Cryptography
People have tried in the past to use both continuous and discrete recursive
maps for the efficient production of cryptographic keys. Such attempts have
been based on the chaotic behavior of such systems, as depicted in their
phase space profile graphs. The attempts presented so far by various
research groups have met with limited success. A new methodology for the
creation of pseudo-random sequences of binary digits has been developed
and extensively tested by our group. The series are of arbitrary length and
suitable for a large spectrum of applications, such as pseudo-random number
generation, encryption in digital networks communication and data transfer,
identity verification et al. The group is now working for the development of a
specific application, with the particular perspective of a specially designed
PLC code for mobile phone communications.
The CAG group results so far:
A. Quantum Key Distribution enabled adaptive communication procedures.
The group has developed a method for the automatization and robotic
implementation of most basic QKD protocols in a secure and easy way,
with the prospective objective to an application where routine
communication, including quantum key creation and distribution,
encryption and decryption of messages and routine security checks will
be performed by the system without human user intervention.
Combined with adaptive communication methods, as developed by our
group, such as training of the robotic system to recognize and adapt
itself to well known as well as totally new methods of illegitimate and
malevolent intruder and eavesdropper attacks, our procedure may be
advanced to the development of an adaptive communication protocol,
for use in global digital communication network environments, such as
the Internet. Adaptive protocol procedures would utilize mathematical
methods for digital signal analysis, classification and characterization,
qualitative analysis of digital communication line noise, as well as traffic
statistical analysis as in state of the art communication security
procedures. It would develop aggressive evasion and “message
content diffusion through oblivious intermediaries” techniques for the
avoidance of malevolent message interception. It would utilize
probabilities and game theory techniques and would apply deception
methods in the form of “dummy” messages and recipients, tactics
which should deplete and exhaust potential illegitimate eavesdroppers’
resources. The analysis and defense against innovative malevolent
attacks, besides providing the best available security to everyday users,
should permit an appropriately enabled robotic network system to
accumulate knowledge and improve its performance if future attack
repetitions, as well as provide assistance to digital forensics. An
adaptive communication protocol, robotically applied by a self –
learning system would provide QKD security at its best potential.
B. A method of creating binary series of arbitrary length and practically
total “apparent randomness” has been developed by our group,
nearing the point of practical application. It is based on the specific
mathematical properties of a class of discrete, discontinuous iterative
maps with very high complexity behavior. These maps and their
appropriately constructed symbolic dynamics may be used as “virtual
encryption devices”, to be used for secure communication in digital
communication networks of high complexity and traffic volume, like the
Internet.
Our work may be best described as follows:

We have a method to generate binary number series of arbitrary length,
to be used as encryption keys in a Vernam type, “one time only use”,
encryption protocol.

The implementation of the key is the same as in all ‘one time key’
applications. The key is added bit by bit, by a XOR operation, to the
unencrypted binary file containing the message. The receiver of the message
applies the same XOR operation to decrypt it.

Our keys are created by the use of a family of discontinuous discrete
dynamic systems and their symbolic dynamics. Yet they appear as ‘random’
series of binary digits to a third party. The apparent ‘randomness’, or, in other
words, the lack of any structure in the series has been theoretically proven by
topological arguments and ascertained by appropriate statistical tests.
In the above mentioned tests, more than two hundred keys of a length of a
million bits have been tested by the most well known commercial tests
available. The NIST tests and those published by Prof. George Marsaglia are
included. Our keys have been 100% SUCCESSFUL. Therefore they are in
principle suitable for ‘one time key’ applications.

The key space created by our methodology can be made to contain an
extremely large number of keys, reaching up to 101000-2000 distinct keys. The
transinformation and cross correlation tests so far confirm the distinctness of
the keys.

Due to the above described property, the usual problems of key
distribution do not exist here. No need for repeated meetings of trusted parties
for distribution of new key pads. The small number of parameters necessary
for the generation of each key may be included in the previous message. This
way the integrity of communication is preserved. Only one initial contact is
required, in order to distribute the exact form of the dynamic system and a first
set of parameters.
The above described communication procedure, may be successfully
combined with adaptive communication methods as described in the previous
section. The QKD protocols, being costly in money, as well as in time,
hardware and resources, in this method would be applied for the initiation of
communication, as well as occasionally for reestablishment in case of
interruptions or periodic security enhancement. This would avoid the
cumbersome application of QKD methods on an everyday routine basis and,
arguably, would present the most viable and reasonable application of QKD
methods in the Internet.
Morphology
A new concept in the area of morphology is introduced. It is a generalization
of the thinning and skeletonization concepts. It can be used in most
applications where skeletons or Voronoi sets are utilized, having specific
advantages over the traditional results due to its rigorous mathematical
definition. A set of rules for the construction of the innovative form of skeleton
are presented, based on a mathematical description of the construction
process. Certain examples are given, with an eye to specific applications,
such as robotic navigation or OCR, among others.
The advantages of the new concept are:
Its mathematical definition based on work developed in the last 20 years in
the fields of Differential Geometry and Topology. This may lead to easy and
straightforward creation of the skeleton by solving a set of nonlinear algebraic
equations and inequalities.
Its easy and natural generalisation in more than two dimensions, due to its
previously mentioned attribute.
Its extension in cases not covered by other similar state of the art definitions
of skeletons, as described in mathematical morphology literature.
The introduction of the “maximum coordinate” metric. This is a metric suitable
for work in discrete lattices, where the usual Euclidean square root metric is
not appropriate.