NNRU, a noncommutative analogue of NTRU

NTRU public key cryptosystem is well studied lattice-based Cryptosystem along with Ajtai-Dwork and GGH systems. Underlying NTRU is a hard mathematical problem of finding short vectors in a certain lattice. (Shamir 1997) presented a lattice-based attack by which he could find the original secret key or alternate key. Shamir concluded if one designs a variant of NTRU where the calculations involved during encryption and decryption are non-commutative then the system will be secure against Lattice based attack.This paper presents a new cryptosystem with above property and we have proved that it is completely secure against Lattice based attack. It operates in the non-commutative ring M=M_k Z[X]/(X^n - I_{kk}, where M is a matrix ring of kk matrices of polynomials in R={Z}[X]/(X^n-1). Moreover We have got speed improvement by a factor of O(k^{1.624) over NTRU for the same bit of information.

💡 Research Summary

The paper introduces NNRU, a non‑commutative analogue of the well‑known NTRU lattice‑based public‑key cryptosystem. The authors observe that the classic NTRU scheme operates in the commutative polynomial ring R = ℤ