Multi function evaluation

External verifiability of the behaviour of participants in a transaction essentially means that there is a variant of this transaction where additional parties can observe the original participants and decide whether they behave correctly. Such a property has not been required explicitiy in any previous definition of signature schemes, but it can easily be fulfilled with some types of schemes and may be needed in some applications. The same property will be needed for other types of schemes in Sections 7.3 and 7.5.2 (zero-knowledge proofs and multi-party function evaluation), and the need for it may become clearer there. 

The obvious advantage of this construction is that the complexity of authentication and disputes is independent of the number of risk bearers. The disadvantage is that a general suitable key-generation protocol is very inefficient however, see the last subsection for more efficient special cases. (Moreover, due to problems with definitions of multi-party function evaluation protocols, I did not even dare to call the security considerations below a proof sketch.)... 

For the transformation of an arbitrary key-generation protocol Gen with one risk bearer into a protocol Gen that generates keys with the same distribution, but in a way that many risk bearers can trust them, a multi-party function evaluation protocol is used. 

Most concrete proposals of multi-party function evaluation protocols are not only protocols for one particular function, but general transformation techniques that can be used to derive a suitable protocol for any given function. 

To apply a multi-party function evaluation protocol to key generation, which is an interactive protocol, it is usefiil to regard Gen as one probabilistic function. This has implicitly been done all the time Gen maps values par to tuples acc, idspi h- f, pk, sk temp). Hence a trusted host performing the entire key generation, i.e.. A, B, and res, will be simulated. The correctness of initialization implies that acc and idsout always TRUE and 1), respectively, in this case. Hence one can omit them. The trusted host would tell the signer s entity both sk and pk, and the other entities obtain pk only. 

This global function is now evaluated with a multi-party function evaluation protocol by the entities of the signer and the risk bearers. Recall that the entities of recipients and courts do not send any messages during initialization of a standard fail-stop signature scheme with special risk bearers they are treated in a special subsection below. 

An algorithm res is needed that the entities of recipients and courts can execute, too. They do not take part in the multi-party function evaluation actively, but they observe the complete protocol execution, which is performed on broadcast channels anyway. (The following means that the protocol from [ChDG88] can easily be equipped with external verifiability as defined in Section 5.2.11.)... 

Whenever one of the active entities is to be excluded, the algorithm res checks if this decision is correct. One can easily see from the protocol description in [ChDG88] that this decision only depends on broadcast messages, and not on any internal secrets of the active entities. The global result acc is TRUE if the entities of the signer and at least one risk bearer remain and execute the multi-party function evaluation protocol without disruption, and idsi isk,out consists of the identities of the remaining risk bearers. 

The security for the users of the multi-party function evaluation protocol, except for the one who is protected information-theoretically, relies on the so-called quadratic-residuosity assumption. Hence the security for risk bearers in a fail-stop signature scheme based on this protocol also relies on this assumption. 

If the protocol Gen is particularly simple, the construction with a multi-party function evaluation protocol can be simplified, too. 

ABSTRACT A non-stationary approach to reliabilily analysis of multi-state series and consecutive "m out of k F systems is presented. Further, the multi-state series-consecutive /n out of k F system with degrading components is defined and the recurrent formulae for its leUabilily function evaluation are proposed. Moreover, the application of the proposed formulae to reliahihly evaluation of the exemplary system composed of multi-state components is illustrated. 

Shan WJ, Huang L, Zhou Q, Meng FC, Li XS (2011) Synthesis, biological evaluation of 9-N-substituted berberine derivatives as multi-functional agents of antioxidant, inhibitors of acetylcholinesterase, butyrylcholinesterase and amyloid- aggregation. Eur J Med Chem 46 5885... 

The formation of type II metal-containing macromolecules obtained by the reaction of bi/multifunctional low molecular weight metal complexes with another bi/multi-functional ligand can be evaluated by usual rate constants, equilibrium and kinetics as known for polycondensation or polyaddition reactions in macromolecular chemistry. Increasing insolubility results easily in chain termination and formation oligomers. 

Field tests to evaluate the feasibility and the effectiveness of a geotechnical reinforcement to improve the stability of a slope failure and to decrease the failure speed were carried out at an old mining site in Zimmersrode, located about 50 km south of Kassel, Germany (see Figure 13.13). Two types of multi-functional geotextiles (MFCs) were considered an optical fibre sensor integrated in geogrids and three optical fibre... 

Abstract. We report on the interest of luminescent and nanosized metal atom clusters for the development of functional silica nanoparticles. Furthermore, multi-functional hybrid nanoparticles have been achieved by associating these luminescent clusters with magnetic y-Fe203 nanocrystals and plasmonic gold nanocrystals. In addition, as part of the risk evaluation before potential applications, the toxicity of the nanoparticles was evaluated both on plants and on human cells. 

Functional evaluations of cardiovascular and pulmonary systems could be incorporated into a non-human primate multi-dose toxicity study. If appropriate, potential reproductive toxicity can be evaluated in a non-human primate. 

Adhesion promoter chemistries, other than those of silanes, have been extensively evaluated for many years. These materials use the same concepts as silane-coupling agents, but they are based on other metallic elements. They have inorganic reactivity on the metallic atom and contain organofunctional groups, such as methacrylate, carboxylate, and others, with dual- or multi-functionality built into the... 

The study was conducted to explore the use of this water-soluble LGC as a prospective drilling mud multi-functional additive and evaluate its thermal stability in both fresh-water and saline-water drilling muds. The mud rheological tests were performed according to the American Petroleum Institute (API] standard specifications by means of a direct-indicating viscometer with... 

Note that this equation holds for any component in a multi-component mixture. The integral on the right-hand side can only be evaluated if the vapor mole fraction y is known as a function of the mole fraction Xr in the still. Assuming phase equilibrium between liquid and vapor in the still, the vapor mole fraction y x ) is defined by the equilibrium curve. Agitation of the liquid in tire still and low boilup rates tend to improve the validity of this assumption. 

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