Contents | |
---|---|

Impenetrable |
Our fractal transformation cyphers cannot be penetrated |

Logic Deduction |
Binary logic deduction proof |

Mathematical Proofs |
Our fractal transformation is infinitely complex |

# Impenetrable

We have proof that the cypher created by our fractal transformation technology is impenetrable.

Impenetrable and uncrackable by any means, including Quantum Computers.

This is a world-first as cryptography has not previously had a form of encryption that is impenetrable.

# Proof

The foundations of our proof rest on logic deduction and mathematical proofs.

## Logic Deduction

The concise deduction is as follows:

As the unknown fractal transform is the same size as the payload,

all random, semi-sensible and sensible cypher bit combinations are payload candidates,

and there is no way to distinguish the payload from other sensible candidates.

The deduction is robust as a binary string of matching length can define all possible text, images, audio and any data whatsoever.

When a cypher is created by transforming a binary payload with an unknown fractal transform stream of the same length, all cypher bit-combinations become payload candidates.

Let's use an example 24 character email payload, allowing 36 characters (26 letters a - z and 10 numbers 0 - 9) and ignoring @ and . characters. We examine 22 binary character combinations where each character uses 8 bits (2 ^ 8 = 256 combinations). To keep things simple we calculate sensible candidates using 2 ^ 5 = 32 combinations (4 less than 36):

Name | Formula | Total Combinations |
---|---|---|

Total Combinations | 2^8^22 | 95,780,971,304,118,100,000,000,000,000,000,000,000,000,000,000,000,000 |

Sensible Candidates | 2^5^22 | 1,298,074,214,633,710,000,000,000,000,000,000 |

In this case sensible candidates make up only **0.000000000000000001355252715607%** of all possible candidates, yet they still amount to **1.298 Undecillion**
sensible email candidates (for a 24 character email), proving that the email payload (which is one of those) cannot be distinguished from all the other sensible candidates.

Similarly, a transformed graphic payload will have equally large numbers of sensible graphic candidates, and the same goes for audio, html, xml, word, excel and pdf payloads.

There is no way to distinguish the payload from all possible sensible bit-combinations, and there are always a great many perfectly sensible bit-combinations.

## Mathematical Proofs

The logic proof relies on a high quality, complex, unique and unpredictable **unknown fractal transform**.

Our **unknown fractal transform** is derived from the Mandelbrot Fractal.

Our **Fractal Transformation** technology maps passwords and keys to an infinite number of possible **Fractal Portals**, each generating highly complex, unique and unpredictable
binary streams.

Mitsuhiro Shishikura has created the formal mathematical proof that the Mandelbrot Fractal is infinitely complex. His proof can be examined here: Mitsuhiro Shishikuras Proof.

It is common knowledge that there is an infinite number of possible x,y locations on a limited plain. The **Mandelbrot Fractal** responds with a unique and unpredictable
value for each of the infinite possible x,y locations.

Our **Fractal Transformation** selects new x,y locations based on the value of previous x,y locations.

As the values of all possible Mandelbrot x,y locations are proven to be infinitely complex, the quality of our **Fractal Transformation** is also infinitely complex.