The Lightest 4 x 4 MDS Matrices over GL ( 4 , F 2 )
نویسندگان
چکیده
Maximal distance separable (MDS) matrices are important components for block ciphers. In this paper, we present an algorithm for searching 4 × 4 MDS matrices over GL(4, F2). By this algorithm, we find all the lightest MDS matrices have only 10 XOR counts. Besides, all these lightest MDS matrices are classified to 3 types, and some necessary and sufficient conditions are presented for them as well. Some theoretical results can be generalized to the case GL(m,F2) easily, and 4× 4 MDS matrices with 10 XOR counts can be constructed directly.
منابع مشابه
The Lightest 4 × 4 MDS Matrices over GL ( 4 , F 2 )
Maximal Distance Separable (MDS) matrices are important components for block ciphers. In this paper, we present an algorithm for searching 4×4 MDS matrices over GL(4,F2). By this algorithm, we find that all the lightest MDS matrices have only 10 XOR counts. Besides, all these lightest MDS matrices can be classified to 3 types, and some necessary and sufficient conditions are presented for them ...
متن کاملConstruction and Filtration of Lightweight Formalized MDS Matrices
Zhang Shi-Yi, Wang Yong-juan, Gao Yang, Wang Tao Corresponding author: Wang Yong-juan, E-mail: [email protected] Abstract: The 4 4 MDS matrix over 2 F is widely used in the design of block cipher's linear diffusion layers. However, considering the cost of a lightweight cipher's implementation, the sum of XOR operations of a MDS matrix usually plays the role of measure. During the research on t...
متن کاملLightweight 4x4 MDS Matrices for Hardware-Oriented Cryptographic Primitives
Linear diffusion layer is an important part of lightweight block ciphers and hash functions. This paper presents an efficient class of lightweight 4x4 MDS matrices such that the implementation cost of them and their corresponding inverses are equal. The main target of the paper is hardware oriented cryptographic primitives and the implementation cost is measured in terms of the required number ...
متن کاملConstruction of Lightweight MDS Matrices over Matrix Polynomial Residue Ring
In this article, we investigate the construction of lightweight MDS matrices over the matrix polynomial residue ring. According to distributions of the minimum polynomial, distributions of XOR count and equivalence classes of MDS matrices, we propose an algorithm, which not only can construct lightest MDS matrices, but also is evidently more efficient than previous methods. Moreover, we investi...
متن کاملOn Constructions of MDS Matrices from Companion Matrices for Lightweight Cryptography
Maximum distance separable (MDS) matrices have applications not only in coding theory but also are of great importance in the design of block ciphers and hash functions. It is highly nontrivial to find MDS matrices which could be used in lightweight cryptography. In a crypto 2011 paper, Guo et. al. proposed a new MDS matrix Serial(1, 2, 1, 4) over F28 . This representation has a compact hardwar...
متن کامل