02-06-2012, 02:13 PM
Chaos Theory and its Application in Modern Cryptography
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INTRODUCTION
The computer from appears to the present, already from
used in calculating the turning point to mainly to use in
theinformation processing. Internet provides the massive
information service for the user every day. Because the
Internet basic agreement is not the completely safe
agreement. Not after the information which specially
encrypts transmits when the network, will directly expose in
the entire network. Modem high performance's computer,
automated analysis and interception procedure each second
may search several million facts, It had has serious pressure
to traditional encryption algorithm constitution. In the past's
ten years, along with to the chaos theory research thorough,
chaos theory's application scope also unceasingly expands
unceasingly. Chaos in cryptology application becomes
popular research area and proposed the massive chaos
encryption algorithm .The majority simulation chaos's
password use chaos synchronization technology, through has
chirp the channel to realize the secret signaling. Because the
chaos theory nearly several dozens years obtained the
enormous development, the innumerable chaos systems may
apply in the cryptology, therefore the chaos must become in
the cryptology the new rich resources.
CHAOS THEORY
CHAOS mathematical MODEL
In recent years, obtained many meaningful results to
chaos phenomenon's experiment, but more results come from
to the nonlinear system mathematical model theoretical
analysis and the computer simulation. There have some
equation to describes these the model: non-line iteration
equation (group), non-line autonomous simultaneous
differential equation and difference differential equation
(group).
The nonlinear system has many kinds of forms from the
non-chaotic state to the chaotic state evolutionary process.
And most typical has three kinds:
1) Time of cyclical furcation process. Supposes some
nonlinear system to occupy the constant state at first, along
with controlled variable's increase, when achieves some
value, the system mode has the sudden change, has the
stable periodic oscilation condition, along with controlled
variable's unceasing increase, system's condition will have a
series of sudden changes, vibrates in the frequency spectrum
to present the frequency division or the cycle doubling
effect. When the system presents non-cyclical the confusion
oscillatory regime, namely chaotic motion condition. The
frequency division phenomenon only then in controlled
variable's some valve value can appear in the nonlinear
system, it is the overture which the chaotic motion produces.
2) Intermittence the chaos process. Regarding has the
time of cyclical furcation evolutionary process nonlinear
system, when after entering the chaotic state, constitutes a
chaos area in controlled variable's some scope. In the chaos
area, is not each controlled variable correspondence is the
chaotic state. Between controlled variable's many plots, is
corresponding the periodic oscilation condition, between
these plots is called in the chaos area the cyclical window.
Nearby the cyclical window, state variable's time behavior
displays the cycle, suddenly to be from time to time chaotic,
jumps stochastically between the two.
3) Half of periodic movement to chaos. If the system
increases along with the controlled variable, presents two in
the vibration frequency spectrum not to be possible the joint
pledge frequency, this kind of movement is called the
quasiperiodic movement. The quasiperiodic and the
frequency-locking appear alternately, enters the chaotic state
finally.
Judges the chaotic motion three main characteristic
quantities
MODERN CRYPTOLOG Y
Cryptology contains the branch which two oppose
mutually,they are Cryptography and Cryptanalytics.
The former seeks the guarantee news secrecy or the
authentic method, but the latter, then the research encryption
news breaks or news fabrication. A privacy system is
composed of the following several parts: definite orders
message space M, secret text message space C, key space Kl
and K2, Under single key system Kl = K2 = K, this time
key K must by send the side after the safe key channel to
pass to the debit; The encryption transforms EKI E E, M
--+C, kl E K1, it is completed by the encryption, the
decipher transforms DK2 ED, C --+M, k2 E K2 ,realizes by
the decipher. Said that the overall (M, C, K1, K2 , EK1,
DK 2) is a privacy system. Regarding assigns definite orders
news m E M, key kl E Kl ,encryption transformation the
definite orders m transformation for scrambled text c,
namely c = f (m, K1) = EKI (m).
CONCLUSION
In the article discussed the chaos and the cryptology, has
made the analysis to between the chaos and the cryptology
relations. Although the digital chaos cryptology obtained the
massive research in recent years, has obtained some research
results. But studies indicated that the chaos system realizes
when the computer, because the limited precision and the
limited condition question, the digitized chaos system and
the ideal real value chaos system in dynamics characteristic
have the quite big difference (characteristic degeneration). In
structure true security chaos password question, but also
lacks the enough theory support to guarantee its true security.