Cryptology ePrint Archive: Report 2021/014

Efficient Multilinear Map from Graded Encoding Scheme

Majid Salimi

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 and turn it into an ID-based MP-NIKE scheme.

Category / Keywords: public-key cryptography / Multilinear map, Self-multilinear map, multi-party key exchange

Date: received 4 Jan 2021, last revised 11 Jan 2021, withdrawn 6 Feb 2021

Contact author: majidsalimi3 at gmail com

Available format(s): (-- withdrawn --)

Version: 20210206:073254 (All versions of this report)

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