This paper studies the security of an image encryption scheme based on the Hill cipher and reports its following problems: 1) there is a simple necessary and sufficient condition that makes a number of secret keys invalid; 2) it is insensitive to the change of the secret key; 3) it is insensitive to the change of the plain-image; 4) it can be broken with only one known/chosen-plaintext; 5) it has some other minor defects.
SEPAR is a lightweight cryptographic algorithm, designed to implement on resource-constrained devices especially those employed in IoT environments. Meanwhile, the mixed structure design of cipher leads to speed improvement while guaranteeing its resistance against common cryptographic attacks, especially differential and linear attacks. In order to confirm the resistance of the cipher against differential attack, an extensive investigation was presented in our previous work. In his study, we conduct new research continuing the previously presented research. We prove that there are enough acti…
MIBS is a light weight block cipher aimed at extremely constrained resources environments such as RFID tags and sensor networks. In this paper, we focus on improved key-recovery attacks on reduced-round MIBS with integral and zero-correlation linear cryptanalysis. By exploring the key-expanding properties and choosing suitable linear approximations with zero-correlation,13-round zero-correlation linear cryptanalysis were presented. Furthermore, we deduced some integral distinguishers from 8-round zero-correlation linear approximations using the relations between them, and as applications, we a…
T-310 is a cipher that was used for encryption of governmental communications in East Germany during the final years of the Cold War. Due to its complexity and the encryption process,there was no published attack for a period of more than 40 years until 2018 by Nicolas T. Courtois et al. in [10]. In this thesis we study the so called 'long term keys' that were used in the cipher, in order to expose weaknesses which will assist the design of various attacks on T-310.
Recently, an image encryption algorithm using block-based scrambling and image filtering has been proposed by Hua et al. In this paper, we analyze the security problems of the encryption algorithm in detail and break the encryption by a codebook attack. We construct an linear relation between plain-images and cipher-images by differential cryptanalysis. With this linear relation, we build a codebook containing $(M \times N + 1)$ pairs of plain-images and cipher-images, where $M\times N$ is the size of images. The proposed codebook attack indicates that the encryption scheme is insecure. To res…
Many real-world cyber-physical systems (CPS) use proprietary cipher algorithms. In this work, we describe an easy-to-use black-box security evaluation approach to measure the strength of proprietary ciphers without having to know the algorithms. We quantify the strength of a cipher by measuring how difficult it is for a neural network to mimic the cipher algorithm. We define new metrics (e.g., cipher match rate, training data complexity and training time complexity) that are computed from neural networks to quantitatively represent the cipher strength. This measurement approach allows us to di…
Block cipher E2, designed and submitted by Nippon Telegraph and Telephone Corporation, is a first-round Advanced Encryption Standard candidate. It employs a Feistel structure as global structure and two-layer substitution-permutation network structure in round function with initial transformation IT function before the first round and final transformation FT function after the last round. The design principles influences several more recent block ciphers including Camellia, an ISO/IEC standard cipher. In this paper, we focus on the key-recovery attacks on reduced-round E2-128/192 taking both I…
CUDA (formerly an abbreviation of Compute Unified Device Architecture) is a parallel computing platform and API model created by Nvidia allowing software developers to use a CUDA-enabled graphics processing unit (GPU) for general purpose processing. This 90-pages tutorial introduces the CUDA concepts in an easy-to-grasp and interactive way with ready-to-run code samples tested on Windows and Linux. Starting from scratch, a complete stand-alone GPU tool is implemented which automatically performs a ciphertext-only attack on ciphertexts encrypted by monoalphabetic substitution and columnar trans…
Cryptolysis is a framework that includes a collection of automated attacks on the classical ciphers based on the article by Clark Dawson on Optimisation heuristics for the automated cryptanalysis of classical ciphers from the Journal of Combinatorial Mathematics and Combinatorial Computing, 1998.
Differential cryptanalysis is one of the most popular methods in attacking block ciphers. However, there still some limitations in traditional differential cryptanalysis. On the other hand, researches of quantum algorithms have made great progress nowadays. This paper proposes two methods to apply quantum algorithms in differential cryptanalysis, and analysis their efficiencies and success probabilities. One method is using quantum algorithm in the high probability differential finding period for every S-Box. The second method is taking the encryption as a whole, using quantum algorithm in thi…
Linear (or differential) cryptanalysis may seem dull topics for a mathematician: they are about super simple invariants characterized by say a word on n=64 bits with very few bits at 1, the space of possible attacks is small, and basic principles are trivial. In contract mathematics offers an infinitely rich world of possibilities. If so, why is that cryptographers have ever found so few attacks on block ciphers? In this paper we argue that black-box methods used so far to find attacks in symmetric cryptography are inadequate and we work with a more recent white-box algebraic methodology. Inva…
Cryptanalysis of knapsack cipher is a fascinating problem which has eluded the computing fraternity for decades. However, in most of the cases either the time complexity of the proposed algorithm is colossal or an insufficient number of samples have been taken for verification. The present work proposes a Genetic Algorithm based technique for cryptanalysis of knapsack cipher. The experiments conducted prove the validity of the technique. The results prove that the technique is better than the existing techniques. An extensive review has been carried out in order to find the gaps in the existin…
Lightweight stream ciphers are highly demanded in IoT applications. In order to optimize the hardware performance, a new class of stream cipher has been proposed. The basic idea is to employ a single Galois NLFSR with maximum period to construct the cipher. As a representative design of this kind of stream ciphers, Espresso is based on a 256-bit Galois NLFSR initialized by a 128-bit key. The $2^{256}-1$ maximum period is assured because the Galois NLFSR is transformed from a maximum length LFSR. However, we propose a Galois-to-Fibonacci transformation algorithm and successfully transform the G…
We answer a question of Paterson, showing that all block systems for the group generated by the round functions of a key-alternating block cipher are the translates of a linear subspace. Following up remarks of Paterson and Shamir, we exhibit a connection to truncated differential cryptanalysis. We also give a condition that guarantees that the group generated by the round functions of a key-alternating block cipher is primitive. This applies in particular to AES.
The block cipher KASUMI is widely used for security in many synchronous wireless standards. It was proposed by ETSI SAGE for usage in 3GPP (3rd Generation Partnership Project) ciphering algorthms in 2001. There are a great deal of cryptanalytic results on KASUMI, however, its security evaluation against the recent zero-correlation linear attacks is still lacking so far. In this paper, we select some special input masks to refine the general 5-round zero-correlation linear approximations combining with some observations on the $FL$ functions and then propose the 6-round zero-correlation linear …
Recently it was shown that permutation-only multimedia ciphers can completely be broken in a chosen-plaintext scenario. Apparently, chosen-plaintext scenario models a very resourceful adversary and does not hold in many practical situations. To show that these ciphers are totally broken, we propose a cipher-text only attack on these ciphers. To that end, we investigate speech permutation-only ciphers and show that inherent redundancies of speech signal can pave the path for a successful cipher-text only attack. For this task different concepts and techniques are merged together. First, Short T…
Recently, an image scrambling encryption algorithm of pixel bit based on chaos map was proposed. Considering the algorithm as a typical binary image scrambling/permutation algorithm exerting on plaintext of size $M\times (8N)$, this paper proposes a novel optimal method to break it with some known/chosen-plaintexts. The spatial complexity and computational complexity of the attack are only $O(32\cdot MN)$ and $O(16\cdot n_0\cdot MN)$ respectively, where $n_0$ is the number of known/chosen-plaintexts used. The method can be easily extended to break any permutation-only encryption scheme exertin…
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.
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.
The Hill cipher is a classical symmetric encryption algorithm that succumbs to the know-plaintext attack. Although its vulnerability to cryptanalysis has rendered it unusable in practice, it still serves an important pedagogical role in cryptology and linear algebra. In this paper, a variant of the Hill cipher is introduced that makes the Hill cipher secure while it retains the efficiency. The proposed scheme includes a ciphering core for which a cryptographic protocol is introduced.
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 …
Two recent Hill cipher modifications which iteratively use interweaving and interlacing are considered. We show that strength of these ciphers is due to non-linear transformation used in them (bit-level permutations). Impact of number of iterations on the avalanche effect is investigated. We propose two Hill cipher modifications using column swapping and arbitrary permutation with significantly less computational complexity (2 iterations are used versus 16). The proposed modifications decrease encryption time while keeping the strength of the ciphers. Numerical experiments for two proposed cip…
In this paper, a variant of the Hill cipher is proposed. In the classical Hill cipher, an invertible matrix is used for encryption but the scheme is vulnerable to the known-plaintext attack which can reveal the matrix. In our proposed cryptosystem, each plaintext block is encrypted by a new invertible key matrix that thwarts the known-plaintext attack. To generate the invertible matrices which serve as the dynamic keys we make use of the vector spaces, randomly generated basis and non-singular linear transformation. Resulting cipher is secure against the known-plaintext attack.
Recent years have seen an increasing involvement of Deep Learning in the cryptanalysis of various ciphers. The present study is inspired by past works on differential distinguishers, to develop a Deep Neural Network-based differential distinguisher for round reduced lightweight block ciphers PRESENT and Simeck. We make improvements in the state-of-the-art approach and extend its use to the two structurally different block ciphers, PRESENT-80 and Simeck64/128. The obtained results suggest the universality of our cryptanalysis method. The proposed method can distinguish random data from the ciph…
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…
One of the major open problems in symmetric cryptanalysis is to discover new specif i c types of invariant properties which can hold for a larger number of rounds of a block cipher. We have Generalised Linear Cryptanalysis (GLC) and Partitioning Cryptanalysis (PC). Due to double-exponential combinatorial explosion of the number of possible invariant properties systematic exploration is not possible and extremely few positive working examples of GLC are known. Our answer is to work with polynomial algebraic invariants which makes partitions more intelligible. We have developed a constructive al…
This thesis aims to use intelligent systems to extend and improve performance and security of cryptographic techniques. Genetic algorithms framework for cryptanalysis problem is addressed. A novel extension to the differential cryptanalysis using genetic algorithm is proposed and a fitness measure based on the differential characteristics of the cipher being attacked is also proposed. The complexity of the proposed attack is shown to be less than quarter of normal differential cryptanalysis of the same cipher by applying the proposed attack to both the basic Substitution Permutation Network an…
Recently Lin et al. proposed a method of using the underdetermined BSS (blind source separation) problem to realize image and speech encryption. In this paper, we give a cryptanalysis of this BSS-based encryption and point out that it is not secure against known/chosen-plaintext attack and chosen-ciphertext attack. In addition, there exist some other security defects: low sensitivity to part of the key and the plaintext, a ciphertext-only differential attack, divide-and-conquer (DAC) attack on part of the key. We also discuss the role of BSS in Lin et al.'s efforts towards cryptographically se…
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 …
In 1976, Whitfield Diffie and Martin Hellman introduced the public key cryptography or asymmetric cryptography standards. Two years later, an asymmetric cryptosystem was published by Ralph Merkle and Martin Hellman called MH, based on a variant of knapsack problem known as the subset-sum problem which is proven to be NP-hard. Furthermore, over the last four decades, Metaheuristics have achieved a remarkable progress in solving NP-hard optimization problems. However, the conception of these methods raises several challenges, mainly the adaptation and the parameters setting. In this paper, we pr…
In this paper, we study applications of Bernstein-Vazirani algorithm and present several new methods to attack block ciphers. Specifically, we first present a quantum algorithm for finding the linear structures of a function. Based on it, we propose new quantum distinguishers for the 3-round Feistel scheme and a new quantum algorithm to recover partial key of the Even-Mansour construction. Afterwards, by observing that the linear structures of a encryption function are actually high probability differentials of it, we apply our algorithm to differential analysis and impossible differential cry…
One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required. Some mechanisms for breaking codes include differential cryptanalysis, advanced statistics and brute-force. Recent works also attempt to use algebraic tools to reduce the cryptanalysis of a block cipher algorithm to the resolution of a system of quadratic equations describing the ciphering structure. In our study, we will also use algebraic tools but in a n…
Traditional cryptography is suffering a huge threat from the development of quantum computing. While many currently used public-key cryptosystems would be broken by Shor's algorithm, the effect of quantum computing on symmetric ones is still unclear. The security of symmetric ciphers relies heavily on the development of cryptanalytic tools. Thus, in order to accurately evaluate the security of symmetric primitives in the post-quantum world, it is significant to improve classical cryptanalytic methods using quantum algorithms. In this paper, we focus on two variants of differential cryptanalysi…
The Hill Cipher is a classical symmetric cipher which breaks plaintext into blocks of size m and then multiplies each block by an m by m key matrix to yield ciphertext. However, it is well known that the Hill cipher succumbs to cryptanalysis relatively easily. As a result, there have been efforts to strengthen the cipher through the use of various techniques e.g. permuting rows and columns of the key matrix to encrypt each plaintext vector with a new key matrix. In this paper, we strengthen the security of the Hill cipher against a known-plaintext attack by encrypting each plaintext matrix by …
This paper aims to review the encountered technical contradictions when an attacker meets the cipher-images encrypted by the image encryption schemes (algorithms) proposed in 2018 from the viewpoint of an image cryptanalyst. The most representative works among them are selected and classified according to their essential structures. Almost all image cryptanalysis works published in 2018 are surveyed due to their small number. The challenging problems on design and analysis of image encryption schemes are summarized to receive the attentions of both designers and attackers (cryptanalysts) of im…
From the security criteria of irreversibility, parallelizability and independence, we cryptanalyzed the key expansion modules of candidate block ciphers of AES, the results revealed that there exist some weaknesses inside, which may be explored by the attacker. Hence, we designed a more secure key expansion module that the round-key can satisfy three criteria above. First, we constructed a non-degenerate 2D chaotic map (2D-πeCM) with ergodicity in phase space and sufficient large chaotic range. Then based on 2D-πeCM and polynomial multiplication over Galois field, we designed an irreversible k…
Privacy is one of the key issues addressed by information Security. Through cryptographic encryption methods, one can prevent a third party from understanding transmitted raw data over unsecured channel during signal transmission. The cryptographic methods for enhancing the security of digital contents have gained high significance in the current era. Breach of security and misuse of confidential information that has been intercepted by unauthorized parties are key problems that information security tries to solve. This paper sets out to contribute to the general body of knowledge in the area …
Every day, millions of credit cards are swiped and transactions are carried out across the world. Due to numerous forms of unethical digital activities, users are vulnerable to credit card fraud, phishing, identity theft, etc. This paper outlines a novel block encryption algorithm involving multiple private keys and a resilient trapdoor function that ensures data security while maintaining an optimal run time and space complexity. The proposed scheme consists of an irrepressible trapdoor based on a depressed cubic function and a unique key generation algorithm that uses Fibonacci sequences and…
In this article, we have proposed a public key cryptography using Affine-Hill cipher with a generalized Fibonacci matrix(called multinacci matrix). Also proposed a key establishment(exchange of key matrix $K=Q_λ^{k}$ of order $λ\timesλ$ for encryption-decryption) scheme with the help of multinacci sequences under prime modulo. In this scheme, instead of exchanging key matrix, we need to exchange the only pair of numbers $(λ, k)$, which reduces the time complexity as well as space complexity and comes with a large key-space.
In this paper, we describe non invertible matrix in GF(2)which can be used as multiplication matrix in Hill Cipher technique for one way hash algorithm. The matrices proposed are permutation matrices with exactly one entry 1 in each row and each column and 0 elsewhere. Such matrices represent a permutation of m elements. Since the invention, Hill cipher algorithm was used for symmetric encryption, where the multiplication matrix is the key. The Hill cipher requires the inverse of the matrix to recover the plaintext from cipher text. We propose a class of matrices in GF(2) which are non inverti…
National University of Defense Technology（国防科技大学）；Hunan Engineering Research Center of Commercial Cryptography Theory and Technology Innovation（湖南省商密理论与技术创新工程研究中心）；State Key Laboratory of Cryptology（密码科学技术国家重点实验室）；Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）；University of Oulu（奥卢大学）
In CRYPTO 2019, Gohr made a pioneering attempt and successfully applied deep learning to the differential cryptanalysis against NSA block cipher SPECK32/64, achieving higher accuracy than the pure differential distinguishers. By its very nature, mining effective features in data plays a crucial role in data-driven deep learning. In this paper, in addition to considering the integrity of the information from the training data of the ciphertext pair, domain knowledge about the structure of differential cryptanalysis is also considered into the training process of deep learning to improve the per…
Recent years have shown that more than ever governments and intelligence agencies try to control and bypass the cryptographic means used for the protection of data. Backdooring encryption algorithms is considered as the best way to enforce cryptographic control. Implementation backdoors (at the protocol/implementation/ma\-nagement level) are generally considered. In this paper we propose to address the most critical issue of backdoors: mathematical backdoors or by-design backdoors, which are put directly at the mathematical design of the encryption algorithm. Considering a particular family (a…
Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient. While cryptography is the science of securing data, cryptanalysis is the science of analyzing and breaking secure communication. Classical cryptanalysis involves an interesting combination of analytical reasoning, application of mathematical tools and pattern finding. The objectives of the proposed work are to propose a new cryptographic method based on the…
We consider the enciphering of a data stream while being compressed by a LZ algorithm. This has to be compared to the classical encryption after compression methods used in security protocols. Actually, most cryptanalysis techniques exploit patterns found in the plaintext to crack the cipher; compression techniques reduce these attacks. Our scheme is based on a LZ compression in which a Vernam cipher has been added. We make some security remarks by trying to measure its randomness with statistical tests. Such a scheme could be employed to increase the speed of security protocols and to decreas…
This paper presents algorithms for local inversion of maps and shows how several important computational problems such as cryptanalysis of symmetric encryption algorithms, RSA algorithm and solving the elliptic curve discrete log problem (ECDLP) can be addressed as local inversion problems. The methodology is termed as the \emph{Local Inversion Attack}. It utilizes the concept of \emph{Linear Complexity} (LC) of a recurrence sequence generated by the map defined by the cryptanalysis problem and the given data. It is shown that when the LC of the recurrence is bounded by a bound of polynomial o…
