Fractal Transformation

New & Revolutionary Cryptographic Science

Fractal Transformation is a new cryptographic science that has emerged from 6 years of R&D into fractals and the generalised application of their infinite complexity to encryption.

Research focused on the Mandelbrot Fractal as it is well known and researched, with pier reviewed papers proving infinite complexity.

While a great many methodologies were uncovered, most were 'ordinary' in the sense that linear or fixed function fractal traversal did not leverage infinite fractal complexity.

That changed when we developed methodologies to traverse the fractal field using the z result at each fractal x,y location!

Key Isolation

Portalz Fractal Transformation isolates the key, preventing it from acting on the payload.

The key is used to identify a multi-dimensional fractal portal using a specialised fractal mapping.

Once the fractal portal is identified the key is discarded, meaning:

• No key → cipher determinism: no Key → Payload → Cipher hooks
• Irreversible key source: cipher cannot be brute forced to extract key
• Breaks Quantum Key Harvesting: qubit key-registers cannot detect key from cipher

The transformation stream generation proceeds from the fractal portal, each iteration irreversible, unpredictable and infinitely complex (see Whole-of-payload transformation).

Whole-of-payload Transformation

Portalz Fractal Transformation generates a fractal stream that proceeds independently from the fractal portal identified by the key (above).

The size of the transformation stream matches the payload, or in the case of multiple passes multiples of the payload.

The fractal stream is generated with multi-dimensional Mandelbrot fractals by:

1. Identifying a fractal portal using the key: a specialised fractal mapping function
2. Obtaining the fractal value: calculate values at multi-dimensional locations
3. Extract transform values: fractal values are added to the fractal stream
4. Extract navigation values: geometric translation values are extracted from the fractal value
5. Navigate to new location: translate all dimension vectors
6. Iterate to step 2: repeat until the desired transform size is reached

The fractal stream generated is added and XORed to the payload to generate the cipher.

Multi-dimensional Mandelbrot Fractal

Portalz Fractal Transformation implements configurable Mandelbrot dimensions.

Conventional Mandelbrot Fractals use two dimensions, X and Y. Portalz Fractal Transformation allows you to configure an unlimited number of dimensions.

This has the following benefits:

• Configurable Complexity: each dimension increases complexity exponentially
• Configurable Key-Space: each dimension adds 112 bits to the key-space
• Configurable Security: configure according to security and key management requirements

Our Fractal Encryption Standard uses 8 dimensions by default, with a 896 bit key-space.

However, it is important to note that this can be increased without limit! This has been tested up to 40,000 dimensions with a 57,344 bit keyspace.

Silo Compartmentalization

The Silo Mapping is a fractal mapping of 65,536 fractal regions.

Fractal regions should not be confused with the Fractal Portals discussed above, rather they are a regional offset mapping determined by 16 bits of the key.

The key selects a fractal gateway for each dimension and then geometrically offsets with remaining key bit values to arrive at the Fractal Portal.

Fractal Silo regions are uniquely generated for each company/department/application as desired, using GUID generated vectors that guarantee global uniqueness.

Fractal Silos have the following benefits:

• Encryption level compartmentalisation: guaranteed unique fractal portals for the same key
• Unique silos for different purposes: an organisation can generate unlimited silos
• Silo based streaming: only components with the same silo can communicate
• Secure silo installation: silos are stored with fractal transformation and require a key to install
• Ultimate versatility: the equivalent of an unlimited number of encryption algorithms

Fractal Silos dramatically mitigate key breaches as keys must match component silos.