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Abstract: NTRU public key cryptosystem is well studied lattice-based Cryptosystem alongwith Ajtai-Dwork and GGH systems. UnderlyingNTRU is a hard mathematical problem of finding short vectors in a certainlattice. Shamir 1997 presented a lattice-based attack by which he could findthe original secret key or alternate key. Shamir concluded if one designs avariant of NTRU where the calculations involved during encryption anddecryption are non-commutative then the system will be secure against Latticebased attack.This paper presents a new cryptosystem with above property and wehave proved that it is completely secure against Lattice based attack. Itoperates in the non-commutative ring M=M k ZX-X^n - I {k*k}, where M is amatrix ring of k*k matrices of polynomials in R={Z}X-X^n-1. Moreover Wehave got speed improvement by a factor of Ok^{1.624 over NTRU for the samebit of information.



Autor: Nitin Vats

Fuente: https://arxiv.org/



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