PairTRU: Pairwise Non-commutative Extension of The NTRU Public key Cryptosystem
نویسندگان
چکیده
We show a novel lattice-based scheme (PairTRU) which is a non-commutative variant of the NTRU. The original NTRU is defined via the ring of quotient with variable in integers and this system works in the ring R = Z[x] . We extend this system over Z× Z and it performs all of operations in the non-commutative ring M = M(k,Z×Z)[x] <(Ik×k,Ik×k)x−(Ik×k,Ik×k)> , where M is a matrix ring of k × k matrices of polynomials in R = (Z×Z)[x] <(1,1)xN−(1,1)> . In PairTRU, encrypting and decrypting are non-commutative and the cryptosystem is secure for linear algebra and Lattice-based attacks. PairTRU is designed using the NTRU core and reflects high levels of security by two-sided matrix multiplication with pairwise entries. Keywords—Public key cryptography, Lattice-based cryptosystem, NTRU, Matrix rings.
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