密码学报2016，Vol.3Issue(3)：211-228,18.DOI:10.13868/j.cnki.jcr.000122
从双线性对到多线性映射*
From Bilinear Pairings to Multilinear Maps
摘要
Abstract
Since 2000 Sakai et al. proposed the identity based key agreement scheme using bilinear pairings on elliptic curves, especially, when Boneh and Franklin implemented the identity based encryption using bilinear pairing in 2001, the research of pairing based cryptography has become a hot topic in the field of public key cryptography. The pairing based research has achieved a great amount of results. In this paper, we firstly introduce the concept of bilinear pairing, then introduce pairing based cryptosystems, from the three party one round key agreement to identity based encryption (IBE), attribute based encryption (ABE), predicate encryption (PE), function encryption (FE) and searchable encryption, from short signature to a variety of signatures. We also introduce the current status of implementation and security of pairing. Bilinear pairing can be generalized to multilinear mapping. Multilinear maps can be used for all kinds of pairing based cryptography, a more powerful feature of multilinear mapping is that it can realize circuits. Multilinear maps can be used to design Attribute-based encryption and indistinguishability obfuscation for all circuits. Due to the strong functionality of multilinear mapping, the research of multilinear mapping based cryptosystems has become a hot research topic. In the second part of this paper, we introduce the definition, construction, and applications of multilinear mapping. Finally, we briefly discuss some open problems and interesting issues for further study in this area.关键词
双线性对/椭圆曲线/多线性映射/格/混淆Key words
bilinear pairing/elliptic curve/multilinear mapping/lattice/obfuscation分类
信息技术与安全科学引用本文复制引用
张方国..从双线性对到多线性映射*[J].密码学报,2016,3(3):211-228,18.基金项目
国家自然科学基金项目(61379154) （61379154）
