Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions

Algebraic and fast algebraic attacks are power tools to analyze stream ciphers. A class of symmetric Boolean functions with maximum algebraic immunity were found vulnerable to fast algebraic attacks at EUROCRYPT'06. Recently, the notion of AAR (algebraic attack resistant) functions was introduced as a unified measure of protection against both classical algebraic and fast algebraic attacks. In this correspondence, we first give a decomposition of symmetric Boolean functions, then we show that almost all symmetric Boolean functions, including these functions with good algebraic immunity, behave badly against fast algebraic attacks, and we also prove that no symmetric Boolean functions are AAR functions. Besides, we improve the relations between algebraic degree and algebraic immunity of symmetric Boolean functions.Comment: 13 pages, submitted to IEEE Transactions on Information Theor

Statistical Methods for Targeted Clinical Trials under Enrichment Design

Background/PurposeAfter completion of the Human Genome Project, disease targets at the molecular level can be identified. Treatment for these specific targets can be developed with the individualized treatment of patients becoming a reality. However, the accuracy of diagnostic devices for molecular targets is not perfect and statistical inference for treatment effects of the targeted therapy is biased. We developed statistical methods for an unbiased inference for the targeted therapy in patients who truly have the molecular targets.MethodsUnder the enrichment design, for binary data, we propose using the expectation maximization (EM) algorithm with the bootstrap method, to incorporate the inaccuracy of the diagnostic device for detection of the molecular targets for inference of the treatment effects. A simulation study was conducted to empirically investigate the performance of the proposed estimation and testing procedures. A numerical example illustrates the application of the proposed method.ResultsSimulation results demonstrated that the proposed estimation method was unbiased, with adequate precision, and the confidence interval provided satisfactory coverage probability. The proposed testing procedure adequately controlled the size with sufficient power. The numerical example showed that a statistically significant treatment effect could be obtained when the inaccuracy of the diagnostic device was taken into account.ConclusionOur proposed estimation and testing procedures are adequate statistical methods for the inference of the treatment effect for patients who truly have the molecular targets

Production of polyploids from cultured shoot tips of Eucalyptus globulus Labill by treatment with colchicine

Polyploids from cultured shoot tips of Eucalyptus globulus were produced by treatment with colchicine. Results showed that the combination of 0.5% colchicine and treating multiple shoot clumps for 4 days was the most appropriate conditions for E. globulus polyploidy induction and the effect of the use of multiple shoot clumps for colchicine polyploidy-induced was better than single buds. By comparing the polyploidy plants with normal diploid ones in morphology, leaves of polyploid plants were thicker, larger, and darker green. The chromosome number of polyploidy plants that had been identified in morphology was 2n = 4x = 44, while that of diploids was 2n = 2x = 22