Mandelbrot introduced the fractal model to describe a certain class of
objects exhibiting a complex behavior. Fractal is a set of primitives to
describe such objects, namely applied to images, whether creation or
compression.
For instance, a tree may be considered to be made up of simple
Y forms and leaves in various sizes and orientations. A complicated coast line
may be a collection of simple triangular forms. Notable in such images are
Julia and Mandelbrot Sets. Fractal has the following properties:
-
Self-similarity
- Fractional dimension
- Formation by iteration
Mandelbrot first applied the fractal model to financial data in
[Mandelbrot, 1963]. The fractal view as presented in [Mandelbrot, 1983] starts
from a basic principle: analyzing an object on different scales, with
different degrees of resolution, and comparing and interrelating the results.
Fractal image compression was studied by Yuval Fisher et al., on whose
study our fractal encryption is based.
In the prior art (i.e., with the currnet encryption methods), vital
information such as password, PIN, or credit card number is transferred over a
network with no encryption (as is) or with one of published or proprietary
encryption techniques, with key(s) (public key and private key; the former is
known to anybody, and the latter is known to each of concerned parties only),
or without keys (such as in proprietary one-time password generator), which
are considered to be mathematically very difficult to crack (i.e., taking a
great amount of time to find the original information). This is also true for
software products or contents (music, images, etc) transferred across a
network or written on CD-ROM (e.g. protection is carried out through a CD key
printed on a label of each CD-ROM or no protection is provided at all) or
other conventional media. Most of regular commercial software products and
contents CD-ROMs are protection-free to allow the pirate business.
However, the prior art as such requires a great amount of computation in
encryption and decryption and may be subject to being cracked in some cases.
In addition, in order to improve security, the number of bits in a key must be
increased, which would further lengthen the computation time and complicate
the logic to implement the algorithm.
NEW ENCRYPTION STANDARD
AES - The National Institute of Standards and Technology (NIST) has been
working with industry and the cryptographic community to develop an Advanced
Encryption Standard (AES). The overall goal is to develop a Federal
Information Processing Standard (FIPS) that specifies an encryption
algorithm(s) capable of protecting sensitive government information well into
the next century. The algorithm(s) is expected to be used by the U.S.
Government and, on a voluntary basis, by the private sector.
On January 2, 1997, NIST announced the initiation of the AES development
effort and made a formal call for algorithms on September 12, 1997. The
algorithm(s) must implement symmetric key cryptography as a block cipher and
(at a minimum) support block sizes of 128-bits and key sizes of 128-, 192-,
and 256-bits.
The AES finalist candidate algorithms are MARS, RC6, Rijndael, Serpent, and
Twofish. NIST has developed a Round 1 Report describing the selection of the
finalists.
On October 2, 2000, NIST announced that it has selected Rijndael to propose
for the AES. A report, press release, and AES fact sheet are available with
that information.
BENEFITS OF FRACTAL ENCRYPTION
SummerSoft Labs' new fractal encryption package, Lavender_C,
allows any file ( any text, image, audio, .doc, compressed file ), to be
used as an encryption key. No certification required. Sample programs are
offered as free downloads. They are designed for Windows 95/98/NT4/XP with IE4 or later.
Fractal encryption is easier to use than the current (prime) number based
encryption, whose keys are limited to predefined (prime) numbers and often
controlled by authorization (certification) agency such as Verisign. With
fractal encryption, we can use any keys - in a form of text, image, voice,
audio, even compressed or Word document files. We don't need to memorize keys
but the names of files we use, which can be changed as often as we choose and
at any time we like.
When we try to send e-mail containing confidential and/or private
information not to be disclosed to anybody other than the intended
recipient(s), we are likely to use some off-the-shelf encryption package to
encipher it and attach it to mail text on Microsoft Outlook Express. Our
encryption key(s) - public, private, or common - though memorized by Microsoft
niceware, are hard to remember (prime) numbers.
There are already so many things we are not supposed to write down, in
addition to those keys, such as PINs of our bank accounts, our credit card
numbers (though engraved conspicuously on our cards), our passwords for many
purposes at home and at office, and so on.
Why is it that encryption keys are numbers (mostly prime numbers) ? Because
the current foremost encryption algorithms are based on the prime number
theory - Factoring Problem- in that large prime numbers, when multiplied with
one another, are hard to crack. Sometimes those keys are supplied from
authorization (certification) agency such as Verisign, not free of charge,
updated annually.
Well then, it may be much more convenient if those keys were any bit
strings such as any characters, images, voices, anything. Is that possible?
Not with the current prime number based encryption, nor with the next
generation elliptic curve function based encryption, which also uses numbers
for keys.
But YES with fractal theory based encryption (fractal encryption for
short). The fractal theory has been applied to image compression/expansion,
fantastic image creation, and hidden signatures (watermarks) in images for
authentication.
When the fractal theory is applied to encryption, it may not be used to
encipher the content itself, because it is impossible to recover the original
content exactly from the enciphered content, which is one of the
characteristics of fractal. Therefore, the theory is applied to a key to
generate an enciphered signature to generate seeds for random number
generation. Those resulting random numbers are then used to encipher the
content.
Such use of any key was conceived for easy encoding and retrieval for even
novice users on both sides of a network. Of course, this method can be used
for off-line storage of files for security.
For instance, today you use a picture of Snoopy or family photo, and
tomorrow a favorite song, maybe 'In Da Club', in an MP3 file It's more fun than
a toil.
In short, fractal encryption is:
- User friendly (users control
their own encryption keys),
- Without size inflation (original file size +
8 bytes), and
- For personalized online distribution (e.g., Music
industries may send music contents via Internet only playable by the
recipient).
APPLICATIONS
I. e-mail encryption
II. Off-line archive encryption
III. B-to-B
transactions
IV. Audio/video distribution via Internet (decypherable only
by each recipient)
V. And more...
RECENT NEWS
DVD encryption was cracked by a European teenager.
New encryption
standard was chosen for the US Government.
SDMI code was cracked by a group of researchers.
RSA-576 was factored by a group of European researchers.
RSA-640 was factored by a group of European researchers (same as above).
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