Wednesday, April 13, 2011

Fractal Based Encryption Systems

Encryption methods based upon nonprobabilistic nondeterminism

In 1987 a discovery led to the formal proof that it is possible to use chaotic functions to arrive at a nonprobabilistic and nondeterministic method normal context of the operation of this system, and by using a virtual operational environment, the investigators are manipulating data in eight dimensions, which require a sixty-four discrete coordinate system, using eight nominative octets. Each octet is further addressed using the characters 0 through 9, and lower- or upper-case letters from A to Z. These provide the ability to address using normal ASCII characters. This format was chosen to ensure backward and forward compatibility with external third-party-written software.

This original discovery has led to the fundamental principle that the main focus of any chaotic system was what the output would look like. After watching hundreds of runs of Edward Lorenz's strange attractors show up in places that were seemingly endless, it was decided that the team would pursue the goal of placing this type of behavior into a software/hardware combination that would supply the necessary functionality and still be robust enough for a PC or minicomputer format. This was accomplished when the first modules of Fortran were created; then, as time went on in the development process, the investigators translated some of the harder features into what languages were available and able to be used.

The system that was decided upon was one where a combination of hardware and software was used. The hardware provided a means of proper transmission and error correction, and the software was utilized to create the front end and all of the virtual mechanisms used to create each message block, or octet as the case may be.

It was also discovered that this same functionality would allow the messages to be combined into still larger messages in a differential cryptographic type of format. When this was demonstrated, a single message contained several megabytes worth of data. The message blocks themselves did not contain more than a minimum of 56K to a maximum of 128K in total length.

There were additional discoveries to be made with this format, and many of these were going to be even more interesting scientifically. It was discovered that the messages could be used for storage after the shell had been created for the final encrypted product. The baseline addressing schemes started at 1024 bits, went to 2048, and then finally stopped at 2048 × 2048, or 4,194,304 bits in the single message matrix. This single matrix was demonstrated to be able to hold several orders of magnitude above the original test shell. In testing, the actual message block has contained a five-to-one ratio of encrypted data to original matrix. The largest block to date is more than five hundred megabytes with a nominal shell of three megabytes.

The message matrix, at the present time, is translated into the standard two-dimensional hardware addressing that the hardware will support. There is additional experimentation with optical methods to ensure that the output of the product is translatable into three and higher mathematical dimensions. While the creative mechanism is based upon a VRML format, the main message unit is easily translatable into any known or projected translational mechanism.

This was arrived at by multiple-level addressing: taking the single address, and then combining them with lower and lower addresses. An example of this would be a situation where the zip code of a city describes a geographic region. The street address is another layer, and finally the house number, describing a physical location.

This addressing schema is error-corrected, and supports existing software and hardware devices to ensure the platform is nonproprietary after the message is encrypted. The encryption mechanism is such that the messages are layered one on top of the other with the error-correcting codes built in. This is to ensure accuracy in the message encryption process, and will enable the message to be recreated accurately in case of damage in transmission, or other electronic disruption.

The next focus of the effort will be a fixed two-dimensional format in the form of a smart card with the addressing scheme engraved into the substrate. The team chose a polyester sub-base with optically opaque infrared-transparent material. This was chosen to ensure tamper resistance for any smart cards or identification cards using this technology.

The greatest difficulty has been scratch resistance for the cards, and message length over suitable networks. The largest experiment to date has been in the transaction protection mechanisms of the test network, where the first live data transmission tests occurred. The tests also showed that the message length was of less importance than the transmission speed at which it was sent.

Another focus has been in the creation of fixed, nonmovable memory arrays on the polyester cards that were part of the original development process. The main limitation on this technology has been the difficulty in obtaining test materials and equipment, due to the size limitations of the test equipment. It is expected that the next phase of testing will be in packetization, and routing mechanisms for transmission of larger volumes of information within the framework of the original message matrix.

In experimentation it was demonstrated that the chaotic functions were robust enough to be used to their theoretical limitations in usage with DES, or Triple-DES functions. This was chosen to allow usage of a Kerboros or other to-be-developed public key infrastructure. The methodology allows this system to be used with independently developed software and hardware. It was originally developed for the protection of a financial transaction network for a client that subsequently went bankrupt.