In this paper, we give modified version of interleaved Montgomery modular multiplication method for lattice-based cryptography. With the proposed algorithms, we improve the multiplication complexity and embed the conversion operation into the algorithm with almost free cost. We implement the proposed methods for the quotient ring (ℤ/qℤ)[x]/(xⁿ − 1) and (ℤ/pℤ)[x]/(xⁿ + 1) on the GPU (NVIDIA Quadro 600) using the CUDA platform. NTRUEncrypt is accelerated approximately 35% on the GPU by using the proposed method. We receive at least 19% improvement with the proposed method for the polynomial multiplication in (ℤ/pℤ)[x]/(xⁿ + 1), where n ∈ {1024, 2048, 4096}.