On Fun tions and Types
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Jonathan M. Borwein1, Xianfu Wang August 13, 1999 ABSTRACT. We prove a \typi al" subdi erentiability prin iple and apply it to a variety of omplete metri spa es of ontinuous fun tions on separable Bana h spa es; so as to obtain existen e of fun tions with maximal subdi erentials when ordered by in lusion. The relationship between ontinuous fun tions with maximal subdi erentials and nowhere mono...
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We des ribe eÆ ient onstru tions for various ryptographi primitives in private-key as well as publi -key ryptography. Our major results are two new onstru tions of pseudorandom fun tions. We prove the pseudo-randomness of one onstru tion under the assumption that fa toring (Blum integers) is hard while the other onstru tion is pseudo-random if the de isional version of the DiÆe-Hellman assumpti...
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Relations between OWFs, PRGs and PRFs (revised) Jan-Erik Ekberg February 19, 2002 1 Introdu tion These le ture notes intend to give an overview of the provable relations between one-way fun tions (OWFs), pseudorandom generators (PRGs) and pseudorandom fun tions (PRFs). Only a sele ted number of proofs and redu tions are thoroughly presented in this paper (most are left to the referen es), but t...
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Barbara Zwi knagl1 and Robert S haba k2 Abstra t: The univariate Taylor formula without remainder allows to reprodu e a fun tion ompletely from ertain derivative values. Thus one an look for Hilbert spa es in whi h the Taylor formula a ts as a reprodu tion formula. It turns out that there are many Hilbert spa es whi h allow this, and they should be alled Taylor spa es. They have ertain reprodu ...
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Integral representations are onsidered of solutions of the Airy di erential equation w z w = 0 for omputing Airy fun tions for omplex values of z. In a rst method ontour integral representations of the Airy fun tions are written as non-os illating integrals for obtaining stable representations, whi h are evaluated by the trapezoidal rule. In a se ond method an integral representation is evaluat...
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