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A NOTE ON SELF-BILINEAR MAPS

  • Published : 2009.03.31

Abstract

Cryptographic protocols depend on the hardness of some computational problems for their security. Joux briefly summarized known relations between assumptions related bilinear map in a sense that if one problem can be solved easily, then another problem can be solved within a polynomial time [6]. In this paper, we investigate additional relations between them. Firstly, we show that the computational Diffie-Hellman assumption implies the bilinear Diffie-Hellman assumption or the general inversion assumption. Secondly, we show that a cryptographic useful self-bilinear map does not exist. If a self-bilinear map exists, it might be used as a building block for several cryptographic applications such as a multilinear map. As a corollary, we show that a fixed inversion of a bilinear map with homomorphic property is impossible. Finally, we remark that a self-bilinear map proposed in [7] is not essentially self-bilinear.

Keywords

cryptography;complexity;elliptic curves;pairing;self-bilinear map

References

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Cited by

  1. A scalable encryption scheme for multi-privileged group communications vol.64, pp.3, 2013, https://doi.org/10.1007/s11227-011-0683-4
  2. Self-Bilinear Map on Unknown Order Groups from Indistinguishability Obfuscation and Its Applications 2016, https://doi.org/10.1007/s00453-016-0250-8