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MDS matrix
About: MDS matrix is a research topic. Over the lifetime, 102 publications have been published within this topic receiving 2000 citations.
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TL;DR: An opposite approach to studying elements for which x → ax could be implemented with only one XOR in hardware, which gives provable binary n × n one-XOR matrices for which the mentioned conditions hold.
Abstract: MDS diffusion layers are critical in the design of modern symmetric ciphers. Lightweight MDS matrices are studied for designing ciphers targeting hardware-oriented applications. In 2016, Be...
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TL;DR: In this article, the authors present low complexity attacks on WIDEA based on truncated differentials, where the Diffie-Hellman diffusion matrix is not active and the MDS diffusion layer is never active.
Abstract: WIDEA is a family of block ciphers designed by Junod and Macchetti in 2009 as an extension of IDEA to larger block sizes (256 and 512 bits for the main instances WIDEA-4 and WIDEA-8) and key sizes (512 and 1024 bits), with a focus on using them to design a hash function. WIDEA is based on the trusted IDEA design, and was expected to inherit its good security properties. WIDEA-w is composed of w parallel copies of the IDEA block cipher, with an MDS matrix to provide diffusion between them. In this paper we present low complexity attacks on WIDEA based on truncated differentials. We show a distinguisher for the full WIDEA with complexity only 2, and we use the distinguisher in a key-recovery attack with complexity w ·2. We also show a collision attack on WIDEA-8 if it is used to build a hash function using the Merkle-Damgard mode of operation. The attacks exploit the parallel structure of WIDEA and the limited diffusion between the IDEA instances, using differential trails where the MDS diffusion layer is never active. In addition, we use structures of plaintext to reduce the data complexity.
01 Jan 2021
TL;DR: A new method to construct the lightweight MDS matrices is given and it is proved that the 2s × 2s involution Hankel MDS matrix does not exist in finite field.
Abstract: Maximal distance separable (MDS) matrices are used as optimal diffusion layers in many block ciphers and hash functions Recently, the designers paid more attention to the lightweight MDS matrices because it can reduce the hardware resource In this paper, we give a new method to construct the lightweight MDS matrices We provide some theoretical results and two kinds of 4 × 4 lightweight Hankel MDS matrices We also prove that the 2s × 2s involution Hankel MDS matrix does not exist in finite field Furthermore, we searched the 4 × 4 Hankel MDS matrices over GL(4, F2) and GL(8, F2) that have the better s-XOR counts until now
01 Jan 2013
TL;DR: A new symmetric cryptosystem having a key dependent operation, enhanced by a rotor with controlled user identification ID and user key with optimal MDS matrix is given.
Abstract: Nowadays, cryptography plays a major role in protecting the information of technology applications. This paper gives a new symmetric cryptosystem having a key dependent operation, enhanced by a rotor with controlled user identification ID and user key. The plaintext block is divided into basic Gaussian subblocks each of thirty-two bits in length. The new Proposal uses optimal MDS matrix. The new Proposal can encrypt blocks of plaintext of length 512 bits into blocks of the same length. Also the key length is 512 bits. The total number of rounds is sixteen rounds. It uses