netru: a non-commutative and secure variant of ctru cryptosystem

In this paper we present a new finite field-based public key cryptosystem (netru) which is a non-commutative variant of ctru. the original ctru is defined by the ring of polynomials in one variable over a finite field f2. this system works in the ring r = f2[x]/ and is already broken by some attacks such as linear algebra attack. we extend this system over finite fields zp, where p is a prime (or prime power) and it operates over the non-commutative ring m = mk(zp)[t; x]/, where m is a matrix ring of k by k matrices of polynomials in r = zp[t; x]/. in the proposed netru, the encryption and decryption computations are non-commutative and hence the system is secure against linear algebra attack as lattice-based attacks. netru is designed based on the ctru core and exhibits high levels of security with two-sided matrix multiplication.