Inverting Onto Fun tions

Inverting Fun tions as Folds

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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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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...

Interpolation and approximation in Taylor spaces

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 ...

Modelling, Analysis and Simulation Computing complex Airy functions by numerical quadrature

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...