Cryptology ePrint Archive: Report 2015/747

Self-bilinear Map from One Way Encoding System and Indistinguishability Obfuscation

Huang Zhang and Fangguo Zhang and Baodian Wei and Yusong Du

Abstract: The bilinear map whose domain and target sets are identical is called the self-bilinear map. Original self-bilinear maps are defined over cyclic groups. This brings a lot of limitations to construct secure self-bilinear schemes. Since the map itself reveals information about the underlying cyclic group, hardness assumptions on DDHP and CDHP may not hold any more. In this paper, we used $i\mathcal{O}$ to construct a self-bilinear map from generic sets. These sets should own several properties. A new notion, One Way Encoding System (OWES), is proposed to describe formally the properties those sets should hold. An Encoding Division Problem is defined to complete the security proof. As an instance of the generic construction, we propose a concrete scheme built on the GGH graded encoding system and state that any $1$-graded encoding system may satisfy the requirements of OWES. Finally, we discuss the hardness of EDP in the GGH graded encoding system.

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Date: received 25 Jul 2015, last revised 5 Oct 2015

Contact author: isszhfg at mail sysu edu cn

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Note: Some improvements

Version: 20151005:153518 (All versions of this report)

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