On Constructions of MDS Matrices from Companion Matrices for Lightweight Cryptography

Gupta, Kishan Chand; Ray, Indranil Ghosh

doi:10.1007/978-3-642-40588-4_3

Cited by 44 publications

(37 citation statements)

References 14 publications

(24 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…If the two branch numbers are larger, the diffusion layer is stronger at resisting differential cryptanalysis and linear cryptanalysis. The diffusion layers with the optimal branch numbers are referred to as maximum distance separable (MDS) (refer to [1][2][3]). Constructing diffusion layers with large branch numbers is a challenge for cryptosystem designers.…”

Section: Dear Editormentioning

confidence: 99%

Construction of MDS block diffusion matrices for block ciphers and hash functions

Zhao

Zhang

et al. 2016

Sci. China Inf. Sci.

View full text Add to dashboard Cite

Dear editor,Block ciphers are one of the most important building blocks in many cryptosystems. Modern block ciphers are often iterations with several rounds, where each round comprises a (nonlinear) confusion layer and a (linear) diffusion layer. The diffusion layer plays a significant role in block ciphers as well as in other cryptographic primitives such as hash functions. The security of a diffusion layer is measured by its differential branch number and the linear branch number. If the two branch numbers are larger, the diffusion layer is stronger at resisting differential cryptanalysis and linear cryptanalysis. The diffusion layers with the optimal branch numbers are referred to as maximum distance separable (MDS) (refer to [1-3]). Constructing diffusion layers with large branch numbers is a challenge for cryptosystem designers.There are two types of diffusion layer according to the underlying fields, where the first is over extension fields of the finite field GF (2), and the second type comprises block matrices over GF (2). In fact, the former is a special case of the latter. In [4] and [5], the second type of diffusion layer was considered, i.e., block matrices where every block is a polynomial in a certain block L. Unfortunately, these previous studies only presented approaches for determining the forms of external matrices and failed to specify how to determine the internal block L.In this letter, we also focus on the construction of block MDS diffusion layers where the blocks are all polynomials in a given block A. In contrast to previous studies, our approach starts from the internal block A. We propose a new method based on the minimal polynomials of matrices (refer to [6]) to test whether a diffusion layer is MDS. More significantly, we then present a new type of operation on matrices, which leads to an equivalence relation that can exponentially reduce the computational effort required when we search for MDS matrices. Thus, we describe a definite algorithm for finding block MDS diffusion layers. Using this algorithm, we find a large number of MDS diffusion layers with certain parameters. We give the detailed proofs and experimental results in the supplementary file associated with this letter. Methodology.

show abstract

Section: Dear Editormentioning

confidence: 99%

Construction of MDS block diffusion matrices for block ciphers and hash functions

Zhao

Zhang

et al. 2016

Sci. China Inf. Sci.

View full text Add to dashboard Cite

show abstract

“…In the linear context, this means that there should be no correlations between linear combinations of a small set of inputs and linear combinations of a small set of outputs. In the diff erential context, small input changes should cause large output changes, and conversely [6]. Maximum Distance Separable matrix (MDS) is a very popular tool to achieve diffusion.…”

Section: Diffusive Componentsmentioning

confidence: 99%

“…As the replacement of permutation layer in SPN with a diff usive linear transformation improves the avalanche characteristics of the block cipher which increases the cipher's resistance to diff erential and linear cryptanalysis [13][14]. Thus the main application of MDS matrix in cryptography is in designing block ciphers that provide security against diff erential and linear cryptanalysis [6].…”

Section: Linear and Differential Cryptanalysismentioning

confidence: 99%

Provably Secure Encryption Algorithm based on Feistel Structure

Rayan¹,

Abdelhafez²,

Hafez³

2016

IJCA

View full text Add to dashboard Cite

In 1997 The National Institute of Standards and Technology (NIST) started a process to select a symmetric-key encryption algorithm instead of DES. NIST determined the evaluation criteria that would be used to compare the candidate algorithms depending on the analyses and comments received, NIST selected five finalist algorithms (RC6, MARS, Rijndael, Serpent and Twofish). At the end, NIST selected Rijndael as the proposed Advanced Encryption Standard algorithm (AES). Although Twofish algorithm based on Feistel structure and possesses a large security margin, it has some drawbacks as The Twofish structure is not easy to analyses, the mixing of various operations makes it hard to give a clean analysis and forces us to use approximation techniques. Moreover, The use of key-dependent S-Boxes adds complexity and greatly increase the effort required to write automated tools to search for characteristics (differentials, linear, …) of the structure. In this paper a proposal of a new Secure Symmetric-key Encryption (SSE) algorithm based on Feistel structure is produced to overcome the previous drawbacks and produce a provable secure algorithm.

show abstract

“…In order to compensate for the weak function, the linear operation is applied to the whole block at a time as a mixing operation. The mixing operation should be such that one bit change in the input x will change m components in the output y, given by maximum distance separable (MDS) matrix [20]. Structurally any block cipher can be broadly categorized either as Feistel structure [21] or Substitution Permutation Network (SPN) [22].…”

Section: Brief Introduction Of Lightweight Block Ciphersmentioning

confidence: 99%

An Evaluation of Lightweight Block Ciphers for Resource-Constrained Applications: Area, Performance, and Security

et al. 2017

View full text Add to dashboard Cite

In March 2017, NIST (National Institute of Standards and Technology) has announced to create a portfolio of lightweight algorithms through an open process. The report emphasizes that with emerging applications like automotive systems, sensor networks, healthcare, distributed control systems, the Internet of Things (IoT), cyber-physical systems, and the smart grid, a detailed evaluation of the so called light-weight ciphers helps to recommend algorithms in the context of profiles, which describe physical, performance, and security characteristics. In recent years, a number of lightweight block ciphers have been proposed for encryption/decryption of data which makes such choices complex. Each such cipher offers a unique combination of resistance to classical cryptanalysis and resource-efficient implementations. At the same time, these implementations must be protected against implementation-based attacks such as side-channel analysis. In this paper, we present a holistic comparison study of four lightweight block ciphers, PRESENT, SIMON, SPECK, and KHUDRA, along with the more traditional Advanced Encryption Standard (AES). We present a uniform comparison of the performance and efficiency of these block ciphers in terms of area and power consumption, on ASIC and FPGA-based platforms. Additionally, we also compare the amenability to side-channel secure implementations for these ciphers on ASIC-based platforms. Our study is expected to help designers make suitable choices when securing a given application, across a wide range of implementation platforms.

show abstract

On Constructions of MDS Matrices from Companion Matrices for Lightweight Cryptography

Cited by 44 publications

References 14 publications

Construction of MDS block diffusion matrices for block ciphers and hash functions

Construction of MDS block diffusion matrices for block ciphers and hash functions

Provably Secure Encryption Algorithm based on Feistel Structure

An Evaluation of Lightweight Block Ciphers for Resource-Constrained Applications: Area, Performance, and Security

Contact Info

Product

Resources

About