General Construction Framework

In this section, a framework for constructing standard fail-stop signature schemes with prekey for signing one message block from a collision-intractable family of bundling homomorphisms is described. Two parameters (the exact family of 

Construction 9.4 (General construction framework). Let the following parameters be given  

As usual, an implementation of this construction is particularly simple if the zero-knowledge proof scheme is only a local verification algorithm. 

Message-block spaces For each prek = ( 1 , 1 , AO e All, the message-block space is simply Mig a,K fro i f e underlying family MFam. 

K must be a component of skjtemp because signing was defined with sk temp and m as the only inputs. One might even let skjemp contain mk, too then mk need not be recomputed in prove. The component 0 is a counter. 

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The following lemmas prove the properties that all implementations of the general construction framework have. It turns out that the only desired property that caimot be proved once and for all is a certain aspect of the security for the signer. 

Now it is summarized what has to be done to make an implementation of the general construction framework secure for the signer. It has just been shown that the a-posteriori probability of a forgery being unprovable is bounded by 2 It... 

Of course, in the present context, the scheme is constructed by using the family of pair exponentiations as bundling homomorphisms from Section 8.5.3 in the general construction framework from Section 9.2. 

In Section 10.4, additional measures are added so that the amount of private storage is small all the time. Those measures are constructed specifically for the general construction framework from Section 9.2 and thus for the efficient schemes based on factoring and discrete logarithms. 

It is now shown how this can be done when top-down tree-authentication is combined with the special one-time signature schemes derived from the general construction framework. Construction 9.4. One also has to take into account that an... 

Construction 10.19. Let a one-time fail-stop signature scheme be given that is a combination of the general construction framework (Construction 9.4) and message hashing (Construction 10.1). 

In this section, we briefly present the general formal framework of quantum error-correction. First, we shall introduce quantum errors in the operator-sum formalism as the operator elements of the quantum operation describing the interaction of the computer with its environment. Then we shall review the main concepts and results of the already well developed theory of quantum error-correcting codes. Finally we will briefly present some of the most important explicit constructive methods to build quantum codes. 

Historically, the first of these efficient schemes was presented in [HePe93], and the construction framework, from [HePP93], is a generalization of that scheme. 

The general features of the monensin synthesis conducted by Kishi et al. are outlined, in retrosynthetic format, in Scheme 1. It was decided to delay the construction of monensin s spiroketal substructure, the l,6-dioxaspiro[4.5]decane framework, to a very late stage in the synthesis (see Scheme 1). It seemed reasonable to expect that exposure of the keto triol resulting from the hydrogen-olysis of the C-5 benzyl ether in 2 to an acidic medium could, under equilibrating conditions, result in the formation of the spiroketal in 1. This proposition was based on the reasonable assumption that the configuration of the spiroketal carbon (C-9) in monensin corresponds to the thermodynamically most stable form, as is the case for most spiroketal-containing natural products.19 Spiro-ketals found in nature usually adopt conformations in which steric effects are minimized and anomeric effects are maximized. 

To a considerable extent, operations research as a formal discipline is occupied with the construction of models. This is closely related to the analysis of alternatives for decision-making. It is generally assumed that it is preferable to have a model to represent an operation, even though it is oversimplified and perhaps imperfect, than to have none. A model may be purely logical or it may be a physical analogue. A mathematical formula is an example of the former, a wind tunnel an illustration of the latter. In both cases, the model provides a ooherent framework for coping with the complexities of a problem. 

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