PMNS FOR CRYPTOGRAPHY: A GUIDED TOUR

The Polynomial Modular Number System (PMNS) offers an alternative to the conventional binary multi -precision representation system for large integers. Its effectiveness has been demonstrated for various cryptosystems using prime field arithmetic [2, 4, 6], with prime sizes ranging from 256 to 736 bits. However, as the size of p increases, the relative performance of PMNS compared to standard arithmetic diminishes. Furthermore, the generation process of a PMNS has a worst -case complexity of O(2n), where n denotes the number of symbols used to represent an integer modulo p in this representation system. In this paper, we present several alternatives and improvements to the construction and implementation processes of PMNS, which are tailored to the size of p.