MDS Matrices Over Rings For Designing Lightweight Block Cİpher

Download

Thesis___G_k_e_Yeti_er.pdf

Date

2021-9-30

Author

Yetişer, Gökçe

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

554
views

512
downloads

The primary intention of this thesis is to generate lightened Maximum Distance Separable (MDS) matrices so as not to have a high implementation cost while providing solid diffusion to a cipher. In this direction, lightweight cryptography along with the current capabilities of devices and some design principles and permutation layer is given briefly. Next, the diffusion property of block cipher design is studied, where the permutation layer is generally an invertible linear transformation, and they are generally represented as matrices. In this thesis, we mainly focus on the design of MDS matrices over rings for efficient block ciphers; in particular, the matrices resulting in better implementation costs are considered. To generate MDS matrices with lower XOR gate number and depth, we advance the technique given by Li et. al. and expand the search space and reach better implementation results. For the implementation cost, we count the number of XOR gates and the depth by benefiting a modified version of Boyar’s SLP heuristic algorithm, with depth awareness, given in the same article. In particular, we tabulate some matrices with good implementation costs. The best involutory MDS matrix, with branch number 5, found in this study has only 64 XOR gates with depth 3, which is a new record. The matrices found could be used in any cipher to provide diffusion, as long as the input size of the one-time multiplication operation is set to be 32 bits. In addition, it also provides a strong permutation with optimal cost.

Subject Keywords

MDS matrices, Block ciphers, Lightweight cryptography

URI

https://hdl.handle.net/11511/93027

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

Electromagnetic target recognition with the fused MUSIC spectrum matrix method: Applications and performance analysis for incomplete frequency data Secmen, Mustafa; Ekmekci, Evren; Sayan, Gönül (2007-01-01) The aim of this paper is to apply an electromagnetic target recognition method, which is based on the use of fused MUSIC spectrum matrices, to the case of incomplete frequency domain data. The aforementioned method was suggested recently and succesfully applied to both canonical and complicated targets in the presence of complete frequency domain data [1]. However, most of the real world applications involve the use of severely incomplete frequency data, especially missing low frequency information. In this...
Fine resolution frequency estimation from three DFT samples: Case of windowed data Candan, Çağatay (2015-09-01) An efficient and low complexity frequency estimation method based on the discrete Fourier transform (DFT) samples is described. The suggested method can operate with an arbitrary window function in the absence or presence of zero-padding. The frequency estimation performance of the suggested method is shown to follow the Cramer-Rao bound closely without any error floor due to estimator bias, even at exceptionally high signal-to-noise-ratio (SNR) values.
Covariance Matrix Estimation of Texture Correlated Compound-Gaussian Vectors for Adaptive Radar Detection Candan, Çağatay; Pascal, Frederic (2022-01-01) Covariance matrix estimation of compound-Gaussian vectors with texture-correlation (spatial correlation for the adaptive radar detectors) is examined. The texture parameters are treated as hidden random parameters whose statistical description is given by a Markov chain. States of the chain represent the value of texture coefficient and the transition probabilities establish the correlation in the texture sequence. An Expectation-Maximization (EM) method based covariance matrix estimation solution is given ...
Relating undisturbed bits to other properties of substitution boxes Makarim, Rusydi H.; Tezcan, Cihangir (2015-01-01) Recently it was observed that for a particular nonzero input difference to an S-Box, some bits in all the corresponding output differences may remain invariant. These specific invariant bits are called undisturbed bits. Undisturbed bits can also be seen as truncated differentials with probability 1 for an S-Box. The existence of undisturbed bits was found in the S-Box of Present and its inverse. A 13-round improbable differential attack on Present was provided by Tezcan and without using the undisturbed bit...
Basic cryptanalysis methods on block ciphers Çelik, Dilek; Doğanaksoy, Ali; Department of Cryptography (2010) Differential cryptanalysis and linear cryptanalysis are the first significant methods used to attack on block ciphers. These concepts compose the keystones for most of the attacks in recent years. Also, while designing a cipher, these attacks should be taken into consideration and the cipher should be created as secure against them. Although di fferential cryptanalysis and linear cryptanalysis are still important, they started to be ine cient due to the improvements in the technology. So, these attacks are ...

Citation Formats

G. Yetişer, “MDS Matrices Over Rings For Designing Lightweight Block Cİpher,” M.S. - Master of Science, Middle East Technical University, 2021.