Design Of Block Ciphers Research Articles

Cryptanalysis of mCrypton‐64

SummaryIn recent years, because of the security requirements of resource‐constrained devices, design and analysis of lightweight block ciphers has received more attention. mCrypton is a lightweight block cipher that has been specifically designed for using in resource‐constrained devices, such as low‐cost radio‐frequency identification tags and sensors. In this paper, we consider cryptanalysis of full‐round mCrypton‐64 using a new extension of biclique attack called non‐isomorphic biclique cryptanalysis. As it is known, effectiveness of the biclique attack is highly dependent to the weakness of key schedule, and it does not seem to be appropriate for block ciphers with strong key scheduling. The non‐isomorphic biclique attack, using an asymmetric key partitioning technique, provides more degrees of freedom to the attacker and makes it possible to use the diffusion layer properties of a block cipher for constructing longer bicliques. Results show that the attack on full‐round mCrypton requires 233.9 chosen plaintexts and a time complexity of 262.67 encryptions. The computational complexity reduces to 262.3, 261.4, and 259.75 encryptions for 10, 8, and 6 rounds of mCrypton‐64, respectively. We also have a discussion on the general form of the computational complexity for non‐isomorphic biclique cryptanalysis. Copyright © 2014 John Wiley & Sons, Ltd.

Efficient Recursive Diffusion Layers for Block Ciphers and Hash Functions

Many modern block ciphers use maximum distance separable (MDS) matrices as the main part of their diffusion layers. In this paper, we propose a very efficient new class of diffusion layers constructed from several rounds of Feistel-like structures whose round functions are linear. We investigate the requirements of the underlying linear functions to achieve the maximal branch number for the proposed 4×4 words diffusion layer, which is an indication of the highest level of security with respect to linear and differential attacks. We try to extend our results for up to 8×8 words diffusion layers. The proposed diffusion layers only require simple operations such as word-level XORs, rotations, and they have simple inverses. They can replace the diffusion layer of several block ciphers and hash functions in the literature to increase their security, and performance. Furthermore, it can be deployed in the design of new efficient lightweight block ciphers and hash functions in future.

Optimum Dynamic Diffusion of Block Cipher Based on Maximum Distance Separable Matrices

Maximum Distance Separable matrices became the state of the art as a diffusion component in block cipher design for example those MDS matrices used in algorithms such as AES and Twofish. This paper firstly reviews the relation between coding theory and cryptography in the context of providing optimal diffusion. Secondly, The Vandermonde and Cauchy based methodologies introduced by Mahdi Sajadieh et al. and J. Nakahara respectively for generating Involutory MDS matrices that are proposed to provide full block diffusion in order to decrease number of rounds of a block cipher were assessed. Finally Punctured MDS matrices are proposed to provide dynamicity of a block cipher, which guaranteed to provide optimum diffusion that should be considered in security proof against Linear and Differential Cryptanalysis of a block cipher.

A NEW BLOCK CIPHER (NAHRAINFISH)BASED ON SOME AES FINALISTS

In this work, we present some deeper insights in the state-of-the-art in block cipher design. This is mainly achieved by assessment of the evaluation process of the AES (Advanced Encryption Standard). We conclude (with may be a little bit surprising result) that the required security level, for a block cipher to be used for the present and foreseeable future, may be underestimated during AES evaluation. In accordance, we propose a new block cipher that we call Nahrainfish, which we believe that it offers the required security level without a big sacrifice in efficiency and other related criteria. Instead of building Nahrainfish totally from scratch, we have made a benefit mainly from some AES finalists to develop the new cipher by an over-engineering approach leading to the required higher security level. Nahrainfish is a classical Feistel network based on a novel combination of both key-dependent S-boxes and data-dependent rotations. It operates on 128-bit blocks and accepts a variable key length up to 1024 bits. The paper also includes some important notes on the security and performance of the cipher.

Algebraic construction of cryptographically good binary linear transformations

Maximum Distance Separable MDS and Maximum Distance Binary Linear MDBL codes are used as diffusion layers in the design of the well-known block ciphers like the Advanced Encryption Standard, Khazad, Camellia, and ARIA. The reason for the use of these codes in the design of block ciphers is that they provide optimal diffusion effect to meet security of a round function of a block cipher. On the other hand, the constructions of these diffusion layers are various. For example, whereas the Advanced Encryption Standard uses a 4×4 MDS matrix over GF28, ARIA uses a 16×16 involutory binary matrix over GF28. The most important cryptographic property of a diffusion layer is the branch number of that diffusion layer, which represents the diffusion rate and measures security against linear and differential cryptanalysis. Therefore, MDS and Maximum Distance Binary Linear codes, which provide maximum branch number for a diffusion layer, are preferred in the design of block ciphers as diffusion layers. In this paper, we present a new algebraic construction method based on MDS codes for 8×8 and 16×16 involutory and non-involutory binary matrices of branch numbers 5 and 8, respectively. By using this construction method, we also show some examples of these diffusion layers. Copyright © 2012 John Wiley & Sons, Ltd.

Design and statistical analysis of a new chaotic block cipher for Wireless Sensor Networks

Security issue is a vital and active topic in the research of Wireless Sensor Networks (WSN). After surveying the existing encryption algorithms for WSN briefly, we propose a new chaotic block cipher for WSN and then compare the performance of this cipher with those of RC5 and RC6 block ciphers. Simulation result demonstrates that better performance in WSN encryption algorithms can be achieved using the new cipher.

Construction of balanced Boolean functions with high nonlinearity and good autocorrelation properties

Boolean functions with high nonlinearity and good autocorrelation properties play an important role in the design of block ciphers and stream ciphers. In this paper, we give a method to construct balanced Boolean functions of n variables, where n ? 10 is an even integer, satisfying strict avalanche criterion (SAC), and with high algebraic degree. Compared with the known balanced Boolean functions with SAC property, the constructed functions possess the highest nonlinearity and the best global avalanche characteristics property.

On construction of involutory MDS matrices from Vandermonde Matrices in GF(2 q )

Due to their remarkable application in many branches of applied mathematics such as combinatorics, coding theory, and cryptography, Vandermonde matrices have received a great amount of attention. Maximum distance separable (MDS) codes introduce MDS matrices which not only have applications in coding theory but also are of great importance in the design of block ciphers. Lacan and Fimes introduce a method for the construction of an MDS matrix from two Vandermonde matrices in the finite field. In this paper, we first suggest a method that makes an involutory MDS matrix from the Vandermonde matrices. Then we propose another method for the construction of 2 n × 2 n Hadamard MDS matrices in the finite field GF(2 q ). In addition to introducing this method, we present a direct method for the inversion of a special class of 2 n × 2 n Vandermonde matrices.

Security of the Misty Structure Using Involutions as Round Functions

In this paper, we study the security of the Misty structure, where each round function is chosen at random from the set of involutions. Based on the game-playing framework, we prove the pseudorandomness of the 3-round R-Misty structure and the 4-round L-Misty structure as well as the super-pseudorandomness of the 5-round R-Misty structure for m « 2n/2, where m denotes the number of queries and 2n denotes the block size. We also give similar results for the Misty structures such that each round function is chosen at random from the set of involutions with a constant number of fixed points. Our results generalize the results of [10] giving the first construction of a (strong) pseudorandom permutation based on random involutions (without any restriction on the number of fixed points), and suggest a new criterion for design of block ciphers in an involutional Misty structure that each round function should have a constant number of fixed points.

Elastic block ciphers: method, security and instantiations

We introduce the concept of an elastic block cipher which refers to stretching the supported block size of a block cipher to any length up to twice the original block size while incurring a computational workload that is proportional to the block size. Our method uses the round function of an existing block cipher as a black box and inserts it into a substitution- permutation network. Our method is designed to enable us to form a reduction between the elastic and the original versions of the cipher. Using this reduction, we prove that the elastic version of a cipher is secure against key-recovery attacks if the original cipher is secure against such attacks. We note that while reduction-based proofs of security are a cornerstone of cryptographic analysis, they are typical when complete components are used as sub-components in a larger design. We are not aware of the use of such techniques in the case of concrete block cipher designs. We demonstrate the general applicability of the elastic block cipher method by constructing examples from existing block ciphers: AES, Camellia, MISTY1, and RC6. We compare the performance of the elastic versions to that of the original versions and evaluate the elastic versions using statistical tests measuring the randomness of the ciphertext. We also use our examples to demonstrate the concept of a generic key schedule for block ciphers.

Seven New Block Cipher Structures with Provable Security against Differential Cryptanalysis

The design and analysis of block ciphers is an established field of study which has seen significant progress since the early 1990s. Nevertheless, what remains on an interesting direction to explore in this area is to design block ciphers with provable security against powerful known attacks such as differential and linear cryptanalysis. In this paper we introduce seven new block cipher structures, named Feistel-variant A, B, CLEFIA and MISTY-FO-variant A, B, C, D structures, and show that these structures are provably resistant against differential cryptanalysis. The main results of this paper are that the average differential probabilities over at least 2 rounds of Feistel-variant A structure and 1 round of Feistel-variant B structure are both upperbounded by p2, while the average differential probabilities over at least 5 rounds of CLEFIA, MISTY-FO-variant A, B, C and D structures are upperbounded by p4 + 2p5, p4, p4, 2p4 and 2p4, respectively, if the maximum differential probability of a round F function is p. We also give provable security for the Feistel-variant A, B and CLEFIA structures against linear cryptanalysis. Our results are attained under the assumption that all of components in our proposed structures are bijective. We expect that our results are useful to design block ciphers with provable security against differential and linear cryptanalysis.

Design of block ciphers by simple chaotic functions

The relationships of chaotic functions and cryptography are investigated in this paper. 128-bit symmetric keys are derived from some chaotic function, called simple logistic function (SLF), for suitable parameters. An improved algorithm of discretization of SLF is introduced and applied to the design of block encryption ciphers and key schedules with proper parameters and initial values. These are chosen by the Lyapunov exponent method for testing chaos. Dynamic S- Boxes of such block ciphers are generated. Security analysis is also given to these S-Boxes.

Automated design of a lightweight block cipher with Genetic Programming

In this paper, we present a general framework for the automated design of cryptographic block ciphers by using Genetic Programming. We evolve highly nonlinear and extremely efficient functions that can be used as core components of any cryptographic construction. As an example, a new block cipher named Raiden is proposed. We present a preliminary security analysis of our proposal and a comparison in terms of performance with similar block ciphers such as TEA. The results show that automatically-obtained schemes, such as the one presented here, could be competitive both in security and speed.

FPGA Implementation(s) of a Scalable Encryption Algorithm

SEA is a scalable encryption algorithm targeted for small embedded applications. It was initially designed for software implementations in controllers, smart cards, or processors. In this letter, we investigate its performances in field-programmable gate array (FPGA) devices. For this purpose, a loop architecture of the block cipher is presented. Beyond its low cost performances, a significant advantage of the proposed architecture is its full flexibility for any parameter of the scalable encryption algorithm, taking advantage of generic VHDL coding. The letter also carefully describes the implementation details allowing us to keep small area requirements. Finally, a comparative performance discussion of SEA with the advanced encryption standard Rijndael and (a cipher purposed for efficient FPGA implementations) is proposed. It illustrates the interest of platform/context-oriented block cipher design and, as far as SEA is concerned, its low area requirements and reasonable efficiency.

Automated design of a lightweight block cipher with Genetic Programming

In this paper, we present a general framework for the automated design of cryptographic block ciphers by using Genetic Programming. We evolve highly nonlinear and extremely efficient functions that...

Fast S-box security mechanism research based on the polymorphic cipher

In this study we propose a new design method for fast S-box construction. Its security is dependent upon the length of pseudorandom numbers generated by two communication parties. As the S-box is being built, we demonstrate that Boolean functions play an important role in the design of both block and stream ciphers. To satisfy a variety of cryptographic test methods, such as strict avalanche criterion (SAC), bit independence criterion (BIC), and nonlinearity, we apply polymorphic cipher (PMC) theory to the permutation function construction. Correlations among the test criteria in a real network environment are also evaluated.

Block Cipher Design after AES and the New Cipher Nahrainfish

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Discrete Lyapunov Exponent and Differential Cryptanalysis

Partly motivated by the developments in chaos-based block cipher design, a definition of the discrete Lyapunov exponent for an arbitrary permutation of a finite lattice was recently proposed. We explore the relation between the discrete Lyapunov exponent and the maximum differential probability of a bijective mapping (i.e., an S-box or the mapping defined by a block cipher). Our analysis shows that good encryption transformations have discrete Lyapunov exponents close to the discrete Lyapunov exponent of a mapping that has a perfect nonlinearity. The converse does not hold.

Linear provable security for a class of unbalanced feistel network

A structure iterated by the unbalanced Feistel networks is introduced. It is showed that this structure is provable resistant against linear attack. The main result of this paper is that the upper bound of r-round (r⩾2m) linear hull probabilities are bounded by q 2 when around function F is bjective and the maximal linear hull probabilities of round function F is q. Application of this structure to block cipher designs brings out the provable security against linear attack with the upper bounds of probabilities.

Construction of Perfect Nonlinear and Maximally Nonlinear Multiple-Output Boolean Functions Satisfying Higher Order Strict Avalanche Criteria

We consider the problem of constructing perfect nonlinear multiple-output Boolean functions satisfying higher order strict avalanche criteria (SAC). Our first construction is an infinite family of 2-output perfect nonlinear functions satisfying higher order SAC. This construction is achieved using the theory of bilinear forms and symplectic matrices. Next we build on a known connection between 1-factorization of a complete graph and SAC to construct more examples of 2- and 3-output perfect nonlinear functions. In certain cases, the constructed S-boxes have optimal tradeoff between the following parameters: numbers of input and output variables, nonlinearity, and order of SAC. In case the number of input variables is odd, we modify the construction for perfect nonlinear S-boxes to obtain a construction for maximally nonlinear S-boxes satisfying higher order SAC. Our constructions present the first examples of perfect nonlinear and maximally nonlinear multiple-output S-boxes satisfying higher order SAC. Finally, we present a simple method for improving the degree of the constructed functions with a small tradeoff in nonlinearity and the SAC property. This yields functions which have possible applications in the design of block ciphers.