A note on self-bilinear maps
Bull. Korean Math. Soc. 2009 Vol. 46, No. 2, 303-309
Printed March 1, 2009
Jung Hee Cheon and Dong Hoon Lee
Seoul National University and ETRI Network and Communications Security Division
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
MSC numbers : Primary 94A60, 11Y16, 68Q15
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