Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves

Journal of mathematical cryptology

article

Dan Boneh¹  Darren Glass²  Daniel Krashen³  Kristin Lauter⁴  Shahed Sharif⁵  Alice Silverberg⁶  Mehdi Tibouchi⁷  Mark Zhandry⁸ 

[1] Stanford University, United States of America;Gettysburg College, United States of America;Rutgers University, United States of America;Microsoft Research, United States of America;California State University San Marcos, United States of America;University of California, United States of America;NTT Corporation;Princeton University, United States of America

关键词: Multilinear maps;    Non-Interactive Key Exchange;    Isogenies;   

DOI  :  10.1515/jmc-2015-0047

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 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.

【 授权许可】

CC BY|CC BY-NC-ND