Efficient Multilinear Map from Graded Encoding Scheme

TL;DR

This paper introduces a novel graded encoding scheme that enhances security and efficiency in constructing multilinear maps and improves multi-party key exchange schemes, addressing key limitations of previous methods.

Contribution

A new graded encoding scheme is proposed that avoids encoding zero, enabling secure multilinear maps and improved multi-party key exchange schemes.

Findings

Proposes a GES that encodes an associated unknown element, not zero or one.

Constructs a secure, efficient multilinear map based on the new GES.

Enhances MP-NIKE scheme to an ID-based version using the new GES.

Abstract

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.