Original Cryptosystem Research Articles

Evaluation of effectiveness of chosen-plaintext attacks on the Rao-Nam cryptosystem over a finite Abelian group

The Rao-Nam cryptosystem is a symmetric version of the McEliece code-based cryptosystem proposed to get rid of the shortcomings inherent in the first symmetric code-based encryption schemes. Almost immediately after the publication of this cryptosystem, attacks on it based on selected plaintexts appeared, which led to the emergence of various improvements and modifications of the original cryptosystem.
 The secret key in the traditional Rao-Nam scheme is a certain Boolean matrix and a set of binary vectors used to generate distortions during encryption. Such vectors must have different syndromes, that is, be different modulo of the code generated by the rows of the specified matrix. The original work of Rao and Nam considered two methods of forming the set of these vectors, the first of which consists in using predetermined vectors of sufficiently large weight, and the second is random selection of these vectors according to the equiprobable scheme. It is known that the first option does not provide the proper security of the Rao – Nam cryptosystem (due to the small number and simple structure of these vectors), but the second option is more meaningful and requires additional research. The purpose of this paper is to obtain estimates of the effectiveness (time complexity for a given upper bound of the error probability) of attacks on a cryptosystem, which generalizes the traditional Rao – Nam scheme to the case of a finite Abelian group (note that the need to study such versions of the Rao – Nam cryptosystem is due to their consideration in recent publications). Two attacks, based on selected plaintext, are presented. The first of them is not mentioned in the works known to the authors of this article and, under certain well-defined conditions, it allows recovering the secret key of the cryptosystem with quadratic complexity.
 The second attack is a generalized and simplified version of the well-known Struik-van Tilburg attack. It is shown that the complexity of this attack depends on the power of the stabilizer of the set of vectors, which forms the second part of the key, in the translation group of the Abelian group, over which the Rao – Nam cryptosystem is considered. In this paper, a bound is obtained for the probability of triviality of the stabilizer under the condition of random choice of this set. From the obtained bound, it follows that Struik-van Tilburg attack is, on average, noticeably more efficient than the worst case considered earlier.

Cryptanalysis of a secure image encryption scheme based on a novel 2D sine–cosine cross‑chaotic map

Recently, a new secure image encryption scheme was proposed based on a novel 2D sine–cosine cross‑chaotic map. The authors claimed that the encryption scheme they proposed was secure enough to resist all the existing cryptanalytic attacks. However, the multi-round original cryptosystem with permutation–bit diffusion structure (PBDS) was found to have three security vulnerabilities and was proved to be equivalent to the one-round cryptosystem with PBDS, which would lead to the original cryptosystem being successfully cracked by chosen-plaintext attack (CPA). Subsequently, two efficient and feasible attack schemes were proposed in this paper, and they require $$\left\lceil {\log_{2} W \times H} \right\rceil + 1$$ and $$\left\lceil {\log_{256} W \times H} \right\rceil + 1$$ times of CPA in total, respectively. Simulation and experimental results have verified the effectiveness and feasibility of the two attack schemes.

A subtree‐based transformation model for cryptosystem using chaotic maps under cloud computing environment for fuzzy user data sharing

SummaryCloud computing technologies have been prospering in recent years and have opened an avenue for a wide variety of forms of adaptable data sharing. Taking advantage of these state‐of‐the‐art innovations, the cloud storage data owner must, however, use a suitable identity‐based cryptographic mechanism to ensure the safety prerequisites while sharing data to large numbers of cloud data users with fuzzy identities. As a successful way to guarantee secure fuzzy sharing of cloud data, the identity‐based cryptographic technology still faces an effectiveness problem under multireceiver configurations. The chaos theory is considered a reasonable strategy for reducing computational complexity while meeting the cryptographic protocol's security needs. In an identity‐based cryptographic protocol, public keys for individual clients are distributed, allowing the clients to separately select their own network identities or names as their public keys. In fact, in a public‐key cryptographic protocol, it is for the best that the confirmation of the public key is done in a safe, private manner, because this way the load of storage on the server's side can be considerably relieved. The objective of this paper is to outline and examine a conversion process that can transfer cryptosystems using Chebyshev's chaotic maps over the Galois field to a subtree‐based protocol in the cloud computing setting for fuzzy user data sharing, as opposed to reconcocting a different structure. Furthermore, in the design of our conversion process, no adjustment of the original cryptosystem based on chaotic maps is needed.

Exploiting ergodicity of the logistic map using deep-zoom to improve security of chaos-based cryptosystems

This paper explores the deep-zoom properties of the chaotic [Formula: see text]-logistic map, in order to propose an improved chaos-based cryptosystem. This map was shown to enhance the random features of the Logistic map, while at the same time reducing the predictability about its orbits. We incorporate its strengths to security into a previously published cryptosystem to provide an optimal pseudo-random number generator (PRNG) as its core operation. The result is a reliable method that does not have the weaknesses previously reported about the original cryptosystem.

Secure Outsourced Calculations with Homomorphic Encryption

With the rapid development of cloud computing, the privacy security incidents occur frequently, especially data security issues. Cloud users would like to upload their sensitive information to cloud service providers in encrypted form rather than the raw data, and to prevent the misuse of data. The main challenge is to securely process or analyze these encrypted data without disclosing any useful information, and to achieve the rights management efficiently. In this paper, we propose the encrypted data processing protocols for cloud computing by utilizing additively homomorphic encryption and proxy cryptography. For the traditional homomorphic encryption schemes with many limitations, which are not suitable for cloud computing applications. We simulate a cloud computing scenario with flexible access control and extend the original homomorphic cryptosystem to suit our scenario by supporting various arithmetical calculations. We also prove the correctness and security of our protocols, and analyze the advantages and performance by comparing with some latest works.

Improved Cryptanalysis and Enhancements of an Image Encryption Scheme Using Combined 1D Chaotic Maps.

This paper presents an improved cryptanalysis of a chaos-based image encryption scheme, which integrated permutation, diffusion, and linear transformation process. It was found that the equivalent key streams and all the unknown parameters of the cryptosystem can be recovered by our chosen-plaintext attack algorithm. Both a theoretical analysis and an experimental validation are given in detail. Based on the analysis of the defects in the original cryptosystem, an improved color image encryption scheme was further developed. By using an image content–related approach in generating diffusion arrays and the process of interweaving diffusion and confusion, the security of the cryptosystem was enhanced. The experimental results and security analysis demonstrate the security superiority of the improved cryptosystem.

Cryptanalysis of a chaotic image encryption scheme based on permutation-diffusion structure

Chaos-based image encryption algorithms have been widely studied since the permutation-diffusion structure (PDS) was proposed. However, the PDS is not secure from attacks, which may lead to security vulnerabilities of PDS based chaotic cryptosystems. In this study, the security problems of PDS are investigated. Then, a new PDS based chaotic image encryption scheme is cryptanalyzed. In the original scheme, a 3D bit matrix permutation was used to address the intrinsic deficiencies of traditional pixel/bit level permutation of image encryption. The double random position permutation provides a high security level. However, it is not unattackable. In this study, a novel attack method will be introduced where all the chaotic mappings or parameters which are functionally equivalent to the keys used in the permutation and diffusion stages of the original cryptosystem can fully be revealed. The encrypted images can then be completely recovered without knowing the secret keys. Both mathematical analysis and experimental results are given to illustrate the effectiveness of the proposed method.

Cryptanalysis of a colour image encryption using chaotic APFM nonlinear adaptive filter

Recently, a novel colour image encryption scheme was proposed based on chaotic Amplitude Phase Frequency Model nonlinear adaptive filter. The authors claim that the scheme achieved sufficient security strength by 14 sub-keys with a total effective key length of 651 bits. However, the attacker can recover the encrypted image without using the secret sub-keys. The critical problem of the original cryptosystem is that the sum of the pixels of the plain image (Mod 256) to generate pseudorandom sequences can be determined. This security weakness leads to collapse of the cryptosystem. By chosen-plaintext attack, two efficient cryptanalysis methods are proposed in this paper, where one has high generality and high computational complexity and the other has low complexity and low generality. Experimental results demonstrate that the cryptosystem can be broken by these two cryptanalysis methods with 774 and 265 pairs of chosen plain/cipher images.

Efficient Cryptosystems From $$\mathbf{2}^{{\varvec{k}}}$$ 2 k -th Power Residue Symbols

Goldwasser and Micali (J Comput Syst Sci 28(2):270---299, 1984) highlighted the importance of randomizing the plaintext for public-key encryption and introduced the notion of semantic security. They also realized a cryptosystem meeting this security notion under the standard complexity assumption of deciding quadratic residuosity modulo a composite number. The Goldwasser---Micali cryptosystem is simple and elegant but is quite wasteful in bandwidth when encrypting large messages. A number of works followed to address this issue and proposed various modifications. This paper revisits the original Goldwasser---Micali cryptosystem using $$2^k$$2k-th power residue symbols. The so-obtained cryptosystems appear as a very natural generalization for $$k \ge 2$$kź2 (the case $$k=1$$k=1 corresponds exactly to the Goldwasser---Micali cryptosystem). Advantageously, they are efficient in both bandwidth and speed; in particular, they allow for fast decryption. Further, the cryptosystems described in this paper inherit the useful features of the original cryptosystem (like its homomorphic property) and are shown to be secure under a similar complexity assumption. As a prominent application, this paper describes an efficient lossy trapdoor function-based thereon.

Discussion and a new method of optical cryptosystem based on interference

A discussion and an objective security analysis of the well-known optical image encryption based on interference are presented in this paper. A new method is also proposed to eliminate the security risk of the original cryptosystem. For a possible practical application, we expand this new method into a hierarchical authentication scheme. In this authentication system, with a pre-generated and fixed random phase lock, different target images indicating different authentication levels are analytically encoded into corresponding phase-only masks (phase keys) and amplitude-only masks (amplitude keys). For the authentication process, a legal user can obtain a specified target image at the output plane if his/her phase key, and amplitude key, which should be settled close against the fixed internal phase lock, are respectively illuminated by two coherent beams. By comparing the target image with all the standard certification images in the database, the system can thus verify the user's legality even his/her identity level. Moreover, in despite of the internal phase lock of this system being fixed, the crosstalk between different pairs of keys held by different users is low. Theoretical analysis and numerical simulation are both provided to demonstrate the validity of this method.

Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains

Recently, a double-image encryption scheme using local pixel scrambling technique and gyrator transform has been proposed [Opt Lasers Eng 2013; 51: 1327–31]. Through our simulations, there is serious cross-talk disturbance in the phase-based image when the encrypted data undergoes noise perturbation or occlusion attack. The disturbance will cause serious deterioration in the retrieved phase-based image and bring about visibility ambiguities to the receiver, and hence downgrades the practicability of the cryptosystem. In this paper, detailed analysis of the cross-talk disturbance in the original scheme will be firstly given out, and then the corresponding improvement is subsequently proposed. Numerical simulations results indicate that the improved scheme well address the cross-talk disturbance and further enhance the security of the original cryptosystem.

Enhancing the Security of the GPT Cryptosystem Against Attacks

The concept of Public key cryptosystems based on error correcting codes was invented by McEliece in 1978. In 1991 Gabidulin, Paramonov and Tretjakov proposed a new mversion of the McEliece cryptosystem (GPT) based on maximum rank distance codes instead of hamming distance codes. Respective structural attacks against dierent variants of the GPT cryptosystem were proposed by Gibson and lately by Overbeck. The Overbeck attack breaks all variants of the GPT cryptosystem and are turned out to be either polynomial or exponential depending on parameters of the cryptosystem. Furthermore, In 2013, Gaborit et al. have presented a decoding attack against the parameters of the simple variant of the GPT cryptosystem which were demonstrated to combat the GPT cryptosystem against Overbeck's attack. In this paper, we introduce two new secure approaches against both the structural (Over-beck's attack) and decoding (brute force) attacks. The rst one is called Distortion Matrix Approach (DMA), and the second is called Advanced Approach for Reducible Rank Codes (ARC). The DMA based on proper choice of a distortion matrix X, while, the ARC based on a proper choice of a scramble matrix P. Furthermore, we evaluate the simple variant of GPT cryptosystem against Gaborit et al. attack and demonstrate a new set of parameters which are secure against all known attacks. Our results show the proposed approaches com- bat the structural and decoding attacks with a large reduction in the key size in comparison to the original McEliece cryptosystem.

Improvement of an image encryption algorithm based on hyper-chaos

In this paper, we propose to enhance a recently proposed image cryptosystem based on hyper-chaos. The updated version has been builded to resist against attacks made to break the original one and to make it faster. The modification concerns the two Boxes, P-Box and S-Box, which composed the original cryptosystem. Compared with classical encryption schemes, AES and Triple-DES, the new version of the cipher shows a better performances in rapidity, in confusion and in the key sensitivity.

Secure Chaotic Map Based Block Cryptosystem with Application to Camera Sensor Networks

Recently, Wang et al. presented an efficient logistic map based block encryption system. The encryption system employs feedback ciphertext to achieve plaintext dependence of sub-keys. Unfortunately, we discovered that their scheme is unable to withstand key stream attack. To improve its security, this paper proposes a novel chaotic map based block cryptosystem. At the same time, a secure architecture for camera sensor network is constructed. The network comprises a set of inexpensive camera sensors to capture the images, a sink node equipped with sufficient computation and storage capabilities and a data processing server. The transmission security between the sink node and the server is gained by utilizing the improved cipher. Both theoretical analysis and simulation results indicate that the improved algorithm can overcome the flaws and maintain all the merits of the original cryptosystem. In addition, computational costs and efficiency of the proposed scheme are encouraging for the practical implementation in the real environment as well as camera sensor network.

Security Analysis of a Block Encryption Algorithm Based on Dynamic Sequences of Multiple Chaotic Systems

Recently, the cryptosystem based on chaos has attracted much attention. Wang and Yu (Commun. Nonlin. Sci. Numer. Simulat. 14 (2009) 574) proposed a block encryption algorithm based on dynamic sequences of multiple chaotic systems. We analyze the potential flaws in the algorithm. Then, a chosen-plaintext attack is presented. Some remedial measures are suggested to avoid the flaws effectively. Furthermore, an improved encryption algorithm is proposed to resist the attacks and to keep all the merits of the original cryptosystem.

Cryptanalysis and improvement on a block cryptosystem based on iteration a chaotic map

Recently, a novel block encryption system has been proposed as an improved version of the chaotic cryptographic method based on iterating a chaotic map. In this Letter, a flaw of this cryptosystem is pointed out and a chosen plaintext attack is presented. Furthermore, a remedial improvement is suggested, which avoids the flaw while keeping all the merits of the original cryptosystem.

Cryptanalysis of a cryptosystem using multiple one-dimensional chaotic maps

Recently, a new chaotic cryptosystem using external 128-bit key and multiple chaotic maps has been proposed. In this paper, a fundamental flaw of this cryptosystem is pointed out and a known plaintext attack is presented. Furthermore, a remedial modification is suggested, which avoids the flaw while keeping all the merits of the original cryptosystem.

Modification of a public-key cryptosystem

A modification of the public-key cryptosystem proposed by Okamoto is presented. This modification appears to be resistant to Shamir's cryptanalytic attacks on the original cryptosystem. In addition, a variant whose data expansion rate due to encryption is less than that of the modification is also proposed.