Randomized nonlinear software-oriented MDS diffusion layers

2019 ◽  
Vol 11 (2) ◽  
pp. 123-131
Author(s):  
Mohammad Reza Mirzaee Shamsabad ◽  
Seyed Mojtaba Dehnavi ◽  
Akbar Mahmoodi Rishakani
Keyword(s):  
Algebraic Structures ◽  
Linear Diffusion ◽  
Diffusion Layers ◽  
Symmetric Ciphers ◽  
Critical Components ◽  
Theoretical Results

Abstract MDS diffusion layers are critical components in the design of symmetric ciphers. In this paper, after introducing some new algebraic structures, we provide new MDS matrices over special types of R-modules. With the help of the proposed methodology, we have more flexibility in designing software-oriented diffusion layers. Most notably, we construct randomized and/or nonlinear MDS diffusion layers, based upon the presented theoretical results, and discuss the resistance of the presented diffusion layers against various kinds of cryptanalysis, compared with classical linear diffusion layers.

scholarly journals Design of Lightweight Linear Diffusion Layers from Near-MDS Matrices

2017 ◽  
pp. 129-155 ◽  
Author(s):  
Chaoyun Li ◽  
Qingju Wang
Keyword(s):  
Finite Fields ◽  
Lower Bounds ◽  
Hadamard Matrices ◽  
Circulant Matrices ◽  
Linear Cryptanalysis ◽  
Implementation Cost ◽  
Linear Diffusion ◽  
Diffusion Layers ◽  
Nonlinear Layer ◽  
Trade Offs

Near-MDS matrices provide better trade-offs between security and efficiency compared to constructions based on MDS matrices, which are favored for hardwareoriented designs. We present new designs of lightweight linear diffusion layers by constructing lightweight near-MDS matrices. Firstly generic n×n near-MDS circulant matrices are found for 5 ≤ n ≤9. Secondly, the implementation cost of instantiations of the generic near-MDS matrices is examined. Surprisingly, for n = 7, 8, it turns out that some proposed near-MDS circulant matrices of order n have the lowest XOR count among all near-MDS matrices of the same order. Further, for n = 5, 6, we present near-MDS matrices of order n having the lowest XOR count as well. The proposed matrices, together with previous construction of order less than five, lead to solutions of n×n near-MDS matrices with the lowest XOR count over finite fields F2m for 2 ≤ n ≤ 8 and 4 ≤ m ≤ 2048. Moreover, we present some involutory near-MDS matrices of order 8 constructed from Hadamard matrices. Lastly, the security of the proposed linear layers is studied by calculating lower bounds on the number of active S-boxes. It is shown that our linear layers with a well-chosen nonlinear layer can provide sufficient security against differential and linear cryptanalysis.

scholarly journals Coexistence for a kind of stochastic three-species competitive models

2019 ◽  
Vol 17 (1) ◽  
pp. 1203-1219
Author(s):  
Nantian Huang ◽  
Jiabing Huang ◽  
Yuming Wei ◽  
Yongjian Liu
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Convergence In Distribution ◽  
Threshold Values ◽  
Linear Diffusion ◽  
Ecological Balance ◽  
Non Linear ◽  
Competitive Model ◽  
Theoretical Results

Abstract The coexistence of species sustains the ecological balance in nature. This paper focuses on sufficient conditions for the coexistence of a three-species stochastic competitive model, where the model has non-linear diffusion parts. Three values λ3z, λ3x and λ3y are introduced and calculated from the coefficients, which can be considered as threshold values. Moreover, convergence in distribution of the positive solution of the model is also addressed. A few numerical simulations are carried out to illustrate the theoretical results.

scholarly journals Beyond-Birthday-Bound Security for 4-round Linear Substitution-Permutation Networks

2020 ◽  
pp. 305-326
Author(s):  
Yuan Gao ◽  
Chun Guo ◽  
Meiqin Wang ◽  
Weijia Wang ◽  
Jiejing Wen
Keyword(s):  
Real World ◽  
Provable Security ◽  
Linear Diffusion ◽  
Popular Approach ◽  
Diffusion Layers ◽  
Linear Substitution ◽  
Non Linear ◽  
Beyond Birthday Bound ◽  
Permutation Networks

Recent works of Cogliati et al. (CRYPTO 2018) have initiated provable treatments of Substitution-Permutation Networks (SPNs), one of the most popular approach to construct modern blockciphers. Such theoretical SPN models may employ non-linear diffusion layers, which enables beyond-birthday-bound provable security. Though, for the model of real world blockciphers, i.e., SPN models with linear diffusion layers, existing provable results are capped at birthday security up to 2n/2 adversarial queries, where n is the size of the idealized S-boxes.In this paper, we overcome this birthday barrier and prove that a 4-round SPN with linear diffusion layers and independent round keys is secure up to 22n/3 queries. For this, we identify conditions on the linear layers that are sufficient for such security, which, unsurprisingly, turns out to be slightly stronger than Cogliati et al.’s conditions for birthday security. These provides additional theoretic supports for real world SPN blockciphers.

scholarly journals Lightweight and Side-channel Secure 4 × 4 S-Boxes from Cellular Automata Rules

2018 ◽  
pp. 311-334
Author(s):  
Ashrujit Ghoshal ◽  
Rajat Sadhukhan ◽  
Sikhar Patranabis ◽  
Nilanjan Datta ◽  
Stjepan Picek ◽  
...  
Keyword(s):  
Cellular Automata ◽  
Low Cost ◽  
Building Blocks ◽  
Block Ciphers ◽  
Side Channel ◽  
Design Strategies ◽  
Cryptographic Primitives ◽  
Linear Diffusion ◽  
Low Area ◽  
Diffusion Layers

This work focuses on side-channel resilient design strategies for symmetrickey cryptographic primitives targeting lightweight applications. In light of NIST’s lightweight cryptography project, design choices for block ciphers must consider not only security against traditional cryptanalysis, but also side-channel security, while adhering to low area and power requirements. In this paper, we explore design strategies for substitution-permutation network (SPN)-based block ciphers that make them amenable to low-cost threshold implementations (TI) - a provably secure strategy against side-channel attacks. The core building blocks for our strategy are cryptographically optimal 4×4 S-Boxes, implemented via repeated iterations of simple cellular automata (CA) rules. We present highly optimized TI circuits for such S-Boxes, that consume nearly 40% less area and power as compared to popular lightweight S-Boxes such as PRESENT and GIFT. We validate our claims via implementation results on ASIC using 180nm technology. We also present a comparison of TI circuits for two popular lightweight linear diffusion layer choices - bit permutations and MixColumns using almost-maximum-distance-separable (almost-MDS) matrices. We finally illustrate design paradigms that combine the aforementioned TI circuits for S-Boxes and diffusion layers to obtain fully side-channel secure SPN block cipher implementations with low area and power requirements.

The Role of the SLP in Autism Spectrum Disorder Screening and Assessment

2008 ◽  
Vol 15 (2) ◽  
pp. 50-59 ◽  
Author(s):  
Amy Philofsky
Keyword(s):  
Language Development ◽  
Critical Role ◽  
Children With Autism ◽  
Autism Spectrum ◽  
Children With Asd ◽  
Prevalence Estimates ◽  
Notable Increase ◽  
Screening Assessment ◽  
Critical Components

AbstractRecent prevalence estimates for autism have been alarming as a function of the notable increase. Speech-language pathologists play a critical role in screening, assessment and intervention for children with autism. This article reviews signs that may be indicative of autism at different stages of language development, and discusses the importance of several psychometric properties—sensitivity and specificity—in utilizing screening measures for children with autism. Critical components of assessment for children with autism are reviewed. This article concludes with examples of intervention targets for children with ASD at various levels of language development.

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