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Journal ArticleDOI

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

This paper suggests a method that makes an involutory MDS matrix from the Vandermonde matrices and proposes another method for the construction of 2n × 2n Hadamard MDS matrices in the finite field GF(2q).
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.

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Book ChapterDOI

Lightweight MDS Involution Matrices

TL;DR: In this article, the authors provide new methods to look for lightweight MDS matrices, and in particular involutory ones, by proving many new properties and equivalence classes for various MDS matrix constructions such as circulant, Hadamard, Cauchy, and Hadhamard-Cauchy.
Book ChapterDOI

On constructions of MDS matrices from companion matrices for lightweight cryptography

TL;DR: In this article, the authors studied the properties of MDS matrices and provided an insight of why Serial(z 0,…,z d − 1) d leads to an MDS matrix.
Book ChapterDOI

Out of Oddity – New Cryptanalytic Techniques Against Symmetric Primitives Optimized for Integrity Proof Systems

TL;DR: This work compares the security levels offered by two recent families of such primitives, namely GMiMC and HadesMiMC, and exhibits low-complexity distinguishers against the GMi MC and Hades MiMC permutations for most parameters proposed in recently launched public challenges for STARK-friendly hash functions.
Book ChapterDOI

On Constructions of Involutory MDS Matrices

TL;DR: An algorithm to construct involutory MDS matrices with low Hamming weight elements to minimize primitive operations such as exclusive-or, table look-ups and xtime operations is provided.
Book ChapterDOI

On Constructions of Circulant MDS Matrices for Lightweight Cryptography

TL;DR: This paper studies and constructs efficient d ×d circulant MDS matrices for d up to 8 and considers their inverses, which are essential for SPN networks and proves that circulants MDS matrix can not be involutory.
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The Theory of Error-Correcting Codes

TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.

Error control coding : fundamentals and applications

TL;DR: This book explains coding for Reliable Digital Transmission and Storage using Trellis-Based Soft-Decision Decoding Algorithms for Linear Block Codes and Convolutional Codes, and some of the techniques used in this work.

The Design of Rijndael: AES - The Advanced Encryption Standard

TL;DR: The underlying mathematics and the wide trail strategy as the basic design idea are explained in detail and the basics of differential and linear cryptanalysis are reworked.
Book ChapterDOI

Linear cryptanalysis method for DES cipher

TL;DR: A new method is introduced for cryptanalysis of DES cipher, which is essentially a known-plaintext attack, that is applicable to an only-ciphertext attack in certain situations.

The Design of Rijndael

TL;DR: This volume is the authoritative guide to the Rijndael algorithm and AES and professionals, researchers, and students active or interested in data encryption will find it a valuable source of information and reference.
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