59 research outputs found
Self-synchronizing stream ciphers and dynamical systems: state of the art and open issues
International audienceDynamical systems play a central role in the design of symmetric cryptosystems. Their use has been widely investigated both in ''chaos-based'' private communications and in stream ciphers over finite fields. In the former case, they get the form of automata named as Moore or Mealy machines. The main charateristic of stream ciphers lies in that they require synchronization of complex sequences generated by the dynamical systems involved at the transmitter and the receiver part. In this paper, we focus on a special class of symmetric ciphers, namely the Self-Synchronizing Stream Ciphers. Indeed, such ciphers have not been seriously explored so far although they get interesting properties of synchronization which could make them very appealing in practice. We review and compare different design approaches which have been proposed in the open literature and fully-specified algorithms are detailed for illustration purpose. Open issues related to the validation and the implementation of Self-Synchronizing Stream Ciphers are developped. We highlight the reason why some concepts borrowed from control theory appear to be useful to this end
Construction and Optimization of Dynamic S-Boxes Based on Gaussian Distribution
Block ciphers are widely used for securing data and are known for their resistance to various types of attacks. The strength of a block cipher against these attacks often depends on the S-boxes used in the cipher. There are many chaotic map-based techniques in the literature for constructing the dynamic S-Boxes. While chaos-based approaches have certain attractive properties for this purpose, they also have some inherent weaknesses, including finite precision effect, dynamical degradation of chaotic systems, non-uniform distribution, discontinuity in chaotic sequences. These weaknesses can limit the effectiveness of chaotic map-based substitution boxes. In this paper, we propose an innovative approach for constructing dynamic S-boxes using Gaussian distribution-based pseudo-random sequences. The proposed technique overcomes the weaknesses of existing chaos-based S-box techniques by leveraging the strength of pseudo-randomness sequences. However, one of the main drawbacks of using Gaussian distribution-based pseudo-random sequences is the low nonlinearity of the resulting S-boxes. To address this limitation, we introduce the use of genetic algorithms (GA) to optimize the nonlinearity of Gaussian distribution-based S-boxes while preserving a high level of randomness. The proposed technique is evaluated using standard S-box performance criteria, including nonlinearity, bit independence criterion (BIC), linear approximation probability (LP), strict avalanche criterion (SAC), and differential approximation probability (DP). Results demonstrate that the proposed technique achieves a maximum nonlinearity of 112, which is comparable to the ASE algorithm
Self-synchronizing stream ciphers and dynamical systems: state of the art and open issues
Dynamical systems play a central role in the design of symmetric cryptosystems. Their use has been widely investigated both in "chaos-based" private communications and in stream ciphers over finite fields. In the former case, they get the form of automata named as Moore or Mealy machines. The main charateristic of stream ciphers lies in that they require synchronization of complex sequences generated by the dynamical systems involved at the transmitter and the receiver part. In this paper, we focus on a special class of symmetric ciphers, namely the SelfSynchronizing Stream Ciphers. Indeed, such ciphers have not been seriously explored so far although they get interesting properties of synchronization which could make them very appealing in practice. We review and compare different design approaches which have been proposed in the open literature and fully-specified algorithms are detailed for illustration purpose. Open issues related to the validation and the implementation of Self-Synchronizing Stream Ciphers are developped. We highlight the reason why some concepts borrowed from control theory appear to be useful to this end
New Enhanced Chaotic Number Generators
We introduce new families of enhanced chaotic number generators in order to
compute very fast long series of pseudorandom numbers. The key feature of these
generators being the use of chaotic numbers themselves for sampling chaotic
subsequence of chaotic numbers in order to hide the generating function. We
explore numerically the properties of these new families and underline their
very high qualities and usefulness as CPRNG when series are computed up to 10
trillions iterations.Comment: 42 pages, 17 figures, to be published in Proceeding 8th International
Conference of Indian Soc. of Indust. and Appl. Math., Jammu,India, 31st March
- 3rd April 2007, Invited conferenc
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
The dynamics of complex systems. Studies and applications in computer science and biology
Our research has focused on the study of complex dynamics and on their use in both information security and bioinformatics. Our first work has been on chaotic discrete dynamical systems, and links have been established between these dynamics on the one hand, and either random or complex behaviors. Applications on information security are on the pseudorandom numbers generation, hash functions, informationhiding, and on security aspects on wireless sensor networks. On the bioinformatics level, we have applied our studies of complex systems to theevolution of genomes and to protein folding
Dynamic block encryption with self-authenticating key exchange
One of the greatest challenges facing cryptographers is the mechanism used
for key exchange. When secret data is transmitted, the chances are that there
may be an attacker who will try to intercept and decrypt the message. Having
done so, he/she might just gain advantage over the information obtained, or
attempt to tamper with the message, and thus, misguiding the recipient.
Both cases are equally fatal and may cause great harm as a consequence.
In cryptography, there are two commonly used methods of exchanging secret
keys between parties. In the first method, symmetric cryptography, the key is
sent in advance, over some secure channel, which only the intended recipient
can read. The second method of key sharing is by using a public key exchange
method, where each party has a private and public key, a public key is shared
and a private key is kept locally. In both cases, keys are exchanged between
two parties.
In this thesis, we propose a method whereby the risk of exchanging keys
is minimised. The key is embedded in the encrypted text using a process
that we call `chirp coding', and recovered by the recipient using a process
that is based on correlation. The `chirp coding parameters' are exchanged
between users by employing a USB flash memory retained by each user. If the
keys are compromised they are still not usable because an attacker can only
have access to part of the key. Alternatively, the software can be configured
to operate in a one time parameter mode, in this mode, the parameters
are agreed upon in advance. There is no parameter exchange during file
transmission, except, of course, the key embedded in ciphertext.
The thesis also introduces a method of encryption which utilises dynamic blocks, where the block size is different for each block. Prime numbers are
used to drive two random number generators: a Linear Congruential Generator
(LCG) which takes in the seed and initialises the system and a Blum-Blum
Shum (BBS) generator which is used to generate random streams to encrypt
messages, images or video clips for example. In each case, the key created is
text dependent and therefore will change as each message is sent.
The scheme presented in this research is composed of five basic modules. The
first module is the key generation module, where the key to be generated is
message dependent. The second module, encryption module, performs data
encryption. The third module, key exchange module, embeds the key into
the encrypted text. Once this is done, the message is transmitted and the
recipient uses the key extraction module to retrieve the key and finally the
decryption module is executed to decrypt the message and authenticate it.
In addition, the message may be compressed before encryption and decompressed
by the recipient after decryption using standard compression tools
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