Important Construction Ideas

This section gives a short overview of important ideas used in the construction of signature schemes with other than ordinary security. Only abstract ideas are presented the number-theoretic ideas follow in Chapter 8. 

One principle is common to all these constractions Even in the information-theoretic sense, the secret information in a signer s entity cannot be uniquely determined from public information. 

The correct secret key is defined as the one that the signer s entity actually has. 

Usually, at least 2 equally probable secret keys correspond to each public key if one aims at information-theoretic security with an error probability of at most 2  

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It is as important to detect reasons for compliance as for non-compliance, not least because it may offer some constructive ideas about how to improve levels of compliance. Managers, supervisors, and safety representatives were asked why they tried to comply with health and safety rules and regulations. Table 10.1 documents their replies. 

Insufficient information about the properties, layout pattern of small defects, potential for their growth in time, usually leads either to an unjustified rejection (repair) or to underestimation of the importance of the defect and, as aconsequence, construction failure. Use of automated computerised means of control allows safe service of the old constructions, periodically repeating the UT and monitoring the development of discontinuities in the metal. The main idea of such policy is periodical UT of development of discontinuities or, in a more general form, monitoring of the metal condition. 

The idea of the effective plate number was introduced and employed by Purnell [4], Desty [5] and others in the late 1950s. Its conception was evoked as a direct result of the introduction of the capillary column or open tubular column. Even in 1960, the open tubular column could be constructed to produce efficiencies of up to a million theoretical plates [6]. However, it became immediately apparent that these high efficiencies were only obtained for solutes eluted at very low (k ) values and, consequently, very close to the column dead volume. More importantly, on the basis of the performance realized from packed columns, the high efficiencies did not... 

The plasma model itself gives an important contribution to the theory of systems containing highly mobile electrons, and particularly its treatment of the screening phenomena is of value. The model has been carefully described in some reviews, and here we would like to refer to Pines (1955). We note that the plasma model has essentially been constructed for treating metals, but it would be interesting to see whether the basic ideas could be applied also to other many-electron systems. 

This is the idea behind the plotting of the closed-loop poles—in other words, construction of root locus plots. Of course, we need mathematical or computational tools when we have more complex systems. An important observation from Example 7.5 is that with simple first and second order systems with no open-loop zeros in the RHP, the closed-loop system is always stable. 

Following Fey nman s original work, several authors pmsued extensions of the effective potential idea to construct variational approximations for the quantum partition function (see, e g., Refs. 7,8). The importance of the path centroid variable in quantum activated rate processes was also explored and revealed, which gave rise to path integral quantum transition state theory and even more general approaches. The Centroid Molecular Dynamics (CMD) method for quantum dynamics simulation was also formulated. In the CMD method, the position centroid evolves classically on the efiective centroid potential. Various analysis and numerical tests for realistic systems have shown that CMD captures the main quantum effects for several processes in condensed matter such as transport phenomena. 

Thus, to completely solve the problem of symmetry reduction within the framework of the formulated algorithm above, we need to be able to perform steps 3-5 listed above. However, solving these problems for a system of partial differential equations requires enormous amount of computations moreover, these computations cannot be fully automatized with the aid of symbolic computation routines. On the other hand, it is possible to simplify drastically the computations, if one notes that for the majority of physically important realizations of the Euclid, Galileo, and Poincare groups and their extensions, the corresponding invariant solutions admit linear representation. It was this very idea that enabled us to construct broad classes of invariant solutions of a number of nonlinear spinor equations [31-33]. 

Since in any catalytic reaction, at least one of the reactants must be chemisorbed, no theory of catalysis can be constructed before the mechanism of chemisorption on the surfaces under investigation is fully understood. In recent years, as a result of the advances in solid-state physics, it became apparent that an important group of adsorbents and catalysts, namely the oxides of the transition metals, were typical semiconductors. This simple idea stimulated both research and speculation in the catalytic field. Its justification is quite simple, at least in qualitative terms. 

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