Efficient Multilinear Map from Graded Encoding Scheme
This addresses a critical open problem in cryptography for applications like secure key exchange, though it appears incremental as it builds on existing GES frameworks.
The paper tackles the problem of constructing secure and efficient multilinear maps by proposing a new Graded Encoding Scheme (GES) that avoids publishing encodings of zero and one, which previously compromised security, and applies it to build a secure multilinear map and an ID-based multi-party non-interactive key exchange (MP-NIKE) scheme.
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.