Though the multilinear maps have many cryptographic applications, secure and efficient construction of such maps is an open problem. Many multilinear maps like GGH, GGH15, CLT, and CLT15 have been and are being proposed, while none of them is both secure and efficient. The construction of some multilinear maps is based on the Graded Encoding Scheme (GES), where, the necessity of announcing zero-testing parameter and encoding of zero has destroyed the security of the multilinear map. Attempt is made to propose a new GES, where, instead of encoding an element, the users can obtain the encoding of an associated but unknown random element. In this new setting, there is no need to publish the encodings of zero and one. This new GES provides the actual functionality of the usual GES and can be applied in constructing a secure and efficient multilinear map and a multi-party non-interactive key exchange (MP-NIKE) scheme. We also improve the MP-NIKE scheme of \cite{Access20} and turn it into an ID-based MP-NIKE scheme.
翻译:虽然多线性地图有许多加密应用程序,但安全高效地绘制这些地图是一个尚未解决的问题。许多多线性地图,如GGH、GGH15、CLT和CLT15等,过去和现在都曾提出过,而且正在提出,尽管其中没有一个是安全和高效的。一些多线性地图的建造是以“分级编码计划”为基础的,其中宣布零测试参数和零编码的必要性破坏了多线性地图的安全性。我们还试图提出一个新的 GES,其中用户可以取得一个相关但未知的随机元素编码,而不是编码一个元素。在此新环境下,不需要公布0和1的编码。这个新的GES提供了通常的GES的实际功能,可用于构建一个安全高效的多线性多线性地图和多党间非交互式关键交换(MP-NIKE)计划。我们还改进了MP-NIKE的\cite{Access20}的MP-NIKE计划,并将其转换成一个基于ID-MP-NIKE的MP-KE计划。