An asymmetric image cryptosystem based on the adaptive synchronization of an uncertain unified chaotic system and a cellular neural network

Chaotic dynamics provide a fast and simple means to create an excellent image cryptosystem, because it is extremely sensitive to initial conditions and system parameters, pseudorandomness, and non-periodicity. However, most chaos-based image encryption schemes are symmetric cryptographic techniques, which have been proven to be more vulnerable, compared to an asymmetric cryptosystem. This paper develops an asymmetric image cryptosystem, based on the adaptive synchronization of two different chaotic systems, namely a unified chaotic system and a cellular neural network. An adaptive controller with parameter update laws is formulated, using the Lyapunov stability theory, to asymptotically synchronize the two chaotic systems. The synchronization controller is embedded in the image cryptosystem and generates a pair of asymmetric keys, for image encryption and decryption. Using numerical simulations, three sets of experiments are conducted to evaluate the feasibility and reliability of the proposed chaos-based image cryptosystem.     

An efficient diffusion approach for chaos-based image encryption

One of the existing chaos-based image cryptosystems is composed of alternative substitution and diffusion stages. A multi-dimensional chaotic map is usually employed in the substitution stage for image pixel permutation while a one-dimensional (1D) chaotic map is used for diffusion purpose. As the latter usually involves real number arithmetic operations, the overall encryption speed is limited by the diffusion stage. In this paper, we propose a more efficient diffusion mechanism using simple table lookup and swapping techniques as a light-weight replacement of the 1D chaotic map iteration. Simulation results show that at a similar security level, the proposed cryptosystem needs about one-third the encryption time of a similar cryptosystem. The effective acceleration of chaos-based image cryptosystems is thus achieved.     

Efficient Rabin-type Digital Signature Scheme

Rabin's cryptosystem was proved to be as hard as factorization. However, Rabin's digital signature schemes is probabilistic. This paper shows two efficient Rabin type digital signature schemes, a basic scheme and an improved scheme. Both schemes run much faster than Rabin's scheme. They are deterministic and the size of a signature is much smaller than that of a signature in Rabin's scheme. Furthermore, it is proved that, by applying the technique of Bellare and Rogaway, the proposed scheme is secure against chosen plaintext attack. More precisely, breaking the proposed digital signature scheme by chosen plaintext attack is as hard as factoring N.     

Analysis of stationary subdivision schemes for curve design based on radial basis function interpolation

This paper provides a large family of interpolatory stationary subdivision schemes based on radial basis functions (RBFs) which are positive definite or conditionally positive definite. A radial basis function considered in this study has a tension parameter λ>0 such that it provides design flexibility. We prove that for a sufficiently large , the proposed 2L-point (L∈N) scheme has the same smoothness as the well-known 2L-point Deslauriers-Dubuc scheme, which is based on 2L-1 degree polynomial interpolation. Some numerical examples are presented to illustrate the performance of the new schemes, adapting subdivision rules on bounded intervals in a way of keeping the same smoothness and accuracy of the pre-existing schemes on R. We observe that, with proper tension parameters, the new scheme can alleviate undesirable artifacts near boundaries, which usually appear to interpolatory schemes with irregularly distributed control points.     

Anonymous Membership Broadcast Schemes

A membership broadcast scheme is a method by which a dealer broadcasts a secret identity among a set of users, in such a way that only a single user is sure that he is the intended recipient. Anonymous membership broadcast schemes have several applications, such as anonymous delegation, cheating prevention, etc. In a w-anonymous membership broadcast scheme any coalition of at most w users, which does not include the user chosen by the dealer, has no information about the identity of the chosen user. Wang and Pieprzyk proposed a combinatorial approach to 1-anonymous membership broadcast schemes. In particular, they proposed a 1-anonymous membership broadcast scheme offering a logarithmic complexity for both communication and storage. However, their result is non-constructive. In this paper, we consider w-anonymous membership broadcast schemes. First, we propose a formal model to describe such schemes and show lower bounds on the communication and randomness complexities of the schemes. Afterwards, we show that w-anonymous membership broadcast schemes can be constructed starting from (w + 1)-wise independent families of permutations. The communication and storage complexities of our schemes are logarithmic in the number of users.     

Group homomorphic encryption: characterizations, impossibility results, and applications

We give a complete characterization both in terms of security and design of all currently existing group homomorphic encryption schemes, i.e., existing encryption schemes with a group homomorphic decryption function such as ElGamal and Paillier. To this end, we formalize and identify the basic underlying structure of all existing schemes and say that such schemes are of shift-type. Then, we construct an abstract scheme that represents all shift-type schemes (i.e., every scheme occurs as an instantiation of the abstract scheme) and prove its IND-CCA1 (resp. IND-CPA) security equivalent to the hardness of an abstract problem called Splitting Oracle-Assisted Subgroup Membership Problem (SOAP) (resp. Subgroup Membership Problem, SMP). Roughly, SOAP asks for solving an SMP instance, i.e., for deciding whether a given ciphertext is an encryption of the neutral element of the ciphertext group, while allowing access to a certain oracle beforehand. Our results allow for contributing to a variety of open problems such as the IND-CCA1 security of Paillier’s scheme, or the use of linear codes in group homomorphic encryption. Furthermore, we design a new cryptosystem which provides features that are unique up to now: Its IND-CPA security is based on the k-linear problem introduced by Shacham, and Hofheinz and Kiltz, while its IND-CCA1 security is based on a new k-problem that we prove to have the same progressive property, namely that if the k-instance is easy in the generic group model, the (k+1)-instance is still hard.     

Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes

Because of their interesting algebraic properties, several authors promote the use of generalized Reed–Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure. Wieschebrink proposed a variant of the McEliece cryptosystem which consists in concatenating a few random columns to a generator matrix of a secretly chosen generalized Reed–Solomon code. More recently, new schemes appeared which are the homomorphic encryption scheme proposed by Bogdanov and Lee, and a variation of the McEliece cryptosystem proposed by Baldi et al. which hides the generalized Reed–Solomon code by means of matrices of very low rank. In this work, we show how to mount key-recovery attacks against these public-key encryption schemes. We use the concept of distinguisher which aims at detecting a behavior different from the one that one would expect from a random code. All the distinguishers we have built are based on the notion of component-wise product of codes. It results in a powerful tool that is able to recover the secret structure of codes when they are derived from generalized Reed–Solomon codes. Lastly, we give an alternative to Sidelnikov and Shestakov attack by building a filtration which enables to completely recover the support and the non-zero scalars defining the secret generalized Reed–Solomon code.     

Experimental study on impulsive synchronization between two modified Chua's circuits

As in many continuous synchronization studies and chaos-based communication systems, the paradigmatic chaos generator, Chua's circuit has been generally used in impulsive synchronization schemes. On the other hand, different versions of Chua's circuit are considered in literature. Nowadays, we realized a new version of Chua's circuit by modifying circuit connections and inserting an additional passive element to the circuit structure. In this study, we have experimentally investigated impulsive synchronization between two modified Chua's circuits. Experimental results show that impulsive synchronization is achieved in the proposed scheme with respect to the switching frequency.     

Cryptanalysis of a chaos-based cryptosystem on DSP

In this work, we cryptanalyse a recently chaos-based cryptosystem on DSP by proposing three different attacks to break it. We report the weakness of this cryptosystem and hence demonstrate that in its actual design, it cannot be used in the real world applications and it needs to be first enhanced by avoiding the design drawbacks reported in this work.     

Modified exponential schemes for convection–diffusion problems

The original exponential schemes of the finite volume approach proposed by Spalding [Spalding DB. A novel finite-difference formulation for differential expressions involving both first and second derivatives. Int J Numer Methods Eng 1972;4:509–51] as well as by Raithby and Torrance [Raithby GD, Torrance KE. Upstream-weighted differencing schemes and their application to elliptic problems involving fluid flow. Comput Fluids 1974;2:191–206], on which the well known hybrid and power-law schemes were based, had been derived without considering the non-constant source term which can be linearized as a function of a scalar variable ϕ. Following a similar method to that of Spalding, we derived three modified exponential schemes, corresponding to the average and integrated source terms, with the last scheme involving matching the analytical solutions of the neighbouring sub-regions by assuming the continuity of the first derivative of scalar variable ϕ. To validate the higher accuracy of the modified exponential schemes, as compared to classical schemes, numerical predictions obtained by various discretization schemes were compared with exact analytical solutions for linear problems. For non-linear problems, with non-constant source term, the solutions of the numerical discretization equations were compared with accurate solutions obtained with fine grids. To test the suitability of the proposed schemes in practical problems of computational fluid dynamics, all schemes were also examined by varying the mass flow rate and the coefficient of the non-constant source term. Finally, the best performing scheme is recommended for applications to CFD problems.     

Security and efficiency data sharing scheme for cloud storage

With the adoption and diffusion of data sharing paradigm in cloud storage, there have been increasing demands and concerns for shared data security. Ciphertext Policy Attribute-Based Encryption (CP-ABE) is becoming a promising cryptographic solution to the security problem of shared data in cloud storage. However due to key escrow, backward security and inefficiency problems, existing CP-ABE schemes cannot be directly applied to cloud storage system. In this paper, an effective and secure access control scheme for shared data is proposed to solve those problems. The proposed scheme refines the security of existing CP-ABE based schemes. Specifically, key escrow and conclusion problem are addressed by dividing key generation center into several distributed semi-trusted parts. Moreover, secrecy revocation algorithm is proposed to address not only back secrecy but efficient problem in existing CP-ABE based scheme. Furthermore, security and performance analyses indicate that the proposed scheme is both secure and efficient for cloud storage.     

Comments on, “A blind source separation-based method for multiple images encryption”

In this paper we have found that proposed cryptosystem a blind source separation for multiple images encryption suffers from the same weakness as of the previous BSS-based cryptosystems proposed by Lin et al. Hence, it is also vulnerable to various types attacks.     

A Linear Algebraic Approach to Metering Schemes

A metering scheme is a method by which an audit agency is able to measure the interaction between servers and clients during a certain number of time frames. Naor and Pinkas (Vol. 1403 of LNCS, pp. 576–590) proposed metering schemes where any server is able to compute a proof (i.e., a value to be shown to the audit agency at the end of each time frame), if and only if it has been visited by a number of clients larger than or equal to some threshold h during the time frame. Masucci and Stinson (Vol. 1895 of LNCS, pp. 72–87) showed how to construct a metering scheme realizing any access structure, where the access structure is the family of all subsets of clients which enable a server to compute its proof. They also provided lower bounds on the communication complexity of metering schemes. In this paper we describe a linear algebraic approach to design metering schemes realizing any access structure. Namely, given any access structure, we present a method to construct a metering scheme realizing it from any linear secret sharing scheme with the same access structure. Besides, we prove some properties about the relationship between metering schemes and secret sharing schemes. These properties provide some new bounds on the information distributed to clients and servers in a metering scheme. According to these bounds, the optimality of the metering schemes obtained by our method relies upon the optimality of the linear secret sharing schemes for the given access structure.     

Unconditionally-secure key pre-distribution for triangular grid based wireless sensor network

We present an unconditionally-secure key pre-distribution scheme for a wireless sensor network using t-degree bivariate polynomials. The proposed scheme is proven to be perfectly resilient against both node disconnection and link failure. The memory requirements, computation and communication overheads of our scheme are also favorable. Our scheme demonstrates superior performance compared to the existing similar schemes.     

Empirical analysis of evolutionary algorithms with immigrants schemes for dynamic optimization

In recent years, there has been a growing interest in studying evolutionary algorithms (EAs) for dynamic optimization problems (DOPs). Among approaches developed for EAs to deal with DOPs, immigrants schemes have been proven to be beneficial. Immigrants schemes for EAs on DOPs aim at maintaining the diversity of the population throughout the run via introducing new individuals into the current population. In this paper, we carefully examine the mechanism of generating immigrants, which is the most important issue among immigrants schemes for EAs in dynamic environments. We divide existing immigrants schemes into two types, namely the direct immigrants scheme and the indirect immigrants scheme, according to the way in which immigrants are generated. Then experiments are conducted to understand the difference in the behaviors of different types of immigrants schemes and to compare their performance in dynamic environments. Furthermore, a new immigrants scheme is proposed to combine the merits of two types of immigrants schemes. The experimental results show that the interactions between the two types of schemes reveal positive effect in improving the performance of EAs in dynamic environments.     

Multivariate public key cryptosystems from diophantine equations

Wang et al. introduced in (A medium-field multivariate public-key encryption scheme. Topics in Cryptology—CTRSA 2006: The Cryptographers’ Track at the RSA Conference, 2006) a multivariate public key cryptosystem, called MFE cryptosystem, and it is appealing as it is based on a simple polynomial identity. Their system, however, was subsequently broken by Ding et al. in (High order linearization equation (hole) attack on multivariate public key cryptosystems. Public key cryptography—PKC 2007: 10th international conference on practice and theory in public-key cryptography, 2007a, ?-Invertible cycles for multivariate quadratic public key cryptography. Public key cryptography—PKC 2007: 10th international conference on practice and theory in public-key cryptography, 2007b). Inspired by their work, we present a more general framework for multivariate public key cryptosystems, which combines ideas from both triangular and oil-vinegar schemes. Within this framework, we propose a new public key cryptosystem based on a solution of a Diophantine equation over polynomial rings.     

A method for image encryption based on fractional-order hyperchaotic systems

By using sequences generated from fractional-order hyperchaotic systems, a color image encryption scheme is investigated. Firstly, a plain image, which is known to users in advance, is chosen as a secret key to confuse the original image. Then, the confused image is encrypted by the sequences generated from the fractional-order hyperchaotic systems. With this simple encryption method, we can get an encrypted image that is fully scrambled and diused. For chaos-based image cryptosystems, this encryption scheme enhances the security and improves the eectiveness. Furthermore, the cryptosystem resists the dierential attack. Experiments show that the algorithm is suitable for image encryption, and some statistical tests are provided to show the high security in the end     

A new two-point scheme for multiple roots of nonlinear equations

In most of the earlier research for multiple zeros, in order to obtain a new iteration function from the existing scheme, the usual practice is to make no change at the first substep. In this paper, we explore the idea that what are the advantages if the flexibility of choice is also given at the first substep. Therefore, we present a new two-point sixth-order scheme for multiple roots (m>1). The main advantages of our scheme over the existing schemes are flexibility at both substeps, simple body structure, smaller residual error, smaller error difference between two consecutive iterations, and smaller asymptotic error constant. The development of the scheme is based on midpoint formula and weight functions of two variables. We compare our methods with the existing methods of the same order with real-life applications as well as standard test problems. From the numerical results, we find that our methods can be considered as better alternates for the existing methods of the same order. Finally, dynamical study of the proposed schemes is presented that confirms the theoretical results.     

Lag synchronization of hyperchaos with application to secure communications

In this paper, hyperchaotic lag synchronization is restated as a nonlinear and lag-in-time observer design issue. This approach leads to a systematic tool, which guarantees the lag synchronization of a wide class of chaotic or hyperchaotic systems via a scalar signal. By exploiting this result, we propose a hyperchaos-based cryptosystem scheme that combines the conventional cryptographic methods and the lag synchronization of chaotic circuits. The computer simulation results show that the lag synchronization scheme and the cryptosystem proposed in this paper are both feasible.