Symmetric Cipher Research Articles

More Constructions of Light MDS Transforms Based on Known MDS Circulant Matrices

Maximum distance separable (MDS) codes have the maximum branch number in cryptography, and they are generally used in diffusion layers of symmetric ciphers. The diffusion layer of the Advanced Encryption Standard (AES) uses the circulant MDS matrix with the row element of {2;3;1;1} in F28. It is the simplest MDS matrix in F2n4, recorded as A=Circ(2;3;1;1). In this paper, we study the more extensive MDS constructions of A in F2n4. By transforming the element multiplication operation in the finite field into the bit-level operation, we propose a multivariable operation definition based on simple operations, such as cyclic shift, shift, and XOR. We apply this multivariable operation to more lightweight MDS constructions of A and discuss the classification of the MDS clusters. We also give an example of the MDS cluster of A. Without changing the structure, elements, and the implementation cost of the known MDS matrix, the number of existing MDS transformations is expanded to n2/2 times that of its original. The constructions in this paper provide rich component materials for the design of lightweight cryptographic algorithms.

MPF based symmetric cipher performance comparison to AES and TDES

This paper presents a performance comparison of newly created matrix power function (MPF) based symmetric cipher realized in cipher-block chaining mode (CBC) with two other standardized ciphers namely AES-128 and triple DES. The encryption rate is compared using 64 bits arithmetic operations. It is shown that the proposed cipher has a significant advantage against compared ciphers. It is achieved by consuming more memory for MPF realization. Mentioned ciphers are compared using the central processing unit (CPU) the number of clock cycles required to encrypt fixed size plaintexts. This paper also includes a comparison of a number of operations required to encrypt plaintext as well as memory requirements for each of the ciphers with pre-determined parameters. The main difference between symmetric cipher based on MPF and other standardized ciphers mentioned in the paper is the ability to work with larger matrix entries in comparison to other algorithms as well as availability to parallelize the process of encrypting a single block.

Survey of Blowfish Algorithm for Cloud

Abstract. Security is the study of encryption and decryption, data hiding, potential attacks, and performance evaluation. Many algorithms perform this purpose. Blowfish is a symmetric block cipher that uses the Feistel network. Although several works employed the Blowfish algorithm for the security of the cloud, there is still no article that lists previous studies. Cloud computing is the transmission of computer services such as servers, storage, databases, networking, software, analytics, and intelligence through the Internet ("the cloud") in order to provide faster innovation, more flexible resources, and cost savings. The most common issue with cloud computing is information security, privacy, confidentiality, and how the cloud provider ensures these services. This paper includes a survey of most previous works that were concerned with using the Blowfish algorithm in achieving cloud security

Factorial number system for nonlinear substitutions generation

Modern cryptographic applications use cryptographic algorithms with a symmetric key. They provide high conversion rates and resistance to crypto-graphic attacks. To complicate the plaintext – cipher-text ratio, symmetric ciphers usually use nonlinear substitutions (S-boxes). S-boxes cryptographic metrics play a crucial role in ensuring resilience to most known attacks (differential, linear, algebraic, and other cryptanalysis methods). However, generating efficient s-boxes is a challenge. Even for small input/output sizes, there are an extremely large number of possible solutions. Usually, the substitution is represented as a set of Boolean functions. This allows you to apply discrete transformations, for example, Walsh-Hadamard, to evaluate cryptographic indicators. However, methods for generating s-boxes by selecting suitable Boolean functions are extremely complex. Therefore, it is necessary to study new mathematical methods for representing nonlinear substitutions, studying their cryptographic properties, and developing generation algorithms. In this paper, we propose applying factorial number systems to represent nonlinear substitutions. Each substitution can be represented in a unique way through a set of inversions, which, in turn, can be transformed into a factorial number. That is, we can naturally arrange all substitutions by numbering them in the factorial number system. We give examples of such numbering and investigate the cryptographic characteristics of S-boxes with their initial numbers. In particular, we show how the variable functions used in heuristic algorithms for generating non-linear substitutions change. The results obtained can be used to simplify heuristic methods in order to speed up the generation of non-linear substitutions.

Study of a new cost function for generating random substitutions of symmetric ciphers

Cryptographic transformations with a secret key play an essential role in providing information and cyber security. Block and stream symmetric ciphers are used in various applications both as a separate cryptographic protection mechanism and as part of other applications (pseudo-random sequence generators, hashing algorithms, electronic signature protocols, etc.). Therefore, the design and study of individual components of symmetric ciphers is a relevant and important scientific task. In this paper we consider and investigates iterative algorithms for generating non-linear substitutions (substitutions, S-boxes), which are used in modern block and stream encryption algorithms with a symmetric key. Cryptographic resistance of symmetric ciphers to statistical, differential, linear and other methods of cryptanalysis is provided by the properties of substitutions. In addition, S-boxes must be random from the point of view of the possibility to use algebraic cryptanalysis. Therefore, the task of quickly generating random S-boxes with the desired cryptographic properties is an urgent, but extremely difficult task. For example, the best known generation algorithm requires more than 65 thousand iterations to find a random bijective 8-bit substitution with a non-linearity of 104. In this paper, we study an iterative algorithm for generating substitutions for hill climbing with different cost functions and propose a new cost function, the use of which can significantly reduce the number of search iterations. In particular, the search for a bijective S-box with nonlinearity 104 requires less than 50 thousand iterations.

Properties of the cost function in the iterative algorithm for generating nonlinear substitution

To ensure the security of information technology, cryptographic information protection tools are used, in particular block and stream encryption algorithms with a symmetric key. Reliability and cryptographic strength of cryptoalgorithms is provided by the properties of the applied primitives. For example, non-linear substitutions (S-boxes) are used as the main component of modern symmetric ciphers. Therefore, generation of substitutions is an important scientific task directly related to the security of information technology and improvement of modern symmetric ciphers. The paper investigates the properties of iterative algorithms for generating non-linear substitutions and special cost functions, which play a decisive role in the heuristic search for S-boxes with the required properties. We consider the cost function of the WCF (Cost Function of the content of the Walsh-Hadamard spectrum) and optimize its parameters. The obtained optimization results in combination with the Hill Climbing iterative search algorithm can reduce significantly the number of iterations. In particular, we show that for a substitution search with a non-linearity of 104, on average, we reduce the computational complexity of generation by more than 20%. In addition, it is possible to increase the success rate of the heuristic search. In particular, for the selected settings, in 100% of cases, a beaktive S-box with a non-linearity of 104 was found.

Quantum cryptanalytic attacks of symmetric ciphers: A review

A review of several latest quantum cryptanalysis techniques of symmetric cryptography is covered. Primarily, the design theory of the quantum cryptanalysis approach is explained and the improvements which can be achieved compared to the classical techniques are presented. The quantum cryptanalysis can achieve speedup from quadratic to exponential factors and most of the symmetric ciphers might be attacked successfully. The information should prove useful for cryptologist to include these new quantum cryptanalysis techniques in their cryptanalysis toolbox and use it to develop post-quantum symmetric ciphers.

A method for synthesis of S-boxes with good avalanche characteristics of component Boolean and quaternary functions

The widespread use of block symmetric ciphers in modern information security systems makes the task of increasing their efficiency urgent, as well as the task of synthesizing high-quality cryptographic primitives used in modern block symmetric ciphers, primarily S-boxes. In particular, the S-boxes must have good avalanche characteristics not only of their component Boolean functions, but also of the component functions of many-valued logic. In this paper, we propose a recursive method for the synthesis of large lengths S-boxes that satisfy the strict avalanche criterion of component 4-functions. As a raw material for the construction of such an S-boxes, small-length S-boxes are used that satisfy the strict avalanche criterion of component 4-functions. In the constructed set of S-boxes that satisfy the strict avalanche criterion of component 4-functions, we found those that simultaneously satisfy the criterion of the maximum avalanche effect of component Boolean functions. The avalanche characteristics of these S-boxes are of high quality both from the point of view of their representation with help of Boolean functions, and from the point of view of their representation using 4-functions. These S-boxes can be recommended for practical use to modernize existing symmetric cryptographic algorithms, as well as to build new perspective ciphers.

Towards a fully homomorphic symmetric cipher scheme resistant to plain-text/cipher-text attacks

Towards a fully homomorphic symmetric cipher scheme resistant to plain-text/cipher-text attacks

Quantum Identity-Based Encryption from the Learning with Errors Problem

To prevent eavesdropping and tampering, network security protocols take advantage of asymmetric ciphers to establish session-specific shared keys with which further communication is encrypted using symmetric ciphers. Commonly used asymmetric algorithms include public key encryption, key exchange, and identity-based encryption (IBE). However, network security protocols based on classic identity-based encryption schemes do not have perfect forward secrecy. To solve this problem, we construct the first quantum IBE (QIBE) scheme based on the learning with errors (LWE) problem, which is also the first cryptographic scheme that applies the LWE problem to quantum encryption. We prove that our scheme is fully secure under the random oracle model and highlight the following advantages: (1) Network security protocols with our QIBE scheme provide perfect forward secrecy. The ciphertext is transmitted in the form of a quantum state unknown to the adversary and cannot be copied and stored. Thus, in network security protocols based on QIBE construction, the adversary does not have any previous quantum ciphertext to decrypt for obtaining the previous session key, even if the private identity key is threatened. (2) Classic key generation centre (KGC) systems can still be used in the QIBE scheme to generate and distribute private identity keys, reducing the cost when implementing this scheme. The classic KGC systems can be used because the master public and secret keys of our scheme are both in the form of classic bits. Finally, we present quantum circuits to implement this QIBE scheme and analyse its required quantum resources for given numbers of qubits, Hadamard gates, phase gates, T gates, and CNOT (controlled-NOT) gates. One of our main findings is that the quantum resources required by our scheme increase linearly with the number of plaintext bits to be encrypted.

Improving the Statistical Qualities of Pseudo Random Number Generators

Pseudo random and true random sequence generators are important components in many scientific and technical fields, playing a fundamental role in the application of the Monte Carlo methods and stochastic simulation. Unfortunately, the quality of the sequences produced by these generators are not always ideal in terms of randomness for many applications. We present a new nonlinear filter design that improves the output sequences of common pseudo random generators in terms of statistical randomness. Taking inspiration from techniques employed in symmetric ciphers, it is based on four seed-dependent substitution boxes, an evolving internal state register, and the combination of different types of operations with the aim of diffusing nonrandom patterns in the input sequence. For statistical analysis we employ a custom initial battery of tests and well-regarded comprehensive packages such as TestU01 and PractRand. Analysis results show that our proposal achieves excellent randomness characteristics and can even transform nonrandom sources (such as a simple counter generator) into perfectly usable pseudo random sequences. Furthermore, performance is excellent while storage consumption is moderate, enabling its implementation in embedded or low power computational platforms.

Converting of Boolean Expression to Linear Equations, Inequalities and QUBO Penalties for Cryptanalysis

There exists a wide range of constraint programming (CP) problems defined on Boolean functions depending on binary variables. One of the approaches to solving CP problems is using specific appropriate solvers, e.g., SAT solvers. An alternative is using the generic solvers for mixed-integer linear programming problems (MILP), but they require transforming expressions with Boolean functions to linear equations or inequalities. Here, we present two methods of such a transformation which applies to any Boolean function defined by explicit rules giving values of the Boolean function for all combinations of its Boolean variables. The first method represents the Boolean function as a linear equation in the original binary variables and, possibly, binary ancillaries, which become additional variables of the MILP problem being composed. The second method represents the Boolean function as a set of linear inequalities in the original binary variables and one additional continuous variable (representing the value of the function). The choice between the first or second method is a trade-off between the number of binary variables and number of linear constraints in the emerging MP problem. The advantage of the proposed approach is that both methods reduce important cryptanalysis problems, such as the preimaging of hash functions or breaking symmetric ciphers as the MILP problems, which are solved by the generic MILP solvers. Furthermore, the first method enables to reduce the binary linear equations to quadratic unconstrained binary optimization (QUBO), by the quantum annealer, e.g., D-Wave.

Timed Automaton-Based Quantitative Feasibility Analysis of Symmetric Cipher in Embedded RTOS: A Case Study of AES

The real-time operating system (RTOS) has a wide range of application domains and provides devices with the ability to schedule resources. Because of the restricted resources of embedded devices and the real-time constraints of RTOS, the application of cryptographic algorithms in these devices will affect the running systems. The existing approaches for RTOS ciphers’ evaluation are mainly provided by experimental data performance analysis, which, however, lack a clear judgment on the affected RTOS performance indicators, such as task schedulability, bandwidth, as well as a quantitative prediction of the remaining resources of RTOS. By focusing on task schedulability in RTOS, this paper provides a timed automaton-based quantitative approach to judge the feasibility of ciphers in embedded RTOS. First, a cryptographic algorithm execution overhead estimation model is established. Then, by combining the overhead model with a sensitivity analysis method, we can analyze the feasibility of the cryptographic algorithm. Finally, a task-oriented and timed automaton-based model is built to verify the analysis results. We take AES as a case study and carry out experiments on embedded devices. The experimental results show the effectiveness of our approach, which will provide specific feasibility indicators for the application of cryptographic algorithms in RTOS.

A Novel Secure Transposition Cipher Technique using Arbitrary Zigzag Patterns

Symmetric cipher cryptography is an efficient technique for encrypting bits and letters to maintain secure communication and data confidentiality. Compared to asymmetric cipher cryptography, symmetric cipher has the speed advantage required for various real-time applications. Yet, with the distribution of micro-devices and the wider utilization of the Internet of Things (IoT) and Wireless Sensor Network (WSN), lightweight algorithms are required to operate on such devices. This paper proposes a symmetric cipher based on a scheme consisting of multiple zigzag patterns, a secret key of variable length, and block data of variable size. The proposed system uses transposition principles to generate various encryption patterns with a particular initial point over a grid. The total number of cells in the grid and its dimension are variable. Various patterns can be created for the same grid, leading to different outcomes on different grids. For a grid of n cells, a total of n! * (n-1!) total patterns can be generated. This information is encapsulated in the private key. Thus, the huge number of possible patterns and the variation of the grid size, which are kept hidden, maintain the security of the proposed technique. Moreover, variable padding can be used; two paddings with different lengths lead to a completely different output even with the same pattern and the same inputs, which improves the security of the proposed system.

K-Order Fibonacci Polynomials on AES-Like Cryptology

The Advanced Encryption Standard (AES) is the most widely used symmetric cipher today. AES has an important place in cryptology. Finite field, also known as Galois Fields, are cornerstones for understanding any cryptography. This encryption method on AES is a method that uses polynomials on Galois fields. In this paper, we generalize the AES-like cryptology on 2 × 2 matrices. We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm. So, this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix.

CBC Mode of MPF Based Shannon Cipher Defined Over a Non-Commuting Platform Group

Commonly modern symmetric encryption schemes (e.g. AES) use rather simple actions repeated many times by defining several rounds to calculate the ciphertext. An idea we previously offered was to trade these multiple repeats for one non-linear operation. Recently we proposed a perfectly secure symmetric encryption scheme based on the matrix power function (MPF). However, the platform group we used was commuting. In this paper, we use a non-commuting group whose cardinality is a power of 2 as a platform for MPF. Due to the convenient cardinality value, our scheme is more suitable for practical implementation. Moreover, due to the non-commuting nature of the platform group, some “natural” constraints on the power matrices arise. We think that this fact complicates the cryptanalysis of our proposal. We demonstrate that the newly defined symmetric cipher possesses are perfectly secure as they were previously done for the commuting platform group. Furthermore, we show that the same secret key can be used multiple times to encrypt several plaintexts without loss of security. Relying on the proven properties we construct the cipher block chaining mode of the initial cipher and show that it can withstand an adaptive chosen plaintext attack.

Analysis of Cryptography Algorithms Implemented in Android Mobile Application

This paper evaluates the performances of numerous encryption algorithms on mobile devices running the Android operating system. The primary objective of our research was to measure and compare the relative performances of tested algorithm implementations (Data Encryption Standard (DES), 3DES, Advanced Encryption Standard (AES), ChaCha20, Blowfish, and Rivest Cipher 4 (RC4)) on the Android platform. The algorithms were compared in terms of CPU utilization by measuring the time required to encrypt and decrypt variable size text files. Besides evaluating the six common symmetric encryption ciphers, a comparison has been conducted for several Password-Based Encryption (PBE) algorithms. Diverse cipher transformations were evaluated for each algorithm by utilizing various feedback modes and padding schemes. Two smartphone devices were used for testing, with different versions of the Android operating system and hardware specifications. The summarized performance outcomes for various cipher transformations are presented to demonstrate the effectiveness of each algorithm.

Nonlinear 4 × 4 MDS diffusion layers

Nonlinear diffusion layers are less studied in cryptographic literature, up to now. In 2018, Liu, Rijmen and Leander studied nonlinear non-MDS diffusion layers and mentioned some advantages of them. As they stated, nonlinear diffusion layers could make symmetric ciphers more resistant against statistical and algebraic cryptanalysis. In this paper, we examine nonlinear MDS mappings and present a family of 4 × 4 nonlinear MDS diffusion layers. Then, we discuss the optimized implementation of the proposed family in software- oriented applications.

Analysis and software implementation of the modified cryptographic Vernam cipher and the Caesar cipher

Problem. Modern cryptography is a very important part of cybersecurity and confidentiality of many operations. It covers almost all parts of our lives, from e-commerce to specialized education of students. Goal. The advantage of symmetric key cryptography is that working with this method is very easy for users, as one key is used for encryption, as well as for decryption purposes, and this key must be secret and should be known only to the sender and recipient and no one else. On the other hand, public key cryptography has two keys. Unfortunately, this exposes the inherent security flaws, as the integrity of the encryption depends entirely on the password. It was decided to consider the implementation of a modified symmetric Vernam cipher that avoids these problems, and its modification and experimental studies should further strengthen data protection. Methodology. Higher mathematics, linear algebra are very important subjects. But if we want to encourage students with cryptography, we need to use all aspects of the IT cluster more effectively. Ideal for this is the implementation of algorithms and programs using programming languages. It is very important and useful for students studying Cybersecurity to illustrate where and how it is possible to create software implementations of encryption / decryption methods. Results. The article presents the analysis and implementation of the modified cryptographic Vernam cipher and Caesar cipher using a concept that combines modern programming languages and the principles of cryptography, which students study in subject-oriented specialties. Originality. An original approach to teaching Cybersecurity students by implementing ciphers using applied programming is described. Practical value. Using cryptography as a learning tool will help students develop their programming skills and effectively understand the concept of cybersecurity in real-world examples.

Quantum Differential Collision Distinguishing Attacks on Feistel Schemes

Feistel schemes are important components of symmetric ciphers, which have been extensively studied in the classical setting. We examine the extension methods of differential distinguishers of Feistel key-function and Feistel function-key schemes. The schemes are subjected to quantum differential collision distinguishing attacks based on the methods. The results show that the complexity is lower than that of differential attacks using only Grover algorithm, and the complexity of differential collision attack based on the Brassard-Høyer-Tapp and Grover algorithms is lower than that of quantization when using only the Grover algorithm. The results also show that different algorithms and methods can be combined to produce a more effective cryptanalysis approach. This provides a research direction for post-quantum cryptographic analysis and design.