Check this out:

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Original idea by Juaquin Anderson in the comments of the

following thread:

https://plus.google.com/+JuaquinAnderson/posts/L9A3Da8ju3BFWIW, here is the content of the comment:

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“This has me thinking.. All the structure, in the reverse

iteration, and the sequence of roots, as well as the structure

of the level sets with the escape time algorithim.

Someone

suggested using fractals for encryption..

A method that would

actually work would be to choose an interesting value of c,

like this one, as the key.

1) If the message has length n bits,

choose a point in the n'th level set. The point can be chosen

by taking a starting point just outside the circle delimiting

the target set, and applying inverse iteration, choosing roots

by sign according to the bits in the sequence to be encoded.

2) the result would be a point (x+yi) that is inside the nth level

set close to the Julia set.

3) encode that point accurately

enough to not confuse with points of a level deeper or further

out, and transmit that point.

4) receive that point.

5) decode

the point by applying forwards iteration with the key value c,

until the point lands in the target set. Tge decoded message

would have n bits determined by writing down the sign of the

imaginary component of the escape orbit for each iteration.

Sounds easy right?

:-)

The efficiency of the encrypted coding scheme has to do with

the fractal dimension of the Julia set, and the degree of

imbalance of the contractivity in the tree traversal of the

Julia set."

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Juaquin Anderson has taken fractal encryption to another level

beyond the stuff I have been experiment with. He is basically

encoding a sequence of bytes inside a single complex number.

The reverse iteration method for a Julia set is being used to

store information. Lets say a byte. Well, a byte is made up of

a number of bits, on or off. These bits are used to decide which

root to choose for the square root of z during reverse iteration

of (z = z^2 + c). After this reverse iteration, one ends up with

an interesting point p. This point p can actually recreate the

bits of the byte when exposed to forward iteration. The number

of iterations for both forward and reverse iteration directly

corresponds to how many bits it stores. I can only do around 40

bits, but the little program I wrote just does 8 for clarity.

So, for encryption c is the secret key and the cipher text is a

list of complex numbers, or a single complex number if one uses

an arbitrary precision library to calculate both the reverse and

forward iterations.

Here is a simple proof of concept program in C++11 that encodes

a single byte:

http://pastebin.com/4Yu8uSKHIf one can encode a single byte, then one can encode multiple

bytes, and arbitrary binary files.

I know that this is going to work like a charm. I am working on

another proof of concept program that shows how to encode multiple

bytes in a single complex number, instead of the single byte

example shown here...

Any thoughts?

What do you think about the code? Is it crap?

;^)

Thank you all.

Also, I have a fractal encryption scheme that is actually compatible with this using minimal changes of incorporation:

http://www.fractalforums.com/fractals-in-nature/fractal-encryption/What do you think of the code?