established enough mathematician yet, and ideas often need a good defense on math messageboards. But I must ask why haven’t you had the motivation to break this down? It would take 5 to 25 minutes to see the pattern in the Prime factors. Admittedly, the “error” or “accuracy” is not easy to see if the problem is practical. However a computer program would deal with the error. You would need to test 0.1; 0.2; to 1 and the error would be solved. I encourage everyone to look at slides 2 through 7 of the first presentation. Look at the equations on the physical slides. There is a pattern. I have shared it so it becomes more than a pattern. I want a solution.

6. Uncultured Oaf
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So in those equations you're trying to solve for q for n = pq correct?

also, here's an n you can try prime factoring using your method. Remember you can't start off knowing either p or q, or how close you are to them.
n = 29447984923635601999430965802159139873300537366664 48929706304421651404721827924626945562316458141285 40478312892249896279024392627234473013534385408884 102818804787147035063680827671
Last edited by SLAYER; 10-02-2015 at 04:27 PM.

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## Need you help to find difference between 0.072 and 0!

Ok mister know it all :b

Only kidding. I cannot yet solve that semi-prime. I have found the error, but I am reliant on Mathematica to solve.

If I set it equal to the error it doesn’t solve for a reason I don’t know why. I am close to that value, but if I set it equal to 0 and in Mathematica the equation is 0.072 it is not equal to zero but for all intense and purposes is close enough to be considered zero.

So I post these equations asking for programming help. It is the same equations I gave my backers.

Test for yourself:

PNP= 85
x=5
((PNP^4+2*(PNP^2*x^2)+x^5)/PNP^3) - (PNP + (2* (x^2/(PNP))))
85
5
25/4913

PNP =15

eqns = {((PNP^4+2*(PNP^2*x^2)+x^5)/PNP^3)- (PNP + (2* (x^2/(PNP)))) }
NSolve[eqns, x]
15
{9/125}
{}

{{eqns->0}}
PNP = 5991
x = 3
((PNP^4+2*(PNP^2*x^2)+x^5)/PNP^3) - (PNP + (2* (x^2/(PNP))))
5991
3
9/7964053973

Where N = p * q or also PNP = x * y

The error is 2 * (x / y)

We still are given only N but maybe there is a graph using calculus that will show the error approaching for a given x.

So if you find a real number in the polynomial equation for x and it is the wrong value divide N by x and take 2 * (x/y) and see what value it is approaching. Plug this error into the equation until
N = x * y

8. Uncultured Oaf
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I was talking about your equations in your slides. Where you have q = (n^2/p+p^2)/n etc...

also post a formal proof on how you got this equation from your previous post.

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## I never wrote a proof yet. At least not formally. Here is a link. Look at equation

Code:
` PNP = 15`
Code:
`eqns = {((PNP^4 + 2*(PNP^2*x^2) + x^5)/PNP^3) - (PNP + 2*( x^2/PNP) ) == 0.072}`

Code:
`NSolve[eqns, x]`
Code:
`Out[32]= 15`

Code:
`Out[33]= {True}`

Code:
`Out[34]= {{}}`

It would take me a while to show how I solved this. I solved it in real time so if you go back over previous threads.

I can't share everything because I have Backers that supported my work.

Now in the above equation, I need help to find how to program 0.072 so it is close to zero but I need it to be within < 0.1

I don't really know how to program that. But we could try solving the polynomial by hand instead of Mathematica.

However if you don't have access to Mathematica, you can use Wolfram Alpha.

I am saying 0.072 is close enough to zero. But for programming it has to be exact.

In the next few weeks I will be making a list of all correct equations. I think I have a few that use trigonometry. You are free to check my math section on www.constructorscorner.net

Viewing my math there will be confusing because of the order. I have some things right, but a lot wrong. I haven’t updated it since 10/14.

I have also posted for programming help on a math site but since you took interest I decided to share with you.

I think the equations work and is more of a programming problem that creating a perfect math equation.

If you do find anything, let me know.

10. Uncultured Oaf
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Posts
1,402
Then my question is how did you arrive at these equations? You just plugged and chugged and when you got a decimal result with a leading 5 you said "eureka"? This doesn't prove a thing. Also, if you back sub n = pq into both of those equations in your slides, you'll find that they do not satisfy the original assumption that p, q are both integers > 1 (they have to be since the requirement is that p,q are primes >= 2, thus n is a composite >= 4).

This is basic algebra and doesn't need calculus to prove. The equations simply aren't even equal to each other. If you want me to show you my work then I'll upload it. You cannot come up with 2 equations and just pretend that they're equal, especially when basic simplification shows that they're not, and say that the difference is an error percentage/value. That's not how math works. Your assumption in the slides on how calculus will prove your equations some how is also wrong. While calculus is based on formal proofs, definitions, lemmas, and corollaries, it's primary use is for providing a means of computation. Not rigorous proof writing. Saying .072 is close to zero is also a huge misconception. because it's really not. Look into limits.

You need some serious practice with your math. I'd suggest going to reddit and math.stackexchange with your equations if you don't believe me. Go back to page one where you were first introduced to modular arithmetic, and a few posts later you claimed that you think RSA is a sham, while admitting you have no idea of the implementation. This is shows how ignorant and out of your element you are when it comes to mathematics, and cryptography. RSA, and other crypto algorithms, rely on modular arithmetic. You need to understand it fully, and the many definitions, lemmas, and theorems that make use of modular arithmetic.

If you really want to learn the math needed to find factors, and implement mechanisms to break crypto schemes, then you're going to need to read up on modern/abstract algebra as well as some linear algebra. As for the calculus, you'll want to look into real/elementary analysis which is the actual theory that calculus is based on (and can be useful for hashing). Coursera, and udacity also have basic crypto courses you can take to get a light intro to how they're used for modern crpytography. Youtube is another great resource, and there are also tons of open coursewares. Just keep in mind that this stuff takes years to learn.

Specific methods for factoring you should read up on are trial division, Pollard's rho algorithm (this is algorithm is easy to code and can factor small keys ~110 bits very quickly) , as well as seives. Look into those algorithms to see what has been done, and how effective they are on today's hardware. You can easily factor a key of ~240 bits in less than a minute on your home pc/laptopn using a seiving program, and a 512 bit key in under a day if you rent a cluster from amazon or microsoft. However even with the best optimized algorithms, that have been proven by mathematicians and computer scientists, a 768 key can take several months, and was first successfully factored in 2009. No one has factored a 1024 bit key (provided it wasn't generated with many other keys using the same seed in the same weak pseudo random number generator, which would make it easy to break by finding the gcd between keys) to this day. Modern implementations use a minimum of 1024 bits. Factoring small numbers like 85 is trivial, which is why it's not a good starting place, but factoring a number 1024 bits+ in length is very hard, and why something closer to that length is a good place to start. Good luck.
Last edited by SLAYER; 11-01-2015 at 01:52 AM.

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