MDS matrix

About: MDS matrix is a research topic. Over the lifetime, 102 publications have been published within this topic receiving 2000 citations.

Dynamic MDS diffusion layers with efficient software implementation

Abstract: Maximum distance separable (MDS) matrices play a crucial role in symmetric ciphers as diffusion layers. Dynamic diffusion layers for software applications are less considered up to now. Dynamic (randomised) components could make symmetric ciphers more resistant against statistical and algebraic attacks. In this paper, after some theoretical investigation we present a family of parametric n × n, binary matrices Aα, n = 4t, such that for 4t many α ∈ Fn2 the matrices Aα, A3α ⊕ I and A7α ⊕ I are non-singular. With the aid of the proposed family of matrices, some well-known diffusion layers including the cyclic AES-like matrices and some recursive MDS diffusion layers could be made dynamic, at little extra cost in software. Then, we provide new families of MDS matrices which could be used as dynamic diffusion layers, using the proposed family of matrices. The implementation cost of every member in the presented families of MDS diffusion layers (except one cyclic family) is equal to its inverse. The proposed diffusion layers have a suitable implementation cost on a variety of modern processors.

Construction of MDS-matrix for linear transformation of symmetric block ciphers

Abstract: The analysis of existing requirements for MDS matrices that are used in block ciphers is performed, the most important requirements are selected, and matrix corresponding to the selected requirements is constructed.

Encryption device encryption method and record medium

Abstract: The invention realizes a high-security cryptographic processing apparatus that increases difficulty in analyzing its key and a method therefor. In Feistel-type common-key-block cryptographic processing that repeatedly executes an SPN-type F-function having the nonlinear conversion section and the linear conversion section over a plurality of rounds, Linear conversion processing of an F-function corresponding to each of the plurality of rounds is carried out by linear conversion processing that applies square MDS (Maximum Distance Separable) matrices. The invention uses a setting that arbitrary m column vectors included in inverse matrices of square MDS matrices being set up at least in consecutive even-numbered rounds and in consecutive odd-numbered rounds, respectively, constitute a square MDS matrix. This structure realizes cryptographic processing whereby resistance to linear cryptanalysis attacks in the common-key-block cipher is improved.

Construction of MDS matrices from minors of an MDS matrix

Abstract: Diffusion layers are an important part of most symmetric ciphers and MDS matrices can be used to construct perfect diffusion layers. However, there are few techniques for constructing these matrices with low implementation cost in software/hardware. Conventional MDS matrices are constructed on finite fields and MDS matrices over commutative rings acting on modules have been characterized by Dong Dong et. al. in 1998. In this paper, we consider MDS matrices over commutative rings acting on corresponding modules and using the minors of such matrices, we construct new MDS diffusion layers.

WARX: efficient white-box block cipher based on ARX primitives and random MDS matrix

Abstract: White-box cryptography aims to provide secure cryptographic primitives and implementations for the white-box attack model, which assumes that an adversary has full access to the implementation of the cryptographic algorithms. Real-world applications require highly efficient and secure white-box schemes, whereas the existing proposals cannot meet this demand. In this paper, we design a new white-box block cipher based on addition/rotation/XOR (ARX) primitives and random maximal distance separable (MDS) matrix, white-box ARX (WARX), aiming for efficient implementations in both black- and white-box models. The implementation of WARX in the black-box model is nine times faster than SPNbox-16 from ASI-ACRYPT’16, and the implementation in the white-box model is more efficient than SPNbox-16 and WEM from CT-RSA’17. Moreover, the security of WARX in both black- and white-box models is analyzed, which ensures its practical applicability. The design of WARX shows that ARX primitives and random linear layer can improve the efficiency of a white-box block cipher. This article may inspire more provably secure and efficient white-box block ciphers and help to narrow the gap between provably secure white-box schemes from academia and highly applicable schemes in great demand from industry.