Showing papers on "MDS matrix published in 2012"
19 Mar 2012
TL;DR: This paper proposes a new class of diffusion layers constructed from several rounds of Feistel-like structures whose round functions are linear, and investigates the requirements of the underlying linear functions to achieve the maximal branch number for the proposed 4×4 words diffusion layer.
Abstract: Many modern block ciphers use maximum distance separable (MDS) matrices as the main part of their diffusion layers In this paper, we propose a new class of diffusion layers constructed from several rounds of Feistel-like structures whose round functions are linear We investigate the requirements of the underlying linear functions to achieve the maximal branch number for the proposed 4×4 words diffusion layer The proposed diffusion layers only require word-level XORs, rotations, and they have simple inverses They can be replaced in the diffusion layer of the block ciphers MMB and Hierocrypt to increase their security and performance, respectively Finally, we try to extend our results for up to 8×8 words diffusion layers
••15 Aug 2012
TL;DR: This paper revisits the design strategy of PHOTON lightweight hash family and the work of FSE 2012, in which perfect diffusion layers are constructed by one bundle-based LFSR, and investigates new strategies to constructperfect diffusion layers using more than one Bundle-Based LFSRs.
Abstract: Diffusion layers with maximum branch numbers are widely used in block ciphers and hash functions. In this paper, we construct recursive diffusion layers using Linear Feedback Shift Registers (LFSRs). Unlike the MDS matrix used in AES, whose elements are limited in a finite field, a diffusion layer in this paper is a square matrix composed of linear transformations over a vector space. Perfect diffusion layers with branch numbers from 5 to 9 are constructed. On the one hand, we revisit the design strategy of PHOTON lightweight hash family and the work of FSE 2012, in which perfect diffusion layers are constructed by one bundle-based LFSR. We get better results and they can be used to replace those of PHOTON to gain smaller hardware implementations. On the other hand, we investigate new strategies to construct perfect diffusion layers using more than one bundle-based LFSRs. Finally, we construct perfect diffusion layers by increasing the number of iterations and using bit-level LFSRs. Since most of our proposals have lightweight examples corresponding to 4-bit and 8-bit Sboxes, we expect that they will be useful in designing (lightweight) block ciphers and (lightweight) hash functions.
TL;DR: 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).
Abstract: 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.
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.