Given a domain Ω⊂ℂ^{$n$}, the Lempert function is a functional on the space $\text{Hol}(\mathbb{D},\Omega)$ of analytic disks with values in Ω, depending on a set of poles in Ω. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the local indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.

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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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