453 research outputs found
Breaking a Chaotic Cryptographic Scheme Based on Composition Maps
Recently, a chaotic cryptographic scheme based on composition maps was
proposed. This paper studies the security of the scheme and reports the
following findings: 1) the scheme can be broken by a differential attack with
chosen-plaintext, where is the size of
plaintext and is the number of different elements in plain-text; 2) the
scheme is not sensitive to the changes of plaintext; 3) the two composition
maps do not work well as a secure and efficient random number source.Comment: 9 pages, 7 figure
Security problems with a chaos-based deniable authentication scheme
Recently, a new scheme was proposed for deniable authentication. Its main
originality lied on applying a chaos-based encryption-hash parallel algorithm
and the semi-group property of the Chebyshev chaotic map. Although original and
practicable, its insecurity and inefficiency are shown in this paper, thus
rendering it inadequate for adoption in e-commerce.Comment: 8 pages, 1 figure, latex forma
A new RSA public key encryption scheme with chaotic maps
Public key cryptography has received great attention in the field of information exchange through insecure channels. In this paper, we combine the Dependent-RSA (DRSA) and chaotic maps (CM) to get a new secure cryptosystem, which depends on both integer factorization and chaotic maps discrete logarithm (CMDL). Using this new system, the scammer has to go through two levels of reverse engineering, concurrently, so as to perform the recovery of original text from the cipher-text has been received. Thus, this new system is supposed to be more sophisticated and more secure than other systems. We prove that our new cryptosystem does not increase the overhead in performing the encryption process or the decryption process considering that it requires minimum operations in both. We show that this new cryptosystem is more efficient in terms of performance compared with other encryption systems, which makes it more suitable for nodes with limited computational ability
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
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
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