Self-Bilinear Map on Unknown Order Groups from Indistinguishability Obfuscation and Its Applications
Self-Bilinear Map on Unknown Order Groups from Indistinguishability Obfuscation and Its Applications
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DOI：
10.1007/s00453-016-0250-8
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发表时间：
2014-08
期刊：
影响因子：
1.1
通讯作者：
Takashi Yamakawa;Shota Yamada;Goichiro Hanaoka;N. Kunihiro
中科院分区：
文献类型：
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作者：
Takashi Yamakawa;Shota Yamada;Goichiro Hanaoka;N. Kunihiro
自双线性映射是域组和目标组相同的双线性映射。本文引入了一种带辅助信息的自双线性映射，它是自双线性映射的一个较弱的变种，基于不可分辨混淆构造了它，并证明了在因式分解假设下，关于我们的构造，一个有用的难度假设成立。通过我们的构造，我们得到了一个具有有趣性质的多线性映射：在建立阶段，多线性程度是不受限制的，群元素的表示是紧凑的，即它们的大小与多线性程度无关。这是具有这些性质的多线性映射的第一次构造。然而，请注意，要评估多线性映射，需要辅助信息。作为多线性映射的应用，我们构造了多方非交互密钥交换和分布式广播加密方案，其中最大用户数在建立阶段不是固定的。除了我们的自双线性映射的直接应用外，我们还证明了我们的技术也可以用于基于不可分辨混淆和隐藏假设的某种同态加密。
A self-bilinear map is a bilinear map where the domain and target groups are identical. In this paper, we introduce aself-bilinear map with auxiliary informationwhich is a weaker variant of a self-bilinear map, construct it based on indistinguishability obfuscation and prove that a useful hardness assumption holds with respect to our construction under the factoring assumption. From our construction, we obtain a multilinear map with interesting properties: the level of multilinearity is not bounded in the setup phase, and representations of group elements are compact, i.e., their size is independent of the level of multilinearity. This is the first construction of a multilinear map with these properties. Note, however, that to evaluate the multilinear map, auxiliary information is required. As applications of our multilinear map, we construct multiparty non-interactive key-exchange and distributed broadcast encryption schemes where the maximum number of users is not fixed in the setup phase. Besides direct applications of our self-bilinear map, we show that our technique can also be used for constructing somewhat homomorphic encryption based on indistinguishability obfuscation and the-hiding assumption.