49 research outputs found
Analysis and Design Security Primitives Based on Chaotic Systems for eCommerce
Security is considered the most important requirement for the success of electronic commerce, which is built based on the security of hash functions, encryption algorithms and pseudorandom number generators. Chaotic systems and security algorithms have similar properties including sensitivity to any change or changes in the initial parameters, unpredictability, deterministic nature and random-like behaviour. Several security algorithms based on chaotic systems have been proposed; unfortunately some of them were found to be insecure and/or slow.
In view of this, designing new secure and fast security algorithms based on chaotic systems which guarantee integrity, authentication and confidentiality is essential for electronic commerce development. In this thesis, we comprehensively explore the analysis and design of security primitives based on chaotic systems for electronic commerce: hash functions, encryption algorithms and pseudorandom number generators. Novel hash functions, encryption algorithms and pseudorandom number generators based on chaotic systems for electronic commerce are proposed. The securities of the proposed algorithms are analyzed based on some well-know statistical tests in this filed. In addition, a new one-dimensional triangle-chaotic map (TCM) with perfect chaotic behaviour is presented.
We have compared the proposed chaos-based hash functions, block cipher and pseudorandom number generator with well-know algorithms. The comparison results show that the proposed algorithms are better than some other existing algorithms. Several analyses and computer simulations are performed on the proposed algorithms to verify their characteristics, confirming that these proposed algorithms satisfy the characteristics and conditions of security algorithms. The proposed algorithms in this thesis are high-potential for adoption in e-commerce applications and protocols
Dynamic S-BOX using Chaotic Map for VPN Data Security
A dynamic SBox using a chaotic map is a cryptography technique that changes
the SBox during encryption based on iterations of a chaotic map, adding an
extra layer of confusion and security to symmetric encryption algorithms like
AES. The chaotic map introduces unpredictability, non-linearity, and key
dependency, enhancing the overall security of the encryption process. The
existing work on dynamic SBox using chaotic maps lacks standardized guidelines
and extensive security analysis, leaving potential vulnerabilities and
performance concerns unaddressed. Key management and the sensitivity of chaotic
maps to initial conditions are challenges that need careful consideration. The
main objective of using a dynamic SBox with a chaotic map in cryptography
systems is to enhance the security and robustness of symmetric encryption
algorithms. The method of dynamic SBox using a chaotic map involves
initializing the SBox, selecting a chaotic map, iterating the map to generate
chaotic values, and updating the SBox based on these values during the
encryption process to enhance security and resist cryptanalytic attacks. This
article proposes a novel chaotic map that can be utilized to create a fresh,
lively SBox. The performance assessment of the suggested S resilience Box
against various attacks involves metrics such as nonlinearity (NL), strict
avalanche criterion (SAC), bit independence criterion (BIC), linear
approximation probability (LP), and differential approximation probability
(DP). These metrics help gauge the Box ability to handle and respond to
different attack scenarios. Assess the cryptography strength of the proposed
S-Box for usage in practical security applications, it is compared to other
recently developed SBoxes. The comparative research shows that the suggested
SBox has the potential to be an important advancement in the field of data
security.Comment: 11 Page
A dynamical systems approach to the discrimination of the modes of operation of cryptographic systems
Evidence of signatures associated with cryptographic modes of operation is
established. Motivated by some analogies between cryptographic and dynamical
systems, in particular with chaos theory, we propose an algorithm based on
Lyapunov exponents of discrete dynamical systems to estimate the divergence
among ciphertexts as the encryption algorithm is applied iteratively. The
results allow to distinguish among six modes of operation, namely ECB, CBC,
OFB, CFB, CTR and PCBC using DES, IDEA, TEA and XTEA block ciphers of 64 bits,
as well as AES, RC6, Twofish, Seed, Serpent and Camellia block ciphers of 128
bits. Furthermore, the proposed methodology enables a classification of modes
of operation of cryptographic systems according to their strength.Comment: 14 pages, 10 figure
Multi-algorithmic Cryptography using Deterministic Chaos with Applications to Mobile Communications
In this extended paper, we present an overview of the principal issues associated with cryptography, providing historically significant examples for illustrative purposes as part of a short tutorial for readers that are not familiar with the subject matter. This is used to introduce the role that nonlinear dynamics and chaos play in the design of encryption engines which utilize different types of Iteration Function Systems (IFS). The design of such encryption engines requires that they conform to the principles associated with diffusion and confusion for generating ciphers that are of a maximum entropy type. For this reason, the role of confusion and diffusion in cryptography is discussed giving a design guide to the construction of ciphers that are based on the use of IFS. We then present the background and operating framework associated with a new product - CrypsticTM - which is based on the application of multi-algorithmic IFS to design encryption engines mounted on a USB memory stick using both disinformation and obfuscation to ‘hide’ a forensically inert application. The protocols and procedures associated with the use of this product are also briefly discussed
Deterministic Chaos in Digital Cryptography
This thesis studies the application of deterministic chaos to digital
cryptography. Cryptographic systems such as pseudo-random generators
(PRNG), block ciphers and hash functions are regarded as a dynamic
system (X, j), where X is a state space (Le. message space)
and f : X -+ X is an iterated function. In both chaos theory and
cryptography, the object of study is a dynamic system that performs
an iterative nonlinear transformation of information in an apparently
unpredictable but deterministic manner. In terms of chaos theory, the
sensitivity to the initial conditions together with the mixing property
ensures cryptographic confusion (statistical independence) and diffusion
(uniform propagation of plaintext and key randomness into cihertext).
This synergetic relationship between the properties of chaotic and
cryptographic systems is considered at both the theoretical and practical
levels: The theoretical background upon which this relationship is
based, includes discussions on chaos, ergodicity, complexity, randomness,
unpredictability and entropy.
Two approaches to the finite-state implementation of chaotic systems
(Le. pseudo-chaos) are considered: (i) floating-point approximation of
continuous-state chaos; (ii) binary pseudo-chaos. An overview is given
of chaotic systems underpinning cryptographic algorithms along with
their strengths and weaknesses. Though all conventional cryposystems
are considered binary pseudo-chaos, neither chaos, nor pseudo-chaos are
sufficient to guarantee cryptographic strength and security.
A dynamic system is said to have an analytical solution Xn = (xo)
if any trajectory point Xn can be computed directly from the initial
conditions Xo, without performing n iterations. A chaotic system with an
analytical solution may have a unpredictable multi-valued map Xn+l =
f(xn). Their floating-point approximation is studied in the context of
pseudo-random generators.
A cryptographic software system E-Larm ™ implementing a multistream
pseudo-chaotic generator is described. Several pseudo-chaotic
systems including the logistic map, sine map, tangent- and logarithm feedback
maps, sawteeth and tent maps are evaluated by means of floating point
computations. Two types of partitioning are used to extract
pseudo-random from the floating-point state variable: (i) combining the
last significant bits of the floating-point number (for nonlinear maps);
and (ii) threshold partitioning (for piecewise linear maps). Multi-round
iterations are produced to decrease the bit dependence and increase non-linearity.
Relationships between pseudo-chaotic systems are introduced
to avoid short cycles (each system influences periodically the states of
other systems used in the encryption session).
An evaluation of cryptographic properties of E-Larm is given using
graphical plots such as state distributions, phase-space portraits, spectral
density Fourier transform, approximated entropy (APEN), cycle length
histogram, as well as a variety of statistical tests from the National Institute
of Standards and Technology (NIST) suite. Though E-Larm passes
all tests recommended by NIST, an approach based on the floating-point
approximation of chaos is inefficient in terms of the quality/performance
ratio (compared with existing PRNG algorithms). Also no solution is
known to control short cycles.
In conclusion, the role of chaos theory in cryptography is identified;
disadvantages of floating-point pseudo-chaos are emphasized although
binary pseudo-chaos is considered useful for cryptographic applications.Durand Technology Limite
Improving Chaotic Cryptographic Primitives Based On Map’s Complexity And Period Length Of The Chaotic Maps
Peta camuk berkentuan menghasilkan ciri-ciri seperti determinisme, ergodisiti, perlakuan
seperti rawak, ketidaklineran, aperiodisiti, entropi yang tinggi, imbangan, ketak kemerostan,
korelasi maklumat yang amat rendah, dan kepekaan/kesensitifan yang amat tinggi terhadap
perubahan yang amat kecil daripada keadaan awal dan parameter kawalan.
Deterministic chaotic maps possess profound characteristics such as determinism,
ergodicity, random-like behavior, nonlinearity, aperiodicity, high entropy, balance,
nondegeneracy, incredibly low correlation of information and extreme sensitivity to very small
changes of the initial condition and control-parameters
Symmetry in Chaotic Systems and Circuits
Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue