2018/07/09 by Boneh, Dan, Glass, Darren, Krashen, Daniel +5
#11Y16 #14K02 (Primary) 14Q20 #94A60 (Secondary) #Algebraic Geometry (math.AG) #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1807.03038
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.