PairTRU: Pairwise Non-commutative Extension of The NTRU Public key Cryptosystem

Özet

—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 = in R =(Z× Z)[x] M(k,Z×Z)[x] , where M is a matrix ring of k × k matrices of polynomials . 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.