- A NOTE ON SELF-BILINEAR MAPS
- Cheon, Jung-Hee ; Lee, Dong-Hoon ;
- Bulletin of the Korean Mathematical Society, volume 46, issue 2, 2009, Pages 303~309
- DOI : 10.4134/BKMS.2009.46.2.303

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.