椭圆曲线上的多方非交互式密钥交换及更多的同构
Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
摘要：
我们描述了一个框架，用于构建一个有效的非交互式密钥交换（NIKE）协议的n方为任何n >= 2。我们的方法是基于问题的计算isogenies之间的isogenies椭圆曲线，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。我们需要完成我们的协议是一个有效的算法，作为输入的阿贝尔品种提出了一个产品的同构椭圆曲线，并输出同构不变量的阿贝尔品种。我们的框架建立了一个密码不变映射，这是一个新的原语密切相关的密码多线性映射，但其范围不一定有一个组结构。尽管如此，我们表明，密码不变的地图可以用来建立几个密码原语，包括耐克，以前从多线性映射和不可分割性混淆。
英文摘要：
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.
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