International Association for Cryptologic Research

International Association
for Cryptologic Research


Chingfang Hsu


A Framework For Fully-Simulatable $h$-Out-Of-$n$ Oblivious Transfer
Zeng Bing Tang Xueming Chingfang Hsu
In this paper, we present a framework for efficient, fully-simulatable $h$-out-of-$n$ oblivious transfer ($OT^{n}_{h}$) with security against nonadaptive malicious adversary. The number of communication round of the framework is six. Compared with existing fully-simulatable $OT^{n}_{h}$, our framework is round-efficient. Conditioning on no trusted common string is available, our DDH-based instantiation is the most efficient protocol for $OT^{n}_{h}$. Our framework uses three abstract tools, i.e. perfectly binding commitment, perfectly hiding commitment and our new smooth projective hash. This allows a simple and intuitive understanding of its security. We instantiate the new smooth projective hash under the lattice, decisional Diffie-Hellman, decisional N-th residuosity, decisional quadratic residuosity assumptions. This indeed shows that the folklore that it is technically difficult to instantiate the projective hash framework under the lattice assumption is not true. What's more, by using this lattice-based instantiation and Brassard's commitment scheme, we gain a $OT^{n}_{h}$ instantiation which is secure against any quantum algorithm.
On Representable Matroids and Ideal Secret Sharing
Chingfang Hsu Qi Cheng
In secret sharing, the exact characterization of ideal access structures is a longstanding open problem. Brickell and Davenport (J. of Cryptology, 1991) proved that ideal access structures are induced by matroids. Subsequently, ideal access structures and access structures induced by matroids have attracted a lot of attention. Due to the difficulty of finding general results, the characterization of ideal access structures has been studied for several particular families of access structures. In all these families, all the matroids that are related to access structures in the family are representable and, then, the matroid-related access structures coincide with the ideal ones. In this paper, we study the characterization of representable matroids. By using the well known connection between ideal secret sharing and matroids and, in particular, the recent results on ideal multipartite access structures and the connection between multipartite matroids and discrete polymatroids, we obtain a characterization of a family of representable multipartite matroids, which implies a sufficient condition for an access structure to be ideal. By using this result and further introducing the reduced discrete polymatroids, we provide a complete characterization of quadripartite representable matroids, which was until now an open problem, and hence, all access structures related to quadripartite representable matroids are the ideal ones. By the way, using our results, we give a new and simple proof that all access structures related to unipartite, bipartite and tripartite matroids coincide with the ideal ones.


Zeng Bing (1)
Qi Cheng (1)
Tang Xueming (1)