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Review on Chaotic Ciphers and its Analysis
Mina Mishra
Assistant Professor
Christian College of Engineering and Technology, Bhilai, Chhattisgarh, India
E-mail: [email protected]
Abstract
This paper identifies the research that has been published in the area of chaos cryptography from basics towards the modern approach of concept of designing and cryptanalysis of chaotic cryptosystem since 1990 to the recent period. Chaos is a concept which presents a behaviors of non-linear systems which lies somewhere in between perfect order and a complete disorder or unbounded stage where the system becomes in deterministic. The signals resulting from chaotic systems are broadband, noise like, unpredictable and have highly random behavior.
Here the role that chaotic cryptography has played and will play in the future relative to the security is analyzed. There exists an interesting relationship between chaos and cryptography. The properties of chaotic cryptosystems such as, sensitivity to initial conditions/system parameters, mixing property, deterministic dynamics and structural complexity found to be similar to the confusion and diffusion with small change in plaintext/secret key, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems .
The work gives reports on the important papers which points towards the development made during the growing years concerning the topic by several researchers. Cryptography and cryptanalysis proves to be the necessary part of communication with the development and advancement of modern techniques in the field. Studies done on chaos and its analysis by many researchers introduces with complex, strange and dynamic behavior of chaos and its application in many fields especially in cryptography. They reported the possibility of using chaos in cryptography for developing secure ciphers as properties of chaotic nature promises to provide robustness against many common attacks which traditional ciphers could not.
Index Terms: Chaos, Chaotic Systems, Chaotic Cryptography, Chaotic Ciphers.
1.
INTRODUCTION
Cryptography has remained important over the centuries, used mainly for military and diplomatic communications. Cryptography has become vital for the functioning of the global economy, and is something that is used by millions of people on a daily basis. Various schemes of encryption using different techniques have been proposed in recent years. The Pseudo random number generators have been used for design of ciphers and found to be fundamental tool in many cryptographic applications like key generation, encryption, masking protocols and for internet gambling.
Chaos is a concept which presents a behavior of non-linear systems which lies somewhere in between
perfect order and a complete disorder or unbounded stage where the system becomes in deterministic ( uncontrollable). The signals resulting from chaotic systems are broadband, noise like, unpredictable and have highly random behavior.
There exists an interesting relationship between chaos and cryptography. The properties of chaotic
cryptosystems such as, sensitivity to initial
conditions/system parameters, mixing property, deterministic dynamics and structural complexity found to be similar to the confusion and diffusion with small change in plaintext/secret key, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems .
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Chaos provides a promising approach for
cryptography. Field of chaos cryptography is very young and has a great potential for research. Much fundamental work as well as practical problems needs to be addressed before high performance perfect chaotic cryptosystem can be designed.
2. MESSAGE-EMBEDDING SCHEME
Different Schemes of using chaotic systems in designing Chaotic ciphers have been developed since the origin of Chaos in Cryptography. Message-embedded is the latest Scheme of third generation also known as generation of chaotic ciphers.
Floriane Anstet et. al compared two encryption schemes, the standard Stream cipher and message embedded cryptosystem. The comparison is based on two main aspects. The first aspect deals with the synchronization of the time-varying keys at the transmission and reception side respectively. The second aspect focuses on the cryptanalysis of the
encryption algorithms. The cryptanalysis is
concerned with the system parameter retrieving [1].
It has been shown that the identifiable parameters may be good candidates to play the role of the static key against brute force attack. A fundamental
conclusion is that the usual cryptosystems
encountered in the literature involving only polynomial nonlinearities are weak against algebraic attacks.
G. Millerioux develops a connection between chaotic and conventional encryption with special emphasis on chaotic message-embedding.Based on the structural analysis, message-embedding have been concluded as a promising technique claiming better than other techniques [2].
3. CRYPTANALYSIS OF CHAOTIC
CIPHERS
With the development of chaotic ciphers, new methods of cryptanalysis have been discovered by new researchers according to the needs and ways to fulfill them for providing perfection in the developed ciphers.
Goce Jakimoski, et.al proposes the analysis of the impact of chaos-based techniques on block
encryption ciphers. They present several chaos based ciphers. Using the well-known principles in the cryptanalysis they show that these ciphers do not behave worse than the standard ones.They have shown that the maps produce ciphers that have
acceptable values of differential and linear
approximation probabilities. The ciphers use only byte operations that can be easily implemented on various processors and in hardware [3].
Hu Guojie, et.al analyzes the secure property of chaos communication system based on chaotic synchronization using the chosen cipher text attack under Kirchhoff principle.They concluded that secure
communication system based on chaotic
synchronization is not highly secure as they can
resolve the parameters (keys) of secure
communication system by chosen-cipher text attack [4].
Gonzalo, Alvarez, et.al Proposes ciphers which are difficult to realize in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a security analysis. Thus, it is hard for the reader to have a hint about their security and performance. In their work they provide a set of guidelines that every new cryptosystem would benefit from adhering to [5].
G. Álvarez, et.al explains how to break a very recent block cipher algorithm based on the logistic map. This cryptosystem uses a 128-bit external key to derive the initial condition and number of iterations, but in a weak way allowing for attack. Using some weaknesses in the system parameter generation another attack can be used to recover the complete key. After accomplishment of an efficient and inexpensive attack which recovers the complete key, it concludes the total lack of security, along with the low encryption speed; discourage the use of the proposed algorithm for secure applications [6].
V. Guglielmi, et.al presents here the security performances of a chaotic cryptosystem implemented on DSP and proposed one encryption scheme using
the chaotic dynamics of two-dimensional
noninvertible maps. The results obtained through a cryptanalytic study shows that the ciphering algorithm is robust [7].
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Henon-map is shown to be weak; its security can be improved using more number of parameters [8].
G.Alvarez, et.al presents the analysis of cryptosystem based on duffings oscillator. Implementations problems have been also discussed. The analysis shows that the proposed method cannot work in practice as it is not robust to real channels [9].
Alvarez, Montoya, et.al analyses the security of two of the most new and interesting ones ciphers, which uses a dynamically updated look up table and also work as stream ciphers. They provide different attack techniques to recover the key streams used by the algorithms. The knowledge of this key stream provides the attacker with the same information as the key and thus the security is broken. An important conclusion drawn from the implementation of proposed algorithm is that the same key cannot be reused by the algorithm, if so, they can be easily broken and the dynamic look up table does not depend on the key but on the plaintext, facilitating cryptanalysis [10].
Chengqing Li, et.al analyzes the security of a new multistage encryption system (MES) recently proposed in ISCAS’2004. After analysis it is found that MES is insecure against a differential chosen plaintext/ cipher text attack. Experiments are given to support the proposed attack. It is also pointed out that the security of MES against brute-force attacks is not sufficiently high [11].
Eli Biham, et.al presents a general framework for the application of the ideas of differential cryptanalysis to stream ciphers. It demonstrates that some differences in the key (or the initial state or the plaintext) are likely to cause predicted differences in the key stream or in the internal state. These stream differences can then be used to analyze the internal state of the cipher and retrieve it efficiently.They conclude that differential cryptanalysis is a versatile and important tool in the crypt analyzer toolbox, even when he/she tries to break stream ciphers [12].
Mehreen Afzal. et. al concentrate on algebraic
cryptanalysis of Grain, a non-linear feedback shift register (NLFSR) based stream cipher. The target here is to analyze generic key generating structure of Grain, that is why, they aims to recover the internal states of cipher rather than the key-bits. Their approach succeeds in recovering (approx) 1/2 of the internal state bits of Grain-1, while other half are guessed. While, in case of Grain-128, only 1/4 of the state bits can be obtained [13].
Floriane, Grilles, et.al proposes a general framework based on the identifiability concept for the
cryptanalysis of a large class of chaotic
cryptosystems and provided a systematic
methodology, in order to test, a priori, during the design stage, whether the parameters of a chaotic cryptosystem may play the role of the secret key or not.They concluded that the identifiable parameters can act as secret key against brute-force attack and also that the system consisting of non-linear polynomials are found to be weak against known plaintext attack [14].
Yong Chen, et.al proposes an encryption system with discretized skew tent map. However, there is a
fundamental weakness with this chaotic
cryptographic scheme. A chosen plaintext attack requiring only two plaintexts is proposed. Theoretical analysis and simulation results show that with only a few pairs of chosen plaintexts, this type of cryptosystem is easily broken by the attack scheme. The test results also indicate that extending the plaintext space, the cipher text space and the key space or changing the number of iterations cannot improve the security of the cryptosystem [15].
I.Belmouhoub, et.al designs exact nonlinear
reconstructor for discrete-time chaotic encrypted messages. They investigate the problem of discrete-time dead-beat observer for system with unknown input. They concluded that with this tool the secure communication and data transmission can be studied with an illustrative example [16].
Di Xiao, et.al analyzes the cause of vulnerability of the original dynamic look-up table based chaotic encryption scheme in detail, and then proposes the corresponding enhancement measures. Theoretical analysis and computer simulation indicate that the modified scheme is more secure than the original one [17].
Muhammad Asim, et.al Proposes, an efficient
method for designing S-boxes based on chaotic maps. The proposed method is based on the mixing property of piecewise linear chaotic maps. The S-box so constructed has very low differential and linear approximation probabilities. The proposed S-box is
more secure against differential and linear
cryptanalysis compared to recently propose chaotic S-boxes [18].
Ralf-Philipp Weinmann, et.al constructs and
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cryptanalysis. The encryption process for this cipher can be described by very simple polynomial equations. For a block and key size of 128 bits, they present ciphers for which practical Grobner Basis Attacks can recover the full cipher key for up to 12 rounds requiring only a minimal number of plaintext/cipher text pairs.They have demonstrated that the block ciphers can resist differential and linear cryptanalysis as well as brute-force attacks for which Grobner bases can be used to recover the key from a plaintext/cipher text pair [19].
Ruming Yin, et.al designs application of linear cryptanalysis to a chaotic stream cipher by strictly using the basic design criterion of cryptosystem – confusion and diffusion. Linear cryptanalysis methods are rarely used to improve the security of chaotic stream ciphers.This work implies that the strict cryptographic tools should be more effectively used in the design and cryptanalysis of chaotic stream ciphers [20].
Vinod patidar, et.al proposes a novel pseudo random bit generator (PRBG) based on two chaotic logistic maps running side-by-side and starting from random independent initial conditions. They also presents the detailed results of the statistical testing on generated bit sequences, done by the most stringent tests of randomness: the NIST suite tests, to detect the specific characteristics expected of truly random sequences.The results of statistical testing are encouraging and show that the proposed PRBG has perfect cryptographic properties and hence can be used in the design of new stream ciphers [21].
Gregory V. Bard introduces with the basics and concepts of Algebraic analysis along with solving
different polynomial equations. Successful
algorithms have been developed and methods of developing them for solving non-linear polynomial are there [22].
Mishra Mina et.al develops a chaotic cipher using message embedded scheme which uses non-linear function and logistic map. Various types of analysis have been done including avalanche effect and the cipher is found to have strength against Brute force attack [23].
Mishra Mina et.al develops and analyzes the chaotic cipher using 2-D chaotic function, Henon and Burger chaotic map with non-linear function using message embedded scheme. It has been concluded that identifiability concept of testing the strength of chaotic ciphers, against brute force attack in prior to
sending message, proves to be quite advantageous. The developed ciphers were found to have identifiable key and good key sensitivity which concludes that they can resist linear and brute force [24].
4. CONCLUSION
Cryptography and cryptanalysis proves to be the
necessary part of communication with the
development and advancement of modern techniques in the field. Studies done on chaos and its analysis by many researchers introduces with complex, strange and dynamic behavior of chaos and its application in many fields especially in cryptography. They
reported the possibility of using chaos in
cryptography for developing secure ciphers as properties of chaotic nature promises to provide robustness against many common attacks which traditional ciphers could not. Many schemes have been invented by the research scholars out of which message-embedded scheme was found to be the recent third generation scheme. Till now very few ciphers as cited in paper have been developed using the scheme that also lack the cryptanalysis part of it, thus, increases the potential of interest towards it. Application of chaos in the field led to an unlimited scope of constructing chaotic ciphers.
AKNOWLEDGEMENT
The author would like to thank the reviewers for their valuable suggestions.
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