Applications of the Galois Model LFSR in Cryptography

The linear feedback shift-register is a widely used tool for generating cryptographic sequences. The properties of the Galois model discussed here offer many opportunities to improve the implementations that already exist. We explore the overall properties of the phases of the Galois model and conjecture a relation with modular Golomb rulers. This conjecture points to an efficient method for constructing non-linear filtering generators which fulfil Golic s design criteria in order to maximise protection against his inversion attack. We also produce a number of methods which can improve the rate of output of sequences by combining particular distinct phases of smaller elementary sequences

Index tables of finite fields and modular golomb rulers

For a Galois field GF(2 n ) defined by a primitive element α with minimal polynomial f, the index table contains in row i the coordinates of α i in the polynomial basis α n − 1, α n − 2,…, α, 1. Each column i in this table equals the m-sequence with characteristic polynomial f, shifted cyclically by some offset h i . In this paper we show that the set of the n shifts h i contains large subsets which are modular Golomb rulers modulo 2 n  − 1 (i.e. all the differences are different). Let D be the set of integers j such that the coefficient of x j in f is non-zero. We prove that the set H D of shifts corresponding to columns j ∈ D can be partitioned into two subsets (the columns in the left half of the table and the ones in the right half) each of which is a modular Golomb ruler. Based on this result and on computational data, we conjecture that in fact the whole set H D is a modular Golomb ruler. We give a polynomial time algorithm for deciding if given a subset of column positions, the corresponding shifts are a modular Golomb ruler. These results are applied to filter generators used in the design of stream ciphers. Golić recommends that in order to withstand his inversion attack, one of the design requirements should be that the inputs of the non-linear filtering function are taken from positions of a Fibonacci LFSR which form a Golomb ruler. We propose using a Galois LFSR instead and selecting positions such that the corresponding shifts form a modular Golomb ruler. This would allow for a larger number of inputs to be selected (roughly n/2 rather than 2n − − √ ) while still satisfying Golić’s requirement

MOESM2 of The detection of great crested newts year round via environmental DNA analysis

Additional file 2: Table S1. Table of the raw data analysed using Genstat v18, VSNi, Rothampstead, UK

Additional file 1: of Community pharmacists’ experiences in mental illness and addictions care: a qualitative study

Interview guide for pharmacists. (DOC 33 kb

1,25(OH)₂D₃ maintains a regulatory T cell phenotype even under inflammatory, Th17 polarising conditions.

<p>CD4+CD25- T cells were stimulated in the presence of recombinant cytokines IL-1β, IL-6, IL-23 and TGFβ as indicated with or without 1,25(OH)₂D₃ and expression of regulatory-associated markers CTLA-4, Foxp3 and CD25 assessed at four days and cytokines IL-2, IL-17, IFNγ, IL-21 and IL-10 measured at five days by flow cytometry. Data are summarised for n≥5 donors. Bars indicate mean values and error bars show the standard deviation. Repeated measures, two factor within subject analysis was used to test interaction between 1,25(OH)₂D₃ and cytokine treatment (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131539#pone.0131539.s002" target="_blank">S1 Table</a>). For markers that did not show interaction the two factor analysis was re-run in the absence of interaction and P values for each factor are shown (1,25(OH)₂D₃ = <i>P</i>_<i>D3</i> and cytokine treatment = <i>P</i>_<i>Cyt</i>. Where interaction was detected, single factor analysis was performed. P values are shown for the effect of cytokine treatment under control (<i>P</i>_{<i>cyt—D3</i>}) and 1,25(OH)₂D₃ (<i>P</i>_{<i>cyt + D3</i>}) conditions separately. Significant contrasts between cytokine treatments are indicated by stars (* = P<0.05, ** = P<0.01, *** = P<0.001).</p

1,25(OH)₂D₃ promotes CTLA-4-mediated B7 depletion from dendritic cells and suppression of T cell proliferation.

<p>CTLA-4 expressing ‘suppressor cells’ were prepared by stimulating CD4+CD25- T cells under Th0 or Th17 conditions in the presence or absence of 1,25(OH)₂D₃. <b>A)</b> Suppressor cells were cultured with autologous DCs and antiCD3 for 24 hours with or without CTLA-4 blocking antibody. Expression of CD80, CD86, CD11c and CD40 by DCs was measured by flow cytometry. Dot plots show the ratio of marker expression in control versus anti-CTLA-4-treated cultures for four donors. <b>B)</b> Suppressor cells were CFDA-SE labeled and added to autologous DC plus antiCD3 stimulations of allogeneic cell trace violet labeled CD4+CD25- T cells (responders) with or without anti-CTLA-4. Parallel stimulations were also prepared in which CFDA-SE-labeled CD4+CD25- were added in place of suppressor T cells as a control for cell number. At five days, proliferation of responder T cells was assessed by flow cytometry. Data are from one donor but representative of four. Shaded histograms show proliferation in the absence of suppressors. Dotted and solid lines indicate proliferation in the presence versus the absence of anti-CTLA-4 respectively.</p

Th17 polarising cytokines reduce CTLA-4 expression.

<p>Cell trace-labelled CD4+CD25- T cells were stimulated for four days with antiCD3CD28 beads under no cytokine supplement (Th0), with TGFβ alone or with the pro-Th17 cocktail (TGFβ with IL-1β, IL-6 and IL-23) as indicated and expression of total CTLA-4 and Foxp3 assessed by flow cytometry. <b>A)</b> Representative FACS plots showing CTLA-4 against Foxp3 expression and cell division, indicated by cell-trace dilution. <b>B)</b> Summary of CTLA-4 expression for 12 donor donors. Bars indicate mean values and error bars show standard deviation. Significance was tested by repeated measures, single factor within subject analysis (* = P<0.05, *** = P<0.001).</p

Transendocytic function of CTLA-4 is promoted by 1,25(OH)₂D₃ and maintained under inflammatory conditions.

<p>CTLA-4 transendocytic function was tested as described in the methods. <b>A)</b> Gating strategy to ensure exclusion of CD86-GFP donor cells from the measurement of T cell GFP acquisition. <b>B)</b> Representative FACS plots of CD86-GFP acquisition versus trafficking CTLA-4. <b>C)</b> Total CTLA-4 mediated CD86 acquisition by T cells summarized for n = 5 donors. Bars indicate mean values and error bars show the standard deviation. P values for the separate effects of Th17 cytokines (P_cyt) and 1,25(OH)₂D₃ (P_D3) are shown as determined by the 2 factor without interaction model since no interaction was detected (P = 0.146).</p

Suppression of CTLA-4 by Th17 polarising cytokines is not specific to IL-17+ T cells.

<p>CD4+CD25- T cells were stimulated in the presence of Th17 polarising cytokines for four days and assessed for IL-17, IFNγ, IL-21, TNFα, IL-2 or Foxp3 in combination with CTLA-4 by flow cytometry. <b>A)</b> Frequency of total CTLA-4+ cells. <b>B)</b> Representative bivariate FACS plot of CTLA-4 versus IL-17 for cells cultured under Th17 polarising conditions. <b>C)</b> CTLA-4 expression in CTLA-4+ T cells gated according to IL-17 expression. <b>D)</b> CTLA-4 expression by CTLA-4+ T cells that expressed IL-17, IFNγ, IL-21, TNFα or IL-2. <b>E)</b> CTLA-4 expression in CTLA-4+ T cells defined by FoxP3 expression. In C, D and E expression under Th17 conditions is expressed relative to the level under Th0 conditions. Data are summarised for n≥7 donors. Bars indicate median values and error bars show the semi interquartile range. Significance with respect to cells expressing the marker under Th0 conditions was tested by Wilcoxon matched paired tests. (* = P<0.05, ** = P<0.01, *** = P<0.001).</p

Relationship between garden area and the total number of microhabitats and percentage occurrence of three key microhabitat features: lawn, tree and hedge.

<p>Error bars +/−95% confidence intervals.</p