This paper constructs two encryption methods using 2-D chaotic maps, Duffings and Arnold's cat maps respectively. Both of the methods are designed using message embedded scheme and are analyzed for their validity, for plaintext sensitivity, key sensitivity, known plaintext and brute-force attacks. Due to the less key space generally many chaotic cryptosystem developed are found to be weak against Brute force attack which is an essential issue to be solved. For this issue, concept of identifiability proved to be a necessary condition to be fulfilled by the designed chaotic cipher to resist brute force attack, which is a basic attack. As 2-D chaotic maps provide more key space than 1-D maps thus they are considered to be more suitable. This work is accompanied with analysis results obtained from these developed cipher. Moreover, identifiable keys are searched for different input texts at various key values. The methods are found to have good key sensitivity and possess identifiable keys thus concluding that they can resist linear attacks and brute-force attacks.
We propose a novel high-speed stream cipher encryption scheme based on the true random key generated by a chaotic semiconductor laser. A 5-Gbits/s non-return-to-zero plaintext is successfully encrypted and decrypted using this cryptography. The scheme can be applied in the areas of real-time high-speed physical encryption.
In this paper we introduce a new chaotic stream cipher Mmohocc which utilizes the fundamental chaos characteristics. The designs of the major components of the cipher are given. Its cryptographic properties of period, auto- and cross-correlations, and the mixture of Markov processes and spatiotemporal effects are investigated. The cipher is resistant to the related-key-IV attacks, Time/Memory/Data tradeoff attacks, algebraic attacks, and chosen-text attacks. The keystreams successfully passed two batteries of statistical tests and the encryption speed is comparable with RC4.
Recently, an image encryption scheme based on chaotic standard and logistic maps was proposed. This paper studies the security of the scheme and shows that it can be broken with only one chosen-plaintext. Some other security defects of the scheme are also reported.
After a brief introduction to a new chaotic stream cipher Mmohocc which utilizes the fundamental chaos characteristics of mixing, unpredictability, and sensitivity to initial conditions, we conducted the randomness statistical tests against the keystreams generated by the cipher. Two batteries of most stringent randomness tests, namely the NIST Suite and the Diehard Suite, were performed. The results showed that the keystreams have successfully passed all the statistical tests. We conclude that Mmohocc can generate high-quality pseudorandom numbers from a statistical point of view.
In this paper we propose a multi-map orbit hopping chaotic stream cipher that utilizes the idea of spread spectrum mechanism for secure digital communications and fundamental chaos characteristics of mixing, unpredictable, and extremely sensitive to initial conditions. The design, key and subkeys, and detail implementation of the system are addressed. A variable number of well studied chaotic maps form a map bank. And the key determines how the system hops between multiple orbits, and it also determines the number of maps, the number of orbits for each map, and the number of sample points for …
The proposed hybrid message embedded scheme consists of hill cipher combined with message embedded chaotic scheme. Message-embedded scheme using non-linear feedback shift register as non-linear function and 1-D logistic map as chaotic map is modified, analyzed and tested for avalanche property and strength against known plaintext attack and brute-force attack. Parameter of logistic map acts as a secret key. As we know that the minimum key space to resist brute-force attack is 2100, and it is observed from analysis that key space of the discussed method is lesser than 2100. But the identifiabil…
We consider the problem of constructing an unconditionally secure cipher for the case when the key length is less than the length of the encrypted message. (Unconditional security means that a computationally unbounded adversary cannot obtain information about the encrypted message without the key.) In this article, we propose data compression and randomization techniques combined with entropically-secure encryption. The resulting cipher can be used for encryption in such a way that the key length does not depend on the entropy or the length of the encrypted message; instead, it is determined …
Recently, Pareek et al. proposed a symmetric key block cipher using multiple one-dimensional chaotic maps. This paper reports some new findings on the security problems of this kind of chaotic cipher: 1) a number of weak keys exists; 2) some important intermediate data of the cipher are not sufficiently random; 3) the whole secret key can be broken by a known-plaintext attack with only 120 consecutive known plain-bytes in one known plaintext. In addition, it is pointed out that an improved version of the chaotic cipher proposed by Wei et al. still suffers from all the same security defects.
In order to keep the data secret, various techniques have been implemented to encrypt and decrypt the secret data. Cryptography is committed to the security of content, i.e. it cannot be restored with a given ciphertext. Steganography is to hiding the existence of a communication channel within a stego. However, it has been difficult to construct a cipher (cypher) that simultaneously satisfy both channel and content security for secure communication. Inspired by the Cardan grille, this paper presents a new generative framework for grille cipher. A digital cardan grille is used for message encr…
This paper discusses mixing of chaotic systems as a dependable method for secure communication. Distribution of the entropy function for steady state as well as plaintext input sequences are analyzed. It is shown that the mixing of chaotic sequences results in a sequence that does not have any state dependence on the information encrypted by them. The generated output states of such a cipher approach the theoretical maximum for both complexity measures and cycle length. These features are then compared with some popular ciphers.
In this paper the author presents a new cryptographic technique to exclude the repetitive terms in a message, when it is to be encrypted, so that it becomes almost impossible for a person to retrieve or predict the original message from the encrypted message. In modern world, cryptography hackers try to break a code or cryptographic algorithm or try to retrieve the key, which is needed to encrypt a message, by analyzing the insertion or presence of repetitive bits / characters (bytes) in the message and encrypted message to find out the encryption algorithm or the key used for it. So it is mus…
In ISNN'04, a novel symmetric cipher was proposed, by combining a chaotic signal and a clipped neural network (CNN) for encryption. The present paper analyzes the security of this chaotic cipher against chosen-plaintext attacks, and points out that this cipher can be broken by a chosen-plaintext attack. Experimental analyses are given to support the feasibility of the proposed attack.
In 2002, Russell and Wang proposed a definition of entropically security that was developed within the framework of secret key cryptography. An entropically-secure system is unconditionally secure, that is, unbreakable, regardless of the enemy's computing power. In 2004, Dodis and Smith developed the results of Russell and Wang and, in particular, stated that the concept of an entropy-protected symmetric encryption scheme is extremely important for cryptography, since it is possible to construct entropy-protected symmetric encryption schemes with keys much shorter than the keys. the length of …
Security of multimedia data is a major concern due to its widespread transmission over various communication channels. Hence design and study of good image encryption schemes has become a major research topic. During the last few decades, there has been a increasing in chaos-based cryptography. This paper proposes an attack on a recently proposed chaos based image encryption scheme. The cryptosystem under study proceed by first shuffling the original image to disturb the arrangement of pixels by applying a chaotic map several times. Second, a keystream is generated using Chen's chaotic system …
The growing potential of modern communications needs the use of secure means to protect information from unauthorized access and use during transmission. In general, encryption a message using cryptography techniques and then hidden a message with a steganography methods provides an additional layer of protection. Furthermore, using these combination reduces the chance of finding the hidden message. This paper proposed a system which combines schemes of cryptography with steganography for hiding secret messages and to add more complexity for steganography. The proposed system secret message en…
Recently, an image encryption scheme based on chaotic standard and logistic maps was proposed by Patidar et al. It was later reported by Rhouma et al. that an equivalent secret key can be reconstructed with only one known/chosen-plaintext and the corresponding ciphertext. Patidar et al. soon modified the original scheme and claimed that the modified scheme is secure against Rhouma et al.'s attack. In this paper, we point out that the modified scheme is still insecure against the same known/chosen-plaintext attack. In addition, some other security defects existing in both the original and the m…
The cipher block chaining (CBC) block cipher mode of operation presents a very popular way of encrypting which is used in various applications. In previous research work, we have mathematically proven that, under some conditions, this mode of operation can admit a chaotic behavior according to Devaney. Proving that CBC mode is chaotic is only the beginning of the study of its security. The next step, which is the purpose of this paper, is to develop the quantitative study of the chaotic CBC mode of operation by evaluating the level of sensibility and expansivity for this mode.
Cryptography is the study of methods of sending messages in disguised form so that only the intended recipients can remove the disguise and read the messages. Information security has become a very critical aspect of modern communication systems. With the global acceptance of the Internet as a medium of communication, virtually every computer in the world is connected to every other. It has created a new risk for the users of the computers with a constant threat of being hacked and being victims of data theft. In this connection data encryption has become an essential part of secure communicat…
Vigenere Cipher is one of the classic cryptographic algorithms and included into symmetric key cryptography algorithm, where to encryption and decryption process use the same key. Vigenere Cipher has the disadvantage that if key length is not equal to the length of the plaintext, then the key will be repeated until equal to the plaintext length, it course allows cryptanalysts to make the process of cryptanalysis. And weaknesses of the symmetric key cryptographic algorithm is the safety of key distribution factor, if the key is known by others, then the function of cryptography itself become us…
We consider the problem of constructing an unconditionally secure cipher with a short key for the case where the probability distribution of encrypted messages is unknown. Note that unconditional security means that an adversary with no computational constraints can obtain only a negligible amount of information ("leakage") about an encrypted message (without knowing the key). Here we consider the case of a priori (partially) unknown message source statistics. More specifically, the message source probability distribution belongs to a given family of distributions. We propose an unconditionall…
In cryptography, block ciphers are the most fundamental elements in many symmetric-key encryption systems. The Cipher Block Chaining, denoted CBC, presents one of the most famous mode of operation that uses a block cipher to provide confidentiality or authenticity. In this research work, we intend to summarize our results that have been detailed in our previous series of articles. The goal of this series has been to obtain a complete topological study of the CBC block cipher mode of operation after proving his chaotic behavior according to the reputed definition of Devaney.
The resource-constrained nature of the Internet of Things (IoT) devices, poses a challenge in designing a secure, reliable, and particularly high-performance communication for this family of devices. Although side-channel resistant ciphers (either block cipher or stream cipher) are the well-suited solution to establish a guaranteed secure communication, the energy-intensive nature of these ciphers makes them undesirable for particularly lightweight IoT solutions. In this paper, we introduce ExTru, a novel encrypted communication protocol based on stream ciphers that adds a configurable switchi…
Utilizing complex dynamics of chaotic maps and systems in encryption was studied comprehensively in the past two and a half decades. In 1989, Fridrich's chaotic image encryption scheme was designed by iterating chaotic position permutation and value substitution some rounds, which received intensive attention in the field of chaos-based cryptography. In 2010, Solak \textit{et al.} proposed a chosen-ciphertext attack on the Fridrich's scheme utilizing influence network between cipher-pixels and the corresponding plain-pixels. Based on their creative work, this paper scrutinized some properties …
Recently, an image block encryption algorithm was proposed based on some well-known chaotic maps. The authors claim that the encryption algorithm achieves enough security level and high encryption speed at the same time. In this paper, we give a thorough security analysis on the algorithm from the perspective of modern cryptology and report some critical security defects on the algorithm. Given five chosen plain-images and the corresponding cipher-images, the attacker can obtain an equivalent secret key to successfully decrypt the other cipher-images encrypted with the same secret key. In addi…
A stream cipher was implemented on a FPGA. The keystream, for some authors the most important element, was developed using an algorithm based on Bernoullis chaotic map. When dynamic systems are digitally implemented, a normal degradation appears and disturbs their behavior; for such reason, a mechanism was needed. The proposed mechanism gives a solution for degradation issue and its implementation is not complicated. Finally, the implemented cipher includes 8 stages and 2 pseudo-random number generators (PRNG), such cipher was tested using NIST testes. Once its designing stage, it was implemen…
We present a stream cipher based on a chaotic dynamical system. Using a chaotic trajectory sampled under certain rules in order to avoid any attempt to reconstruct the original one, we create a binary pseudo-random keystream that can only be exactly reproduced by someone that has fully knowledge of the communication system parameters formed by a transmitter and a receiver and sharing the same initial conditions. The plaintext is XORed with the keystream creating the ciphertext, the encrypted message. This keystream passes the NISTs randomness test and has been implemented in a videoconference …
The security of chaotic optical communication using time-frequency (TF) representation is analyzed in this paper. The mean scalogram ratio (MSR) of TF representation and peak sidelobe level of MSR are defined to detect message. Algorithm for message detection and extraction is presented in detail. Two typical message encryption schemes, chaos masking and chaos modulation, are analyzed. The results reveal that it is not secure to transmit message when the message frequency locates at low power on power spectrum portrait. The proposed method is very useful for estimating the security level of me…
The weakness of the vigenere cipher lies in its short key and is repeated, so there is a key loop in encrypting messages, this is used by cryptanalysts using the Kasiski method to know the key length so it can solve this algorithm. The Kasiski method uses repetitive cryptograms found in the ciphertext to determine the key length. Modification of the vigenere cipher solves strengthen the cipher by using arranged keys to make it difficult to crack the keys against the Kasiski method attacks. This study analyzes the strength of the vigenere cipher ciphertext and the modification of the vigenere c…
The cipher block chaining (CBC) block cipher mode of operation was invented by IBM (International Business Machine) in 1976. It presents a very popular way of encrypting which is used in various applications. In this paper, we have mathematically proven that, under some conditions, the CBC mode of operation can admit a chaotic behaviour according to Devaney. Some cases will be properly studied in order to put in evidence this idea.
This paper presents a novel efficient chaotic image encryption scheme, in which the temp-value feedback mechanism is introduced to the permutation and diffusion procedures. Firstly, a simple trick is played to map the plain-image pixels to the initial condition of the Logistic map. Then, a pseudorandom number sequence (PRNS) is obtained from iterating the map. The permutation procedure is carried out by a permutation sequence which is generated by comparing the PRNS and its sorted version. The diffusion procedure is composed of two reversely executed rounds. During each round, the current plai…
In recent years, a lot of research has gone into creating multi-layer chaotic mapping-based cryptosystems. Random-like behavior, a continuous broadband power spectrum, and a weak baseline condition dependency are all characteristics of chaotic systems. Chaos could be helpful in the three functional components of compression, encryption, and modulation in a digital communication system. To successfully use chaos theory in cryptography, chaotic maps must be built in such a way that the entropy they produce can provide the necessary confusion and diffusion. A chaotic map is used in the first laye…
In this paper it has been developed an algorithm for cryptography, using the Mellin's transform. Cryptography is very important to protect data to ensure that two people, using an insecure channel, may communicate in a secure way. In the present age, ensure the communications will essential to shared data that have to be protected. The original message is a plain text, and the encrypted form as cipher text. The cipher text message contains all the information of the plain text, but is cannot be read from a human without a key and a method to decrypt it.
In year 2000, an efficient hierarchical chaotic image encryption (HCIE) algorithm was proposed, which divides a plain-image of size $M\times N$ with $T$ possible value levels into $K$ blocks of the same size and then operates position permutation on two levels: intra-block and inter-block. As a typical position permutation-only encryption algorithm, it has received intensive attention. The present paper analyzes specific security performance of HCIE against ciphertext-only attack and known/chosen-plaintext attack. It is found that only $O(\lceil\log_T(M\cdot N/K) \rceil)$ known/chosen plain-im…
This paper presents a comprehensive analysis on the security of the Yi-Tan-Siew chaotic cipher proposed in [IEEE TCAS-I 49(12):1826-1829 (2002)]. A differential chosen-plaintext attack and a differential chosen-ciphertext attack are suggested to break the sub-key K, under the assumption that the time stamp can be altered by the attacker, which is reasonable in such attacks. Also, some security Problems about the sub-keys $α$ and $β$ are clarified, from both theoretical and experimental points of view. Further analysis shows that the security of this cipher is independent of the use of the chao…
This paper presents a novel and robust chaos-based cryptosystem for secure transmitted images and four other versions. In the proposed block encryption/decryption algorithm, a 2D chaotic map is used to shuffle the image pixel positions. Then, substitution (confusion) and permutation (diffusion) operations on every block, with multiple rounds, are combined using two perturbed chaotic PWLCM maps. The perturbing orbit technique improves the statistical properties of encrypted images. The obtained error propagation in various standard cipher block modes demonstrates that the proposed cryptosystem …
This paper introduces Freestyle, a randomized and variable round version of the ChaCha cipher. Freestyle uses the concept of hash based halting condition where a decryption attempt with an incorrect key is likely to take longer time to halt. This makes Freestyle resistant to key-guessing attacks i.e. brute-force and dictionary based attacks. Freestyle demonstrates a novel approach for ciphertext randomization by using random number of rounds for each block, where the exact number of rounds are unknown to the receiver in advance. Freestyle provides the possibility of generating $2^{128}$ differ…
In this paper, a new stream cipher is designed as a clock-controlled one, but with a new mechanism of altering steps based on system theory in such a way that the structures used in it are resistant to conventional attacks. Our proposed algorithm (PALS) uses the main key with the length of 256 bits and a 32-bit message key. The most important criteria considered in designing the PALS are resistance to known attacks, maximum period, high linear complexity, and good statistical properties. As a result, the output keystream is very similar to the perfectly random sequences and resistant to conven…
A process for the secure transmission of data is presented that has to a certain degree the advantages of the one-time pad (OTP) cipher, that is, simplicity, speed, and information-theoretically security, but overcomes its fundamental weakness, the necessity of securely exchanging a key that is as long as the message. For each transmission, a dedicated one-time pad is generated for encrypting and decrypting the plaintext message. This one-time pad is built from a randomly chosen set of basic keys taken from a public library. Because the basic keys can be chosen and used multiple times, the met…
This paper shows that the Hirschfeld-Gebelein-Rényi maximal correlation between the message and the ciphertext provides good secrecy guarantees for cryptosystems that use short keys. We first establish a bound on the eavesdropper's advantage in guessing functions of the message in terms of maximal correlation and the Rényi entropy of the message. This result implies that maximal correlation is stronger than the notion of entropic security introduced by Russell and Wang. We then show that a small maximal correlation $ρ$ can be achieved via a randomly generated cipher with key length $\approx2\l…
A discrete-time discrete-value pseudo-chaotic encoder/decoder system is presented. The pseudo-chaotic module is a 3D discrete version of the well-known Lorenz dynamical system. Scaling and biasing transformations as well as natural number arithmetics are employed in order to simplify realizations on a small size Field Programmable Gate Array (FPGA. The encryption ability is improved by using only the least significant byte of one of the pseudo chaotic state variables as the key to encrypt the plain text. The key is periodically perturbed by another chaotic state variable. The statistical prope…
A During last two decades, there has been a prolific growth in the chaos based image encryption algorithms. Up to an extent these algorithms have been able to provide an alternative to exchange large media files (images and videos) over the networks in a secure way. However, there have been some issues with the implementation of chaos based image ciphers in practice. One of them is reduced/small key space due to the fact that chaotic behavior is only observed for certain range of system parameters/initial conditions of the chaotic system used in such algorithms. To overcome this difficulty, we…
In this work, we present an algorithm for the design of $n\times n$-bits substitution boxes (S-boxes) based on time series of a discrete dynamical system with chaotic behavior. The elements of a $n\times n$-bits substitution box are given by binary sequences generated by time series with uniform distribution. Particularly, time series with uniform distribution are generated via two lag time chaotic series of the logistic map. The aim of using these two lag time sequences is to hide the map used, and thus U-shape distribution of the logistic map is avoided and uncorrelated S-box elements are ob…
In this paper, we propose to improve the security performance of a recently proposed color image encryption algorithm which is based on multi-chaotic systems. The existing cryptosystem employed a pixel-chaotic-shuffle mechanism to encrypt images, in which the generation of shuffling sequences are independent to the plain-image/cipher-image. As a result, it fails to the chosen-plaintext and known-plaintext attacks. Moreover, the statistical features of the cryptosystem are not up to the standard. Therefore, the security improvements are framed to make the above attacks infeasible and enhance th…
This article describes a new family of cryptographically secure pseudorandom number generators, based on coupled chaotic maps, that will serve as keystream in a stream cipher. The maps are a modification of a piecewise linear map, by dynamic changing of the coefficient values and perturbing its lesser significant bits.
We have designed a new class of public key algorithms based on quasigroup string transformations using a specific class of quasigroups called multivariate quadratic quasigroups (MQQ). Our public key algorithm is a bijective mapping, it does not perform message expansions and can be used both for encryption and signatures. The public key consist of n quadratic polynomials with n variables where n=140, 160, ... . A particular characteristic of our public key algorithm is that it is very fast and highly parallelizable. More concretely, it has the speed of a typical modern symmetric block cipher -…
The previous work showed that the Y00 protocol could stay secure with the eavesdropper's guessing probability on the secret keys being strictly less than one under an unlimitedly long known-plaintext attack with quantum memory. However, an assumption that at least a fast correlation attack is completely disabled by irregular mapping. The present study shows that the Y00 protocol can be information-theoretic secure under any quantum-computational crypto-analyses if the Y00 system is well designed. The Y00 protocol directly encrypts messages with short secret keys expanded into pseudo-random run…
This project involves an implementation of the Rivest Shamir Adleman (RSA) encryption algorithm in C. It consists of generation of two random prime numbers and a number co- prime to phi(n) also called euler toitent function. These three are used to generate a public key and private key. The user has to enter a message which is encrypted by the public key. The algorithm also decrypts the generated cipher text with the help of the private key and returns the plain text message which was encrypted earlier.
The average conditional entropy of the key given the message and its corresponding cryptogram, H(K|M,C), which is reffer as a key appearance equivocation, was proposed as a theoretical measure of the strength of the cipher system under a known-plaintext attack by Dunham in 1980. In the same work (among other things), lower and upper bounds for H(S}_{M}|M^L,C^L) are found and its asymptotic behaviour as a function of cryptogram length L is described for simple substitution ciphers i.e. when the key space S_{M} is the symmetric group acting on a discrete alphabet M. In the present paper we consi…
Pseudo-Random Bit Generation (PRBG) is required in many aspects of cryptography as well as in other applications of modern security engineering. In this work, PRBG based on 2D symmetrical chaotic mappings of logistic type is considered. The sequences generated with a chaotic PRBG of this type, are statistically tested and the computational effectiveness of the generators is estimated. Considering this PRBG valid for cryptography, the size of the available key space is also calculated. Different cryptographic applications can be suitable to this PRBG, being a stream cipher probably the most imm…
Internet of Things connects lots of small constrained devices to the Internet. As in any other environment, communication security is important and cryptographic algorithms are one of many elements that we use in order to keep messages secure. Because of the constrained nature of these environments, it is necessary to use algorithms that do not require high computational power. Lightweight ciphers are therefore ideal candidates for this purpose. In this paper, we explore a possibility of attacking an ultra-lightweight cipher PRESENT by using a multiple fault attack. Utilizing the Differential …
This paper proposes a chaotic map-based multicast scheme for multiuser speech wireless communication and implements it in an ARM platform. The scheme compresses the digital audio signal decoded by a sound card and then encrypts it with a three-level chaotic encryption scheme. First, the position of every bit of the compressed data is permuted randomly with a pseudo-random number sequence (PRNS) generated by a 6-D chaotic map. Then, the obtained data are further permuted in the level of byte with a PRNS generated by a 7-D chaotic map. Finally, it is operated with a multiround chaotic stream cip…
