In this article, the authors cryptanalyze a k-out-of-n oblivious transfer protocol proposed in [12]. Their protocol is one of the most efficient k-out-of-n oblivious transfer protocols and is directly built from a 1-out-of-n oblivious transfer protocol. However, their analysis shows that the proposed k-out-of-n oblivious transfer protocol is insecure, though the primitive 1-out-of-n oblivious transfer protocol is secure. The weakness is that with high probability the receiver in their protocol can get all n secret messages encrypted by the sender. Finally, they fix the serious flaw and introduce an improved k-out-of-n oblivious transfer protocol without increasing any cost.

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Let$X$(-ϱ$B$^{$m$}×$C$^{$n$}be a compact set over the unit sphere ϱ$B$^{$m$}such that for each$z$∈ϱ$B$^{$m$}the fiber$X$_{$z$}={ω∈$C$^{$n$};($z, ω$)∈$X$} is the closure of a completely circled pseudoconvex domain in$C$^{$n$}. The polynomial hull $$\hat X$$ of$X$is described in terms of the Perron-Bremermann function for the homogeneous defining function of$X$. Moreover, for each point ($z$_{0},$w$_{0})∈Int $$\hat X$$ there exists a smooth up to the boundary analytic disc$F$:Δ→$B$^{$m$}×$C$^{$n$}with the boundary in$X$such that$F$(0)=($z$_{0},$w$_{0}).

The α-modulation spaces$M$^{$s$,α}_{$p$,$q$}($R$^{$d$}), α∈[0,1], form a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that a pseudodifferential operator σ($x$,$D$) with symbol in the Hörmander class$S$^{$b$}_{ρ,0}extends to a bounded operator σ($x$,$D$):$M$^{$s$,α}_{$p$,$q$}($R$^{$d$})→$M$^{$s$-$b$,α}_{$p$,$q$}($R$^{$d$}) provided 0≤α≤ρ≤1, and 1<$p$,$q$<∞. The result extends the well-known result that pseudodifferential operators with symbol in the class$S$^{$b$}_{1,0}maps the Besov space$B$^{$s$}_{$p$,$q$}($R$^{$d$}) into$B$^{$s$-$b$}_{$p$,$q$}($R$^{$d$}).