Information Technology Reference
In-Depth Information
Cryptosystem with One Dimensional Chaotic Maps
J.A. Martínez-Ñonthe 1 , A. Díaz-Méndez 2 , M. Cruz-Irisson 1 , L. Palacios-Luengas 1
J.L. Del-Río-Correa 3 and R. Vázquez-Medina 1,*
1 Instituto Politécnico Nacional, ESIME-Culhuacan, Santa Ana 1000,
04430, D.F., México
2 Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro 1,
Tonantzintla, Puebla, México
3 Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186,
09340, D.F., México
{jmartinezn9800,ruvazquez}@ipn.mx, lpalacios@ieee.org,
ajdiaz@inaoep.mx, jlrc@xanum.uam.mx
Abstract. This paper presents a 64-bits chaotic block cryptosystem, which uses
as noise generator one-dimensional chaotic maps with 8 bits sub-blocks data.
These chaotic maps use a control parameter that allows them to operate in the
chaotic region, which guarantees that each sub-block of data is mixed with un-
predictable random noise. Statistical mechanic tools such as: bifurcation dia-
gram, Lyapunov exponent, and invariant distribution have been used to analyze
and evaluate the behavior of the noise generator. The cryptosystem has been
evaluated using concepts of information theory, such as: entropy, as a diffusion
measure in the encryption process, and mutual information as a measure of rela-
tionship between plaintext and its respective cryptogram. The noise generator
has been used on the non-balanced and dynamic network proposed by L. Ko-
carev. The randomness of the cryptograms has been evaluated using the NIST
random tests. The proposed cryptosystem can be a component in software ap-
plications that provides security to stored or communicated information. The
proposed cryptosystem has a similar behavior to the one of currently used
cryptosystems and it has been designed with chaotic sequence generators,
which are aperiodic by definition.
Keywords: Chaotic cryptosystem, Block cryptosystem, Chaotic maps.
1 Introduction
The term chaos in scientific terms was popularized after 1961, it is related to mathe-
matics and physics and it is connected to some kind of unpredictable behavior of
Dynamic Systems (DS). A chaotic system (CS) is a non-linear, deterministic DS that
has sensitive dependence on initial conditions, and presents an evolution through a
phase space that seems to be random. Mathematicians agree that, for the special case
of iterated functions, there are three common characteristics of the chaos [1]: Sensi-
tive dependence on initial conditions, mixing, and dense periodic points. These prop-
erties are relevant for cryptographic applications, since it is very difficult to establish
* Correspondind author.
 
Search WWH ::




Custom Search