Differential Analysis of Block Ciphers SIMON and SPECK

In this paper we continue the previous line of research on the analysis of the differential properties of the lightweight block ciphers Simon and Speck. We apply a recently proposed technique for automatic search for differential trails in ARX ciphers and improve the trails in Simon32 and Simon48 previously reported as best. We further extend the search technique for the case of differen- tials and improve the best previously reported differentials on Simon32, Simon48 and Simon64 by exploiting more effectively the strong differential effect of the cipher. We also present improved trails and differentials on Speck32, Speck48 and Speck64. Using these new results we improve the currently best known attacks on several versions of Simon and Speck. A second major contribution of the paper is a graph based algorithm (linear time) for the computation of the exact differential probability of the main building block of Simon: an AND operation preceded by two bitwise shift operations. This gives us a better insight into the differential property of the Simon round function and differential effect in the cipher. Our algorithm is general and works for any rotation constants. The presented techniques are generic and are therefore applicable to a broader class of ARX designs

Improved Differential-Linear Attacks with Applications to ARX Ciphers

We present several improvements to the framework of differential-linear attacks with a special focus on ARX ciphers. As a demonstration of their impact, we apply them to Chaskey and ChaCha and we are able to significantly improve upon the best attacks published so far

Improved algebraic cryptanalysis of QUAD, Bivium and trivium via graph partitioning on equation systems

We present a novel approach for preprocessing systems of polynomial equations via graph partitioning. The variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a tremendous speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting certain vertices on the graph, the variable-sharing graph could be disconnected in a balanced fashion, and in turn the system of polynomial equations would be separated into smaller systems of near-equal sizes. In graph theory terms, this process is equivalent to finding balanced vertex partitions with minimum-weight vertex separators. The techniques of finding these vertex partitions are discussed, and experiments are performed to evaluate its practicality for general graphs and systems of polynomial equations. Applications of this approach in algebraic cryptanalysis on symmetric ciphers are presented: For the QUAD family of stream ciphers, we show how a malicious party can manufacture conforming systems that can be easily broken. For the stream ciphers Bivium and Trivium, we nachieve significant speedups in algebraic attacks against them, mainly in a partial key guess scenario. In each of these cases, the systems of polynomial equations involved are well-suited to our graph partitioning method. These results may open a new avenue for evaluating the security of symmetric ciphers against algebraic attacks

Unadjusted and Adjusted Association Between 25-Hydroxyvitamin D (per 10 nmol/L increase) and Non-Fasting Serum Lipids (mg/dL) Among Children 1 to 5 Years of Age in TARGet Kids!, 2008–2011.

<p>^aAdjusted for age, sex, season, vitamin D supplementation, daily volume of cow’s milk intake, daily minutes of outdoor play, daily minutes of screen time, zBMI, and skin pigmentation.</p><p>^bP-values for secondary objectives adjusted for multiple testing using a false discovery rate controlling procedure correction. Statistical significance is defined as an adjusted P-value <0.05.</p><p>^cTriglyceride values were log transformed for analysis and back transformed results are presented.</p><p>Unadjusted and Adjusted Association Between 25-Hydroxyvitamin D (per 10 nmol/L increase) and Non-Fasting Serum Lipids (mg/dL) Among Children 1 to 5 Years of Age in TARGet Kids!, 2008–2011.</p

Adjusted Association Between 25-Hydroxyvitamin D (per 10 nmol/L increase) and Non-HDL (mg/dL) Among Children 1 to 5 Years of Age in TARGet Kids!, 2008–2011.

<p>^aTo convert from mg/dL to SI units divide the results for non-HDL, Total Cholesterol, LDL and HDL by 38.6, and divide by 88.6 for triglycerides.</p><p>Adjusted Association Between 25-Hydroxyvitamin D (per 10 nmol/L increase) and Non-HDL (mg/dL) Among Children 1 to 5 Years of Age in TARGet Kids!, 2008–2011.</p