Various implementations relate to a data processing system comprising instructions embodied in a non-transitory computer readable medium, the instructions for a cryptographic operation including a masked decomposition of a polynomial a having ns arithmetic shares into a high part a1 and a low part a0 for lattice-based cryptography in a processor, the instructions, including: performing a rounded Euclidian division of the polynomial a by a base α to compute t(⋅)A; extracting Boolean shares a1(⋅)B from n low bits of t by performing an arithmetic share to Boolean share (A2B) conversion on t(⋅)A and performing an AND with ζ−1, where ζ=−α−1 is a power of 2; unmasking a1 by combining Boolean shares of a1(⋅)B; calculating arithmetic shares a0(⋅)A of the low part a0; and performing a cryptographic function using a1 and a0(⋅)A.