Paper 2015/128

Self-bilinear Map on Unknown Order Groups from Indistinguishability Obfuscation and Its Applications

Takashi Yamakawa, Shota Yamada, Goichiro Hanaoka, and Noboru Kunihiro


A self-bilinear map is a bilinear map where the domain and target groups are identical. In this paper, we introduce a self-bilinear map with auxiliary information which 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 Phi-hiding assumption.

Note: This is the full version of our paper in CRYPTO 2014.

Available format(s)
Public-key cryptography
Publication info
A major revision of an IACR publication in CRYPTO 2014
self-bilinear mapindistinguishability obfuscationmultilinear map
Contact author(s)
yamakawa @ it k u-tokyo ac jp
2015-02-26: revised
2015-02-26: received
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Short URL
Creative Commons Attribution


      author = {Takashi Yamakawa and Shota Yamada and Goichiro Hanaoka and Noboru Kunihiro},
      title = {Self-bilinear Map on Unknown Order Groups from Indistinguishability Obfuscation and Its Applications},
      howpublished = {Cryptology ePrint Archive, Paper 2015/128},
      year = {2015},
      note = {\url{}},
      url = {}
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