Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
复制标题
DOI：
10.1515/jmc-2015-0047
复制
发表时间：
2018-07
影响因子：
1.2
通讯作者：
D. Boneh;D. Glass;D. Krashen;K. Lauter;Shahed Sharif;A. Silverberg;Mehdi Tibouchi;Mark Zhandry
中科院分区：
文献类型：
--
作者：
D. Boneh;D. Glass;D. Krashen;K. Lauter;Shahed Sharif;A. Silverberg;Mehdi Tibouchi;Mark Zhandry
摘要针对任意n≥2的n方，我们描述了一个构造有效的非交互密钥交换协议的框架。我们的方法是基于计算等均椭圆曲线之间的等同性的问题，这被认为是困难的。我们没有得到一个工作协议，因为缺少一个步骤，目前是一个开放的数学问题。我们需要一个有效的算法来完成我们的协议，该算法将一个表示为等次椭圆曲线乘积的阿贝尔变量作为输入，并输出该阿贝尔变量的同构不变量。我们的框架构建了一个密码不变映射，它是一种与密码多线性映射密切相关的新原语，但其范围不一定具有群结构。然而，我们证明了一个密码不变映射可以用来构建几个密码原语，包括NIKE，这些原语以前是由多线性映射和不可区分混淆构造的。
Abstract We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n ≥ 2. Our approach is based on the problem of computing isogenies between isogenous elliptic curves, which is believed to be difficult. We do not obtain a working protocol because of a missing step that is currently an open mathematical problem. What we need to complete our protocol is an efficient algorithm that takes as input an abelian variety presented as a product of isogenous elliptic curves, and outputs an isomorphism invariant of the abelian variety. Our framework builds a cryptographic invariant map, which is a new primitive closely related to a cryptographic multilinear map, but whose range does not necessarily have a group structure. Nevertheless, we show that a cryptographic invariant map can be used to build several cryptographic primitives, including NIKE, that were previously constructed from multilinear maps and indistinguishability obfuscation.