On a Certain Algebraic Property of Block Ciphers

This is a study on a certain group theoretic property of the set of encryption functions of a block cipher. We have shown how to construct a subset which has this property in a given symmetric group by a computer algebra software GAP4.2 (Groups, Algorithms, and Programming, Version 4.2). These observations on group structures of block ciphers suggest us that we may be able to set a trapdoor based on meet-in-the-middle attack on block ciphers.

on a class of pseudorandom sequences from elliptic curves over finite fields

Following the idea of Xing et al., we investigate a general method for constructing families of pseudorandom sequences with low correlation and large linear complexity from elliptic curves over finite fields in this correspondence. With the help of the tool of exponential sums on elliptic curves, we study their periods, linear complexities, linear complexity profiles, distributions of r-patterns, periodic correlation, partial period distributions, and aperiodic correlation in detail. The results show that they have nice randomness.

Reversed capillary electrochromatography: Investigation of peak symmetry for eluting curves of solutes

The transport processes of components in capillary electrochromatographic column was investigated based on the basic model of relaxation theory. A principal transport equation of chromatographic relaxation theory was established and mathematical expressions for eluting curves were obtained under the situations of both capillary electrophoresis and chromatography. Characteristics of peak symmetry and its effecting factors are discussed. Tailing peaks, symmetrical peaks and fronting peaks would be observed simultaneously, which was further proved with reversed capillary electrochromatographic experiments.

Radiation effects on the immiscible polymer blend of nylon1010 and high-impact polystyrene (HIPS) I: Gel/dose curves, mathematical expectation theorem and thermal behaviour

This paper studies the radiation properties of the immiscible blend of nylon1010 and HIPS. The gel fraction increased with increasing radiation dose. The network was found mostly in nylon1010, the networks were also found in both nylon1010 and HIPS when the dose reaches 0.85 MGy or more. We used the Charleby-Pinner equation and the modified Zhang-Sun-Qian equation to simulate the relationship with the dose and the sol fraction. The latter equation fits well with these polymer blends and the relationship used by it showed better linearity than the one by the Charleby-Pinner equation. We also studied the conditions of formation of the network by the mathematical expectation theorem for the binary system. Thermal properties of polymer blend were observed by DSC curves. The crystallization temperature decreases with increasing dose because the cross-linking reaction inhibited the crystallization procession and destroyed the crystals. The melting temperature also reduced with increasing radiation dose. The dual melting peak gradually shifted to single peak and the high melting peak disappeared at high radiation dose. However, the radiation-induced crystallization was observed by the heat of fusion increasing at low radiation dose. On the other hand, the crystal will be damaged by radiation. A similar conclusion may be drawn by the DSC traces when the polymer blends were crystallized. When the radiation dose increases, the heat of fusion reduces dramatically and so does the heat of crystallization. (C) 1999 Elsevier Science Ltd. All rights reserved.

AN ALGEBRAIC METHOD TO ESTIMATE GENERAL TYPE OF PHASES OF STRUCTURE FACTORS

The algebraic formulas of 1.5 and 2.5 rank are given for four space groups P2(1), Pn, Pna2(1), P2(1)2(1)2(1). It is better that the results of applying them to estimating general type of phases for four correspondent crystal structures. And a method of transforming algebraic formulas from 1.5(2.5) rank is proposed.

THE ALGEBRAIC-METHOD ESTIMATING +/-PI/2 TYPE OF PHASES OF STRUCTURE FACTORS

The algebraic formulas of 1.5 and 2.5 rank which can be applied to estimating +/- pi/2 type of phases for P2(1)2(1)2(1) space group were derived using the method of structure factor algebra. Both types of the formulas are satisfactory for two known crystal structures in estimating their +/- pi/2 type of phases.