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1. (WO2018124869) QUATERNION-BASED, EFFICIENT FULLY-HOMOMORPHIC CRYPTOSYSTEM

Pub. No.:    WO/2018/124869    International Application No.:    PCT/MA2018/050005
Publication Date: Fri Jul 06 01:59:59 CEST 2018 International Filing Date: Thu Mar 01 00:59:59 CET 2018
IPC: H04L 9/00
Applicants: UNIVERSITE MOHAMMED V RABAT
Inventors: MOHAMED, Dafir El Kettani
AHMED, El Yahyaoui
Title: QUATERNION-BASED, EFFICIENT FULLY-HOMOMORPHIC CRYPTOSYSTEM
Abstract:
The present invention relates to an efficient fully-homomorphic cryptosystem based on a new homomorphic and probabilistic transform between ring ℤ⁄2ℤ (ring of the residual integers modulo 2) and the modular Lipschitz integer ring. The cryptosystem of the invention can process clear messages in the form of input bits and supply ciphertexts in the form of Lipschitz quaternion matrices modulo a large even natural number η in a non-deterministic manner. The security of the present cryptosystem is based on the difficulty of solving a system of multivariate polynomial equations in a non-commutative ring. The cryptosystem can be used to further reduce multiplication computation time in fully-homomorphic encryption algorithms, since it allows the size of a secret key to be minimised and the expansion of ciphertexts to be reduced.